Ryu floating point output patch
Started by Andrew Gierthabout 7 years ago84 messages
This is a mostly cleaned-up version of the test patch I posted
previously for floating-point output using the Ryu algorithm.
Upstream source: github.com/ulfjack/ryu/ryu at commit 795c8b57a
From the upstream, I've taken only specific files which are
Boost-licensed, removed code not of interest to us, removed C99-isms,
applied project style for things like type names and use of INT64CONST,
removed some ad-hoc configuration #ifs in favour of using values
established by pg_config.h, and ran the whole thing through pgindent and
fixed up the resulting wreckage.
On top of that I made these functional changes:
1. Added an alternative fixed-point output format so that values with
exponents not less than -4 and less than the default precision for the
type are formatted in fixed-point, as sprintf does.
2. Exponents now always have a sign and at least two digits, also as per
sprintf formatting rules.
The fixed-point output hasn't been micro-optimized to the same extent as
the rest of the code, and there is a measurable performance effect - but
it's not that significant compared to the speedup over the existing code.
As for the extent of that speedup: in my tests, float8 output is now as
fast or marginally faster than bigint output, and roughly one order of
magnitude faster than the existing float8 output.
This version of the patch continues to use extra_float_digits to select
whether Ryu output is used - but I've also changed the default, so that
Ryu is used unless you explicitly set extra_float_digits to 0 or less.
This does mean that at the moment, about 13 regression tests fail on
this patch due to the higher precision of float output. I have
intentionally not yet adjusted those results, pending discussion.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu.patchtext/x-patchDownload
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index cf9327f885..24d41c2e89 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/float.h"
@@ -29,7 +30,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -246,6 +247,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -462,6 +469,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 6fe1939881..6e223335bc 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index ec8139f014..ae89dd8c5e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,8 +44,8 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..e7d7f2a14c
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,974 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((1ull << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+/* m <<= 2; */
+/* uint128 b0 = ((uint128) m) * mul[0]; // 0 */
+/* uint128 b2 = ((uint128) m) * mul[1]; // 64 */
+/* */
+/* uint128 hi = (b0 >> 64) + b2; */
+/* uint128 lo = b0 & 0xffffffffffffffffull; */
+/* uint128 factor = (((uint128) mul[1]) << 64) + mul[0]; */
+/* uint128 vpLo = lo + (factor << 1); */
+/* *vp = (uint64) ((hi + (vpLo >> 64)) >> (j - 64)); */
+/* uint128 vmLo = lo - (factor << mmShift); */
+/* *vm = (uint64) ((hi + (vmLo >> 64) - (((uint128) 1ull) << 64)) >> (j - 64)); */
+/* return (uint64) (hi >> (j - 64)); */
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ const uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1;
+ {
+ /* m is maximum 55 bits */
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp;
+ /* overflow into hi */
+
+ {
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+ }
+ }
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe.
+ * Smaller values may still be safe, but it's more difficult
+ * to reason about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) -
+ * 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q -
+ * 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ {
+ /*
+ * Step 4: Find the shortest decimal representation in the
+ * interval of legal representations.
+ */
+ uint32 removed = 0;
+ uint8_t lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below
+ * are relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these
+ * two digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+ }
+
+ return index;
+}
+
+int
+ryu_d2s_buffered_n(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) malloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..7934db3b14
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,354 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/* These tables are generated by PrintDoubleLookupTable. */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..db70395f82
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if defined(RYU_OPTIMIZE_SIZE) || !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..b509402dc5
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,668 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/* This table is generated by PrintFloatLookupTable. */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8_t lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) malloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..c601c747a7
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_LONG < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
Re: Ryu floating point output patch
Hi,
On 2018-12-13 19:41:55 +0000, Andrew Gierth wrote:
This is a mostly cleaned-up version of the test patch I posted
previously for floating-point output using the Ryu algorithm.
Nice!
From the upstream, I've taken only specific files which are
Boost-licensed, removed code not of interest to us, removed C99-isms,
applied project style for things like type names and use of INT64CONST,
removed some ad-hoc configuration #ifs in favour of using values
established by pg_config.h, and ran the whole thing through pgindent and
fixed up the resulting wreckage.
Removed C99isms? Why, we allow that these days? Did you mean C11?
+static inline uint64 +mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j, + uint64 *const vp, uint64 *const vm, const uint32 mmShift) +{ +/* m <<= 2; */ +/* uint128 b0 = ((uint128) m) * mul[0]; // 0 */ +/* uint128 b2 = ((uint128) m) * mul[1]; // 64 */ +/* */ +/* uint128 hi = (b0 >> 64) + b2; */ +/* uint128 lo = b0 & 0xffffffffffffffffull; */ +/* uint128 factor = (((uint128) mul[1]) << 64) + mul[0]; */ +/* uint128 vpLo = lo + (factor << 1); */ +/* *vp = (uint64) ((hi + (vpLo >> 64)) >> (j - 64)); */ +/* uint128 vmLo = lo - (factor << mmShift); */ +/* *vm = (uint64) ((hi + (vmLo >> 64) - (((uint128) 1ull) << 64)) >> (j - 64)); */ +/* return (uint64) (hi >> (j - 64)); */ + *vp = mulShift(4 * m + 2, mul, j); + *vm = mulShift(4 * m - 1 - mmShift, mul, j); + return mulShift(4 * m, mul, j); +}
What's with all the commented out code? I'm not sure that keeping close
alignment with the original codebase with things like that has much
value given the extent of the reformatting and functional changes?
+/* These tables are generated by PrintDoubleLookupTable. */
This kind of reference is essentially dangling now, so perhaps we should
rewrite that?
+++ b/src/common/d2s_intrinsics.h
+static inline uint64 +umul128(const uint64 a, const uint64 b, uint64 *const productHi) +{ + return _umul128(a, b, productHi); +}
These are fairly generic names, perhaps we ought to prefix them?
Greetings,
Andres Freund
Re: Ryu floating point output patch
"Andres" == Andres Freund <andres@anarazel.de> writes:
From the upstream, I've taken only specific files which are
Boost-licensed, removed code not of interest to us, removed
C99-isms, applied project style for things like type names and use
of INT64CONST, removed some ad-hoc configuration #ifs in favour of
using values established by pg_config.h, and ran the whole thing
through pgindent and fixed up the resulting wreckage.
Andres> Removed C99isms? Why, we allow that these days? Did you mean
Andres> C11?
My understanding is that we do not allow // comments or mixed
declarations and code (other than loop control variables).
This code in particular was very heavily into using mixed declarations
and code throughout. Removing those was moderately painful.
Andres> What's with all the commented out code?
Just stuff from upstream I didn't take out.
Andres> I'm not sure that keeping close alignment with the original
Andres> codebase with things like that has much value given the extent
Andres> of the reformatting and functional changes?
Probably not, but otherwise I did not remove much in the way of upstream
comments or edit them except for formatting.
+/* These tables are generated by PrintDoubleLookupTable. */
Andres> This kind of reference is essentially dangling now, so perhaps
Andres> we should rewrite that?
Well, it's probably still useful to point out that they're generated
(though not by us); I guess it should make clear where the generator is.
+++ b/src/common/d2s_intrinsics.h
+static inline uint64 +umul128(const uint64 a, const uint64 b, uint64 *const productHi) +{ + return _umul128(a, b, productHi); +}
Andres> These are fairly generic names, perhaps we ought to prefix
Andres> them?
Maybe, but presumably nothing else is going to include this file.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Hi,
On 2018-12-13 20:23:51 +0000, Andrew Gierth wrote:
"Andres" == Andres Freund <andres@anarazel.de> writes:
From the upstream, I've taken only specific files which are
Boost-licensed, removed code not of interest to us, removed
C99-isms, applied project style for things like type names and use
of INT64CONST, removed some ad-hoc configuration #ifs in favour of
using values established by pg_config.h, and ran the whole thing
through pgindent and fixed up the resulting wreckage.Andres> Removed C99isms? Why, we allow that these days? Did you mean
Andres> C11?My understanding is that we do not allow // comments or mixed
declarations and code (other than loop control variables).
Ah, that makes sense.
This code in particular was very heavily into using mixed declarations
and code throughout. Removing those was moderately painful.
I wonder if we should instead relax those restriction for the largely
foreign pieces of code?
+/* These tables are generated by PrintDoubleLookupTable. */
Andres> This kind of reference is essentially dangling now, so perhaps
Andres> we should rewrite that?Well, it's probably still useful to point out that they're generated
(though not by us); I guess it should make clear where the generator is.
Right it should definitely be explained. But I do think pointing at the
source, would be good. I kind of wonder if we should, if we were to
accept something like this patch, clone the original ryu repository to
either git.pg.org, or at least into pg's github repository? It'd be
annoying if the original authors moved on and deleted the repository.
Greetings,
Andres Freund
Re: Ryu floating point output patch
"Andres" == Andres Freund <andres@anarazel.de> writes:
This code in particular was very heavily into using mixed
declarations and code throughout. Removing those was moderately
painful.
Andres> I wonder if we should instead relax those restriction for the
Andres> largely foreign pieces of code?
Do we have any reason for the restriction beyond stylistic preference?
Andres> Right it should definitely be explained. But I do think
Andres> pointing at the source, would be good. I kind of wonder if we
Andres> should, if we were to accept something like this patch, clone
Andres> the original ryu repository to either git.pg.org, or at least
Andres> into pg's github repository? It'd be annoying if the original
Andres> authors moved on and deleted the repository.
Keeping a copy on git.pg.org seems like a reasonable thing to do.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Hi,
On 2018-12-13 20:53:23 +0000, Andrew Gierth wrote:
"Andres" == Andres Freund <andres@anarazel.de> writes:
This code in particular was very heavily into using mixed
declarations and code throughout. Removing those was moderately
painful.Andres> I wonder if we should instead relax those restriction for the
Andres> largely foreign pieces of code?Do we have any reason for the restriction beyond stylistic preference?
No. Robert and Tom were against allowing mixing declarations and code, a
few more against // comments. I don't quite agree with either, but
getting to the rest of C99 seemed more important than fighting those out
at that moment.
Greetings,
Andres Freund
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> This code in particular was very heavily into using mixed
Andrew> declarations and code throughout. Removing those was moderately
Andrew> painful.
And it turns out I missed one, sigh.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> This code in particular was very heavily into using mixed
Andrew> declarations and code throughout. Removing those was moderately
Andrew> painful.
Andrew> And it turns out I missed one, sigh.
Updated patch.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu2.patchtext/x-patchDownload
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index cf9327f885..24d41c2e89 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/float.h"
@@ -29,7 +30,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -246,6 +247,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -462,6 +469,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 6fe1939881..6e223335bc 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index ec8139f014..ae89dd8c5e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,8 +44,8 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..5155dceeea
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,961 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((1ull << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ const uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1;
+ {
+ /* m is maximum 55 bits */
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp;
+ /* overflow into hi */
+
+ {
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+ }
+ }
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe.
+ * Smaller values may still be safe, but it's more difficult
+ * to reason about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) -
+ * 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q -
+ * 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ {
+ /*
+ * Step 4: Find the shortest decimal representation in the
+ * interval of legal representations.
+ */
+ uint32 removed = 0;
+ uint8_t lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below
+ * are relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these
+ * two digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+ }
+
+ return index;
+}
+
+int
+ryu_d2s_buffered_n(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) malloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..f23f94b51c
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,357 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated by PrintDoubleLookupTable from the upstream
+ * sources at github.com/ulfjack/ryu, and then modified by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..db70395f82
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if defined(RYU_OPTIMIZE_SIZE) || !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..cb42fa4a3f
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,667 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/* This table is generated by PrintFloatLookupTable. */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8_t lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) malloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..4de7ccd8af
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
Re: Ryu floating point output patch
On Fri, Dec 14, 2018 at 8:00 AM Andres Freund <andres@anarazel.de> wrote:
Hi,
On 2018-12-13 20:53:23 +0000, Andrew Gierth wrote:
"Andres" == Andres Freund <andres@anarazel.de> writes:
This code in particular was very heavily into using mixed
declarations and code throughout. Removing those was moderately
painful.Andres> I wonder if we should instead relax those restriction for the
Andres> largely foreign pieces of code?Do we have any reason for the restriction beyond stylistic preference?
No. Robert and Tom were against allowing mixing declarations and code, a
few more against // comments. I don't quite agree with either, but
getting to the rest of C99 seemed more important than fighting those out
at that moment.
-1 for making superficial changes to code that we are "vendoring",
unless it is known to be dead/abandoned and we're definitively forking
it. It just makes it harder to track upstream's bug fixes and
improvements, surely?
--
Thomas Munro
http://www.enterprisedb.com
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> This code in particular was very heavily into using mixed
Andrew> declarations and code throughout. Removing those was moderately
Andrew> painful.
Andrew> And it turns out I missed one, sigh.
Andrew> Updated patch.
And again to fix the windows build - why does Mkvcbuild.pm have its own
private copy of the file list for src/common?
--
Andrew (irc:RhodiumToad)
Attachments:
ryu3.patchtext/x-patchDownload
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index cf9327f885..24d41c2e89 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/float.h"
@@ -29,7 +30,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -246,6 +247,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -462,6 +469,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 6fe1939881..6e223335bc 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index ec8139f014..02622f8c48 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,8 +44,10 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..5155dceeea
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,961 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((1ull << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ const uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1;
+ {
+ /* m is maximum 55 bits */
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp;
+ /* overflow into hi */
+
+ {
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+ }
+ }
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe.
+ * Smaller values may still be safe, but it's more difficult
+ * to reason about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) -
+ * 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q -
+ * 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ {
+ /*
+ * Step 4: Find the shortest decimal representation in the
+ * interval of legal representations.
+ */
+ uint32 removed = 0;
+ uint8_t lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below
+ * are relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these
+ * two digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+ }
+
+ return index;
+}
+
+int
+ryu_d2s_buffered_n(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) malloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..f23f94b51c
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,357 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated by PrintDoubleLookupTable from the upstream
+ * sources at github.com/ulfjack/ryu, and then modified by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..db70395f82
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if defined(RYU_OPTIMIZE_SIZE) || !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..cb42fa4a3f
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,667 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/* This table is generated by PrintFloatLookupTable. */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8_t lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) malloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..4de7ccd8af
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 2921d193a1..70cafcce8e 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -117,7 +117,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
On 2018-Dec-13, Andrew Gierth wrote:
And again to fix the windows build - why does Mkvcbuild.pm have its own
private copy of the file list for src/common?
I think at some point the Makefile parsing code was too stupid to deal
with the src/port Makefile, so it was hardcoded; later probably I
cargo-culted that into the src/common makefile. Maybe the parser has
already improved (or the makefile simplified) that the msvc tooling can
extract the files from the makefile? Dunno.
--
�lvaro Herrera https://www.2ndQuadrant.com/
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> And again to fix the windows build
And again to see if it actually compiles now...
--
Andrew (irc:RhodiumToad)
Attachments:
ryu4.patchtext/x-patchDownload
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index cf9327f885..24d41c2e89 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/float.h"
@@ -29,7 +30,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -246,6 +247,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -462,6 +469,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 6fe1939881..6e223335bc 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index ec8139f014..02622f8c48 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,8 +44,10 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..131b762b1e
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,961 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((1ull << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1;
+ {
+ /* m is maximum 55 bits */
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp;
+ /* overflow into hi */
+
+ {
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+ }
+ }
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe.
+ * Smaller values may still be safe, but it's more difficult
+ * to reason about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) -
+ * 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q -
+ * 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ {
+ /*
+ * Step 4: Find the shortest decimal representation in the
+ * interval of legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below
+ * are relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these
+ * two digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+ }
+
+ return index;
+}
+
+int
+ryu_d2s_buffered_n(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) malloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..f23f94b51c
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,357 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated by PrintDoubleLookupTable from the upstream
+ * sources at github.com/ulfjack/ryu, and then modified by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..db70395f82
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if defined(RYU_OPTIMIZE_SIZE) || !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..108bc00669
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,667 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/* This table is generated by PrintFloatLookupTable. */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) malloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..4de7ccd8af
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 2921d193a1..70cafcce8e 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -117,7 +117,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
"Thomas" == Thomas Munro <thomas.munro@enterprisedb.com> writes:
Do we have any reason for the restriction beyond stylistic preference?
No. Robert and Tom were against allowing mixing declarations and
code, a few more against // comments. I don't quite agree with
either, but getting to the rest of C99 seemed more important than
fighting those out at that moment.
Thomas> -1 for making superficial changes to code that we are
Thomas> "vendoring", unless it is known to be dead/abandoned and we're
Thomas> definitively forking it. It just makes it harder to track
Thomas> upstream's bug fixes and improvements, surely?
Well, the question there is how far to take that principle; do we avoid
pgindent'ing the code, do we avoid changing uint64_t etc. to uint64
etc., and so on.
(I notice that a stray uint8_t that I left behind broke the Windows
build but not the linux/bsd one, so something would have to be fixed in
the windows build in order to avoid having to change that.)
The Ryu code is perhaps an extreme example because it follows almost the
exact reverse of our coding standard.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
"Thomas" == Thomas Munro <thomas.munro@enterprisedb.com> writes:
Thomas> -1 for making superficial changes to code that we are
Thomas> "vendoring", unless it is known to be dead/abandoned and we're
Thomas> definitively forking it. It just makes it harder to track
Thomas> upstream's bug fixes and improvements, surely?
Well, the question there is how far to take that principle; do we avoid
pgindent'ing the code, do we avoid changing uint64_t etc. to uint64
etc., and so on.
The Ryu code is perhaps an extreme example because it follows almost the
exact reverse of our coding standard.
My heart kind of sinks when looking at this patch, because it's a
large addition of not-terribly-well-documented code that nobody here
really understands, never mind the problem that it's mostly not close
to our own coding standards.
Our track record in borrowing code from "upstream" projects is pretty
miserable: almost without exception, we've found ourselves stuck with
maintaining such code ourselves after a few years. I don't see any
reason to think that wouldn't be true here; in fact there's much more
reason to worry here than we had for, eg, borrowing the regex code.
The maintenance track record of this github repo appears to span six
months, and it's now been about four months since the last commit.
It might be abandonware already.
Is this a path we really want to go down? I'm not convinced the
cost/benefit ratio is attractive.
If we do go down this path, though, I'm not too worried about making
it simple to absorb upstream fixes; I bet there will be few to none.
(Still, you might want to try to automate and document the coding
format conversion steps, along the line of what I've done recently
for our copy of tzcode.)
regards, tom lane
Re: Ryu floating point output patch
Hi,
On 2018-12-14 13:25:29 -0500, Tom Lane wrote:
Our track record in borrowing code from "upstream" projects is pretty
miserable: almost without exception, we've found ourselves stuck with
maintaining such code ourselves after a few years. I don't see any
reason to think that wouldn't be true here; in fact there's much more
reason to worry here than we had for, eg, borrowing the regex code.
The maintenance track record of this github repo appears to span six
months, and it's now been about four months since the last commit.
It might be abandonware already.
It's been absorbed into MSVC's standard library and a bunch of other
projects, so there's certainly some other prominent adoption.
The last commit was a month ago, no? November 6th afaict.
Is this a path we really want to go down? I'm not convinced the
cost/benefit ratio is attractive.
float->text conversion is one of the major bottlenecks when backing up
postgres, it's definitely a pain-point in practice. I've not really seen
a nicer implementation anywhere, not even close.
Greetings,
Andres Freund
Re: Ryu floating point output patch
Andres Freund <andres@anarazel.de> writes:
On 2018-12-14 13:25:29 -0500, Tom Lane wrote:
The maintenance track record of this github repo appears to span six
months, and it's now been about four months since the last commit.
It might be abandonware already.
The last commit was a month ago, no? November 6th afaict.
Hmm, the commit history I was looking at ended on Aug 19, but I must've
done something wrong, because going in from a different angle shows
me commits up to November.
It's been absorbed into MSVC's standard library and a bunch of other
projects, so there's certainly some other prominent adoption.
If we think that's going on, maybe we should just sit tight till glibc
absorbs it.
regards, tom lane
Re: Ryu floating point output patch
Hi,
On 2018-12-14 13:47:53 -0500, Tom Lane wrote:
Andres Freund <andres@anarazel.de> writes:
It's been absorbed into MSVC's standard library and a bunch of other
projects, so there's certainly some other prominent adoption.If we think that's going on, maybe we should just sit tight till glibc
absorbs it.
All the stuff it'll have to put above it will make it slower
anyway. It's not like this'll be a feature that's hard to rip out if all
libc's have fast roundtrip safe conversion routines, or if something
better comes along.
Greetings,
Andres Freund
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Tom> The maintenance track record of this github repo appears to span
Tom> six months,
The algorithm was only published six months ago.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Tom> The maintenance track record of this github repo appears to span
Tom> six months,
The algorithm was only published six months ago.
Doesn't really affect my point: there's little reason to believe that
there will be an active upstream several years down the pike.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Tom> (Still, you might want to try to automate and document the coding
Tom> format conversion steps, along the line of what I've done recently
Tom> for our copy of tzcode.)
Working around our declaration-after-statement prohibition required
manually moving some lines of code, manually separating some
declarations from their assignments (removing const qualifiers), and as
a last resort introducing new code blocks. I doubt it could be automated
in any sane way. (This might be an argument to relax that rule.)
Mechanical search-and-replace accounted for the _t suffix on types, the
addition of the UINT64CONSTs, and changing assert to Assert; that much
could be automated.
pgindent did a pretty horrible job on the comments, a script could
probably do better.
I guess removal of the unwanted #ifs could be automated without too much
difficulty.
(But I'm not likely going to do any of this in the forseeable future,
because I don't expect it to be useful.)
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Andres" == Andres Freund <andres@anarazel.de> writes:
Is this a path we really want to go down? I'm not convinced the
cost/benefit ratio is attractive.
Andres> float->text conversion is one of the major bottlenecks when
Andres> backing up postgres, it's definitely a pain-point in practice.
Also an issue with queries. I got into this whole area after diagnosing
a problem for a user on IRC who was seeing a 4x slowdown for PG as
compared to MSSQL, from 30 seconds to 120 seconds. We determined that
the _entire_ difference was accounted for by float conversion.
Now that was an unusual case, downloading a large dataset of floats at
once into a statistics program, but it's very easy to show
proportionally large overheads from float output:
(using this table:
create table flttst4 as
select i a, i b, i c, i d, i::float8 e, random() f
from generate_series(1::bigint, 10000000::bigint) i;
)
postgres=# copy flttst4(d) to '/dev/null'; -- bigint column
COPY 10000000
Time: 2166.001 ms (00:02.166)
postgres=# copy flttst4(e) to '/dev/null'; -- float8 col, integer values
COPY 10000000
Time: 4233.005 ms (00:04.233)
postgres=# copy flttst4(f) to '/dev/null'; -- float8 col, random()
COPY 10000000
Time: 7261.421 ms (00:07.261)
-- vs. timings with Ryu:
postgres=# copy flttst4(e) to '/dev/null'; -- float8 col, integer values
COPY 10000000
Time: 2391.725 ms (00:02.392)
postgres=# copy flttst4(f) to '/dev/null'; -- float8 col, random()
COPY 10000000
Time: 2245.699 ms (00:02.246)
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Rebased this patch onto current master. No functional changes; just
fixed up the copyright dates and a couple of stray missing UINT64CONSTs.
Regression tests still fail because how to fix them depends on the
issues below. Likewise docs are not changed yet for the same reason.
Decisions that need to be made in order to proceed:
1. Should exact output become the default, or is it more important to
preserve the historical output?
I will argue very strongly that the default output should be exact.
2. How far do we need to go to support existing uses of
extra_float_digits? For example, do we need a way for clients to
request that they get the exact same output as previously for
extra_float_digits=2 or 3, rather than just assuming that any
round-trip-exact value will do?
(this would likely mean adding a new GUC, rather than basing
everything off extra_float_digits as the patch does now)
3. Do we need to do anything about how conversions from floats to
numeric work? At present they _ignore_ extra_float_digits (presumably
on immutability grounds) and convert using only DBL_DIG digits of
precision.
I have no very strong position on this but incline to keeping the
existing behavior, though possibly it would be good to add functions
to get the round-trip value and possibly even the true exact value.
(It would be sort of nice if CAST(floatval AS numeric(400,18)) or
similar could work as you'd expect, but currently we treat that as
floatval::numeric::numeric(400,18) so the cast function doesn't know
about the eventual typmod.)
4. Can we allow declaration-after-statement please? That would allow
keeping this code significantly closer to its upstream.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu5.patchtext/x-patchDownload
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..6c6f031b4a 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -31,7 +32,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -252,6 +253,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +475,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index f81e0424e7..404ba2bfa0 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..7e6e1237c5 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..1c63fb198a
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,961 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1;
+ {
+ /* m is maximum 55 bits */
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp;
+ /* overflow into hi */
+
+ {
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+ }
+ }
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe.
+ * Smaller values may still be safe, but it's more difficult
+ * to reason about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) -
+ * 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q -
+ * 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ {
+ /*
+ * Step 4: Find the shortest decimal representation in the
+ * interval of legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below
+ * are relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these
+ * two digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+ }
+
+ return index;
+}
+
+int
+ryu_d2s_buffered_n(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..897378afcb
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,670 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0
+ * bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ {
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..c5c4b97ffc
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..e226450d1f 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -117,7 +117,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
Does the project have an established view on non-ASCII names in
sources or docs?
AFAICS [1]https://dl.acm.org/citation.cfm?id=3192369, the name of the algorithm may be Ryū.
-Chap
Re: Ryu floating point output patch
Hi,
On 2019-01-10 23:02:01 -0500, Chapman Flack wrote:
Does the project have an established view on non-ASCII names in
sources or docs?AFAICS [1], the name of the algorithm may be Ryū.
I think it'd be a really bad idea to start having non-ascii
filenames, and I quite doubt that I'm alone in that.
- Andres
Re: Ryu floating point output patch
Andres Freund <andres@anarazel.de> writes:
On 2019-01-10 23:02:01 -0500, Chapman Flack wrote:
Does the project have an established view on non-ASCII names in
sources or docs?
AFAICS [1], the name of the algorithm may be Ryū.
I think it'd be a really bad idea to start having non-ascii
filenames, and I quite doubt that I'm alone in that.
Non-ASCII filenames seem right out. I thought the question was
about whether we even want to have non-ASCII characters within
source code (my view: avoid if possible) or in docs (we do,
but it's better if you can make it into html entities).
regards, tom lane
Re: Ryu floating point output patch
On Thu, Jan 10, 2019 at 11:10 PM Tom Lane <tgl@sss.pgh.pa.us> wrote:
Andres Freund <andres@anarazel.de> writes:
On 2019-01-10 23:02:01 -0500, Chapman Flack wrote:
Does the project have an established view on non-ASCII names in
sources or docs?
AFAICS [1], the name of the algorithm may be Ryū.I think it'd be a really bad idea to start having non-ascii
filenames, and I quite doubt that I'm alone in that.Non-ASCII filenames seem right out. I thought the question was
about whether we even want to have non-ASCII characters within
source code (my view: avoid if possible) or in docs (we do,
but it's better if you can make it into html entities).
+1 to all that.
I don't have an opinion on the code that is part of this patch, but
the benchmark results are impressive.
--
Robert Haas
EnterpriseDB: http://www.enterprisedb.com
The Enterprise PostgreSQL Company
Re: Ryu floating point output patch
"Robert" == Robert Haas <robertmhaas@gmail.com> writes:
Robert> I don't have an opinion on the code that is part of this patch
At this point, frankly, I'm less interested in opinions on the code
itself (which can be addressed later if need be) than on answers to (or
discussion of) the questions asked upthread.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On Fri, Jan 11, 2019 at 12:33 PM Andrew Gierth
<andrew@tao11.riddles.org.uk> wrote:
"Robert" == Robert Haas <robertmhaas@gmail.com> writes:
Robert> I don't have an opinion on the code that is part of this patch
At this point, frankly, I'm less interested in opinions on the code
itself (which can be addressed later if need be) than on answers to (or
discussion of) the questions asked upthread.
Unfortunately, I can't help you very much there. My knowledge is
insufficient to give intelligent answers to those questions, and I
don't think giving you unintelligent answers is a good idea. About as
much as I can say is that if you commit this patch, and as a result, a
dump-and-restore from v11 to v12 causes a change in the bits on disk
that would not have occurred without this patch, that's very bad.
What ramifications there will be if the output changes in ways that
don't affect the bits that get written to the platter -- I don't know.
--
Robert Haas
EnterpriseDB: http://www.enterprisedb.com
The Enterprise PostgreSQL Company
Re: Ryu floating point output patch
Hi,
On 2019-01-11 02:40:25 +0000, Andrew Gierth wrote:
Decisions that need to be made in order to proceed:
1. Should exact output become the default, or is it more important to
preserve the historical output?I will argue very strongly that the default output should be exact.
Same.
2. How far do we need to go to support existing uses of
extra_float_digits? For example, do we need a way for clients to
request that they get the exact same output as previously for
extra_float_digits=2 or 3, rather than just assuming that any
round-trip-exact value will do?
I think it might be ok to say that any positive value will yield
round-trip-exact values, even if they're not precisely the same as the
ones before.
3. Do we need to do anything about how conversions from floats to
numeric work? At present they _ignore_ extra_float_digits (presumably
on immutability grounds) and convert using only DBL_DIG digits of
precision.I have no very strong position on this but incline to keeping the
existing behavior, though possibly it would be good to add functions
to get the round-trip value and possibly even the true exact value.
(It would be sort of nice if CAST(floatval AS numeric(400,18)) or
similar could work as you'd expect, but currently we treat that as
floatval::numeric::numeric(400,18) so the cast function doesn't know
about the eventual typmod.)
Hm. What's the argument to not just always use roundtrip-safe conversion
here?
4. Can we allow declaration-after-statement please? That would allow
keeping this code significantly closer to its upstream.
As I said on IRC: I'm personally on-board with changing this styilistic
requirement, but I also think that it'd be OK to just disable the
warning for the individual object files when they're imported (likely
using target specific makefile variable assignements) if we cannot get
agreement on the global policy change.
Greetings,
Andres Freund
Re: Ryu floating point output patch
Hi,
On 2019-01-11 12:55:54 -0500, Robert Haas wrote:
About as much as I can say is that if you commit this patch, and as a
result, a dump-and-restore from v11 to v12 causes a change in the bits
on disk that would not have occurred without this patch, that's very
bad. What ramifications there will be if the output changes in ways
that don't affect the bits that get written to the platter -- I don't
know.
Are you trying to highlight the potential dangers of this patch, or are
you seeing a concrete risk of that in the discussion? Both ryu's and the
current output (as used by pg_dump, with extra_float_digits = 3) ought
to be roundtrip safe. There's possibly some chance for differences in
insignificant bits, but that ought to be pretty much it?
The current discussion would probably change the data that's stored on disk
between ryu/non-ryu for queries like
CREATE TABLE AS SELECT floatcol::text::float FROM ...
or
CREATE TABLE AS SELECT floatcol::text FROM ...
when not specifyiung extra_float_digits = 3, but the ryu case would be
more precise, so that ought to be good?
Greetings,
Andres Freund
Re: Ryu floating point output patch
On Fri, Jan 11, 2019 at 1:30 PM Andres Freund <andres@anarazel.de> wrote:
On 2019-01-11 12:55:54 -0500, Robert Haas wrote:
About as much as I can say is that if you commit this patch, and as a
result, a dump-and-restore from v11 to v12 causes a change in the bits
on disk that would not have occurred without this patch, that's very
bad. What ramifications there will be if the output changes in ways
that don't affect the bits that get written to the platter -- I don't
know.Are you trying to highlight the potential dangers of this patch, or are
you seeing a concrete risk of that in the discussion? Both ryu's and the
current output (as used by pg_dump, with extra_float_digits = 3) ought
to be roundtrip safe. There's possibly some chance for differences in
insignificant bits, but that ought to be pretty much it?The current discussion would probably change the data that's stored on disk
between ryu/non-ryu for queries like
CREATE TABLE AS SELECT floatcol::text::float FROM ...
or
CREATE TABLE AS SELECT floatcol::text FROM ...when not specifyiung extra_float_digits = 3, but the ryu case would be
more precise, so that ought to be good?
I'm not complaining about the patch. I'm saying that the patch can't
change people's existing data when they dump and restore. If you're
saying it doesn't, cool. I don't mind if the answers to queries get
more precise -- that's good, as you say -- just that we don't change
their data.
--
Robert Haas
EnterpriseDB: http://www.enterprisedb.com
The Enterprise PostgreSQL Company
Re: Ryu floating point output patch
Hi,
On 2019-01-11 13:33:54 -0500, Robert Haas wrote:
On Fri, Jan 11, 2019 at 1:30 PM Andres Freund <andres@anarazel.de> wrote:
On 2019-01-11 12:55:54 -0500, Robert Haas wrote:
About as much as I can say is that if you commit this patch, and as a
result, a dump-and-restore from v11 to v12 causes a change in the bits
on disk that would not have occurred without this patch, that's very
bad. What ramifications there will be if the output changes in ways
that don't affect the bits that get written to the platter -- I don't
know.Are you trying to highlight the potential dangers of this patch, or are
you seeing a concrete risk of that in the discussion? Both ryu's and the
current output (as used by pg_dump, with extra_float_digits = 3) ought
to be roundtrip safe. There's possibly some chance for differences in
insignificant bits, but that ought to be pretty much it?The current discussion would probably change the data that's stored on disk
between ryu/non-ryu for queries like
CREATE TABLE AS SELECT floatcol::text::float FROM ...
or
CREATE TABLE AS SELECT floatcol::text FROM ...when not specifyiung extra_float_digits = 3, but the ryu case would be
more precise, so that ought to be good?I'm not complaining about the patch. I'm saying that the patch can't
change people's existing data when they dump and restore. If you're
saying it doesn't, cool. I don't mind if the answers to queries get
more precise -- that's good, as you say -- just that we don't change
their data.
It'd potentially change data between an non-ryu->{ryu,non-ryu} and
ryu->ryu versions, for dumps that didn't specify extra_float_digits =
3. But that'd not be pg_dump, and already broken previously, so I don't
have particularly much sympathy?
And of course it'd change the dump's text contents between ryu and
non-ryu backends even with extra_float_digits = 3, but the resulting
floats ought to be the same. It's just that ryu is better at figuring
out what the minimal text representation is than the current code.
Greetings,
Andres Freund
Re: Ryu floating point output patch
On Fri, Jan 11, 2019 at 1:40 PM Andres Freund <andres@anarazel.de> wrote:
It'd potentially change data between an non-ryu->{ryu,non-ryu} and
ryu->ryu versions, for dumps that didn't specify extra_float_digits =
3. But that'd not be pg_dump, and already broken previously, so I don't
have particularly much sympathy?
Agreed.
And of course it'd change the dump's text contents between ryu and
non-ryu backends even with extra_float_digits = 3, but the resulting
floats ought to be the same. It's just that ryu is better at figuring
out what the minimal text representation is than the current code.
wfm.
--
Robert Haas
EnterpriseDB: http://www.enterprisedb.com
The Enterprise PostgreSQL Company
Re: Ryu floating point output patch
Andres Freund <andres@anarazel.de> writes:
And of course it'd change the dump's text contents between ryu and
non-ryu backends even with extra_float_digits = 3, but the resulting
floats ought to be the same. It's just that ryu is better at figuring
out what the minimal text representation is than the current code.
I'm fairly concerned about this blithe assertion that the ryu code is
smarter than the rest of the world. In particular, how does it know
how every strtod() on the planet will react to specific input?
regards, tom lane
Re: Ryu floating point output patch
Hi,
On 2019-01-11 14:54:55 -0500, Tom Lane wrote:
Andres Freund <andres@anarazel.de> writes:
And of course it'd change the dump's text contents between ryu and
non-ryu backends even with extra_float_digits = 3, but the resulting
floats ought to be the same. It's just that ryu is better at figuring
out what the minimal text representation is than the current code.I'm fairly concerned about this blithe assertion that the ryu code is
smarter than the rest of the world.
The paper on which ryu is based seems to have quite some careful
analysis behind it, explaining why it's correct (i.e. why the algorithm
generates the minimal output, but not output that's imprecise). Although
I certainly didn't invest substantial amounts of time reviewing the
correctness of the logic therein, and would quite possibly fail due to
insufficient maths chops if I tried.
In particular, how does it know how every strtod() on the planet will
react to specific input?
strtod()'s job ought to computationally be significantly easier than the
other way round, no? And if there's buggy strtod() implementations out
there, why would they be guaranteed to do the correct thing with our
current output, but not with ryu's?
Greetings,
Andres Freund
declaration-after-statement (was Re: Ryu floating point output patch)
"Andres" == Andres Freund <andres@anarazel.de> writes:
4. Can we allow declaration-after-statement please? That would allow
keeping this code significantly closer to its upstream.
Andres> As I said on IRC: I'm personally on-board with changing this
Andres> styilistic requirement, but I also think that it'd be OK to
Andres> just disable the warning for the individual object files when
Andres> they're imported (likely using target specific makefile
Andres> variable assignements) if we cannot get agreement on the global
Andres> policy change.
So are there any strong disagreements with the idea of disabling the
warning at least for these specific files? If I don't hear any
objections, I'll go for that in the next version of the patch.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Andres" == Andres Freund <andres@anarazel.de> writes:
3. Do we need to do anything about how conversions from floats to
numeric work? At present they _ignore_ extra_float_digits
(presumably on immutability grounds) and convert using only DBL_DIG
digits of precision.I have no very strong position on this but incline to keeping the
existing behavior, though possibly it would be good to add functions
to get the round-trip value and possibly even the true exact value.
(It would be sort of nice if CAST(floatval AS numeric(400,18)) or
similar could work as you'd expect, but currently we treat that as
floatval::numeric::numeric(400,18) so the cast function doesn't know
about the eventual typmod.)
Andres> Hm. What's the argument to not just always use roundtrip-safe
Andres> conversion here?
Hmm.
I was thinking that the fact that the existing conversion didn't respect
extra_float_digits probably meant that people didn't care. But
searching, I do find some complaints about it, though mostly they get
brushed off with some variant of "you're doing it wrong". (Arguably any
float to numeric conversion is a fairly dubious practice.)
But I guess the case could be made for using the shortest-roundtrip-safe
value here too.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On Jan 11, 2019, at 10:40 AM, Andres Freund <andres@anarazel.de> wrote:
And of course it'd change the dump's text contents between ryu and
non-ryu backends even with extra_float_digits = 3, but the resulting
floats ought to be the same. It's just that ryu is better at figuring
out what the minimal text representation is than the current code.
+1. I spent some time reading the Ryu paper, and I'm convinced.
I think Ryu will be a good choice we want to have as many digits as possible
(and roundtrip-safe). Since we have the extra_float_digits and ndig, the Ryu may
give us more digits than we asked.
Maybe one way to respect ndig is to clear the last few digits of (a, b, c)
(This is the notation in the paper. I think the code used different var names)
in base 10,
https://github.com/ulfjack/ryu/blob/b2ae7a712937711375a79f894106a0c6d92b035f/ryu/d2s.c#L264-L266
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
uint64_t vr, vp, vm;
int32_t e10;
for Ryu to generate the desired string?
Also I wonder why do we need to make this change?
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
Re: Ryu floating point output patch
On Sunday, January 13, 2019, Donald Dong <xdong@csumb.edu> wrote:
Also I wonder why do we need to make this change? -int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */ +int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
From the original post:
“This version of the patch continues to use extra_float_digits to select
whether Ryu output is used - but I've also changed the default, so that
Ryu is used unless you explicitly set extra_float_digits to 0 or less.”
David J.
Re: Ryu floating point output patch
"Andres" == Andres Freund <andres@anarazel.de> writes:
In particular, how does it know how every strtod() on the planet
will react to specific input?
Andres> strtod()'s job ought to computationally be significantly easier
Andres> than the other way round, no? And if there's buggy strtod()
Andres> implementations out there, why would they be guaranteed to do
Andres> the correct thing with our current output, but not with ryu's?
Funny thing: I've been devoting considerable effort to testing this, and
the one failure mode I've found is very interesting; it's not a problem
with strtod(), in fact it's a bug in our float4in caused by _misuse_ of
strtod().
In particular, float4in thinks it's ok to do strtod() on the input, and
then round the result to a float. It is wrong to think that, and here's
why:
Consider the (float4) bit pattern x15ae43fd. The true decimal value of
this, and its adjacent values are:
x15ae43fc = 7.0385300755536269169437150392273653469292493678466371420654468238353729248046875e-26
midpoint 7.0385303837024180189014515281838361605176203339429008565275580622255802154541015625e-28
x15ae43fd = 7.038530691851209120859188017140306974105991300039164570989669300615787506103515625e-26
midpoint 7.0385310000000002228169245060967777876943622661354282854517805390059947967529296875e-26
x15ae43fe = 7.03853130814879132477466099505324860128273323223169199991389177739620208740234375e-26
Now look at what happens if you pass '7.038531e-26' as input for float4.
From the above values, the correct result is x15ae43fd, because any
other value would be strictly further away. But if you input the value
as a double first, here are the adjacent representations:
x3ab5c87fafffffff = 7.038530999999999074873222531206633286975087635036133540...e-26
midpoint 7.0385309999999996488450735186517055373347249505857809130...e-28
x3ab5c87fb0000000 = 7.03853100000000022281692450609677778769436226613542828545...e-28
midpoint 7.03853100000000079678877549354185003805399958168507565784...e-28
x3ab5c87fb0000001 = 7.03853100000000137076062648098692228841363689723472303024...e-28
So the double value is x3ab5c87fb0000000, which has a mantissa of
(1).01011100100001111111101100000...
which when rounded to 23 bits (excluding the implied (1)), is
010 1110 0100 0011 1111 1110 = 2e43fe
So the rounded result is incorrectly x15ae43fe, rather than the expected
correct value of x15ae43fd.
strtof() exists as part of the relevant standards, so float4in should be
using that in place of strtod, and that seems to fix this case for me.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Funny thing: I've been devoting considerable effort to testing this, and
the one failure mode I've found is very interesting; it's not a problem
with strtod(), in fact it's a bug in our float4in caused by _misuse_ of
strtod().
In particular, float4in thinks it's ok to do strtod() on the input, and
then round the result to a float.
Hm. I'm not sure how much weight to put on this example, since we don't
guarantee that float4 values will round-trip with less than 9 digits of
printed precision. This example corresponds to extra_float_digits = 1
which doesn't meet that minimum. However, I agree that it's rounding
the presented input in the less desirable direction.
strtof() exists as part of the relevant standards, so float4in should be
using that in place of strtod, and that seems to fix this case for me.
To clarify that: strtof() is defined in C99 but not older standards
(C89 and SUSv2 lack it).
While we've agreed that we'll require C99 *compilers* going forward,
I'm less enthused about supposing that the platform's libc is up to
date, not least because replacing libc on an old box is orders of
magnitude harder than installing a nondefault version of gcc.
As a concrete example, gaur lacks strtof(), and I'd be pretty much
forced to retire it if we start requiring that function. Putting
a more modern gcc on that machine wasn't too painful, but I'm not
messing with its libc.
But I'd not object to adding a configure check and teaching
float4in to use strtof() if available.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
On a slightly unrelated note, is the small-is-zero variant output file
for the float tests still required?
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
On a slightly unrelated note, is the small-is-zero variant output file
for the float tests still required?
Hm, good question. I had been about to respond that it must be,
but looking more closely at pg_regress.c I see that the default
expected-file will be tried if the one fingered by resultmap isn't
an exact match. So if everybody is matching float8.out these
days, we wouldn't know it.
The only one of the resultmap entries I'm in a position to try
right now is x86 freebsd, and I can report that FreeBSD/x86
matches the default float8.out, and has done at least back to
FreeBSD 8.4.
It wouldn't be an unreasonable suspicion to guess that the other
BSDen have likewise been brought up to speed to produce ERANGE
on underflow, but I can't check it ATM.
On the other hand, cygwin is probably pretty frozen-in-time,
so it might still have the old behavior. Can anyone check that?
regards, tom lane
Re: Ryu floating point output patch
On Jan 15, 2019, at 2:37 AM, Andrew Gierth <andrew@tao11.riddles.org.uk> wrote:
Andres> strtod()'s job ought to computationally be significantly easier
Andres> than the other way round, no? And if there's buggy strtod()
Andres> implementations out there, why would they be guaranteed to do
Andres> the correct thing with our current output, but not with ryu's?Funny thing: I've been devoting considerable effort to testing this, and
the one failure mode I've found is very interesting; it's not a problem
with strtod(), in fact it's a bug in our float4in caused by _misuse_ of
strtod().
Hi,
I'm trying to reproduce the results by calling float4in in my test code. But I
have some difficulties linking the code:
testfloat4.c:(.text+0x34): undefined reference to `float4in'
testfloat4.c:(.text+0x3c): undefined reference to `DirectFunctionCall1Coll'
I tried offering float.o to the linker in addition to my test program. I also
tried to link all the objects (*.o). But the errors still exist. I attached my
changes as a patch.
I wonder if creating separated test programs is a good way of testing the code,
and I'm interested in learning what I missed.
Thank you.
Attachments:
test_float4.patchapplication/octet-stream; name=test_float4.patch; x-unix-mode=0644Download
diff --git a/src/test/examples/Makefile b/src/test/examples/Makefile
index a67f456904..4bcc2f88df 100644
--- a/src/test/examples/Makefile
+++ b/src/test/examples/Makefile
@@ -14,7 +14,7 @@ override CPPFLAGS := -I$(libpq_srcdir) $(CPPFLAGS)
LDFLAGS_INTERNAL += $(libpq_pgport)
-PROGS = testlibpq testlibpq2 testlibpq3 testlibpq4 testlo testlo64
+PROGS = testlibpq testlibpq2 testlibpq3 testlibpq4 testlo testlo64 testfloat4
all: $(PROGS)
diff --git a/src/test/examples/testfloat4.c b/src/test/examples/testfloat4.c
new file mode 100644
index 0000000000..a2256f067d
--- /dev/null
+++ b/src/test/examples/testfloat4.c
@@ -0,0 +1,35 @@
+/*
+ * Include the same headers as
+ * src/backend/utils/adt/numeric.c
+ */
+#include "postgres.h"
+
+#include <ctype.h>
+#include <float.h>
+#include <limits.h>
+#include <math.h>
+
+#include "access/hash.h"
+#include "catalog/pg_type.h"
+#include "common/int.h"
+#include "funcapi.h"
+#include "lib/hyperloglog.h"
+#include "libpq/pqformat.h"
+#include "miscadmin.h"
+#include "nodes/nodeFuncs.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/guc.h"
+#include "utils/int8.h"
+#include "utils/numeric.h"
+#include "utils/sortsupport.h"
+
+int
+main()
+{
+ char *tmp = "3.14";
+ // undefined reference
+ DirectFunctionCall1(float4in, CStringGetDatum(tmp));
+ return 0;
+}
Re: Ryu floating point output patch
"Donald" == Donald Dong <xdong@csumb.edu> writes:
Donald> Hi,
Donald> I'm trying to reproduce the results by calling float4in in my
Donald> test code. But I have some difficulties linking the code:
Donald> testfloat4.c:(.text+0x34): undefined reference to `float4in'
Donald> testfloat4.c:(.text+0x3c): undefined reference to `DirectFunctionCall1Coll'
The way you're doing that isn't really a good way to test it - those
other programs being built by that rule are all frontend code, whereas
float4in is a backend function. If you want to add your own test it, you
could do a loadable module for it, or just do tests from SQL.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Next version.
Changes since previous patch:
1. Remove "ryu_" from the name of interface functions; it seems better
to name them according to functionality rather than enshrining the
algorithm name. double_to_shortest_decimal*() and
float_to_shortest_decimal*() are the new names. common/ryu.h renamed
to common/shortest_dec.h accordingly.
2. Revert the removal of upstream's declaration-after-statements, and
add makefile foo to compile without warning about same. Other style
aspects (indentation, comments) still follow our style rather than
upstream's.
3. This patch _includes_ the strtof() patch that was also posted
separately; this is because we need accurate float4in in order to get
round-trip conversions to work for the edge case.
4. Passes regression tests (existing tests either by changing the
output, where the result is reasonably expected to be bit-exact; or by
locally setting extra_float_digits=0 to restore the old output, where
the output is not expected to be bit-exact).
Still to be done: docs, which are still waiting on final decisions on
the questions I asked upthread.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu6.patchtext/x-patchDownload
diff --git a/configure b/configure
index 06fc3c6835..e3176e24e9 100755
--- a/configure
+++ b/configure
@@ -15802,6 +15802,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 4efb912c4d..bdaab717d7 100644
--- a/configure.in
+++ b/configure.in
@@ -1703,6 +1703,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..5c792c86f9 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -31,7 +32,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +105,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +162,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +170,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +222,17 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +268,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +282,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +504,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index c216ed0922..e792ae9922 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2653,11 +2653,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..bd3a506f9e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): override CFLAGS := $(filter-out -Wdeclaration-after-statement,$(CFLAGS))
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..b247e48ce1
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,932 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..9da123f32d
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,660 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..c5c4b97ffc
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..ee602d7d9a
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+void double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+void float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 9d99816eae..84ca929439 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index 1a89a8c24e..793897271c 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index a55c473262..a6950c1526 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..0d957dc663
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,112 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs.
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ (fresult != 0.0 && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 finite value (or
+ * NaN) without error, then return that to the caller without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..ffa4d8e186
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,893 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+with testdata(bits) as (values
+ (x'00000000'),
+ -- small subnormals
+ (x'00000001'), (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'),
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'0053c4f4'), -- 7693e-42
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'006c85c4'), -- 996622e-44
+ (x'15ae43fd'), -- 7038531e-32
+ (x'0041ca76'), -- 60419369e-46
+ (x'2cf757ca'), -- 702990899e-20
+ (x'004b7678'), -- 6930161142e-48
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'00424fe2'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'00000007'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'00000001'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00000001 | 1e-45 | 1e-45 | \x00000001 | t
+ \x00000002 | 3e-45 | 3e-45 | \x00000002 | t
+ \x00000003 | 4e-45 | 4e-45 | \x00000003 | t
+ \x00000010 | 2.2e-44 | 2.2e-44 | \x00000010 | t
+ \x00000011 | 2.4e-44 | 2.4e-44 | \x00000011 | t
+ \x00000100 | 3.59e-43 | 3.59e-43 | \x00000100 | t
+ \x00000101 | 3.6e-43 | 3.6e-43 | \x00000101 | t
+ \x00004000 | 2.2959e-41 | 2.2959e-41 | \x00004000 | t
+ \x00004001 | 2.296e-41 | 2.296e-41 | \x00004001 | t
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+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(278 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..cfba2af112 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,572 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+with testdata(bits) as (values
+ (x'00000000'),
+ -- small subnormals
+ (x'00000001'), (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'),
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'0053c4f4'), -- 7693e-42
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'006c85c4'), -- 996622e-44
+ (x'15ae43fd'), -- 7038531e-32
+ (x'0041ca76'), -- 60419369e-46
+ (x'2cf757ca'), -- 702990899e-20
+ (x'004b7678'), -- 6930161142e-48
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'00424fe2'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'00000007'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'00000001'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00000001 | 1e-45 | 1e-45 | \x00000001 | t
+ \x00000002 | 3e-45 | 3e-45 | \x00000002 | t
+ \x00000003 | 4e-45 | 4e-45 | \x00000003 | t
+ \x00000010 | 2.2e-44 | 2.2e-44 | \x00000010 | t
+ \x00000011 | 2.4e-44 | 2.4e-44 | \x00000011 | t
+ \x00000100 | 3.59e-43 | 3.59e-43 | \x00000100 | t
+ \x00000101 | 3.6e-43 | 3.6e-43 | \x00000101 | t
+ \x00004000 | 2.2959e-41 | 2.2959e-41 | \x00004000 | t
+ \x00004001 | 2.296e-41 | 2.296e-41 | \x00004001 | t
+ \x00080000 | 7.34684e-40 | 7.34684e-40 | \x00080000 | t
+ \x00080001 | 7.34685e-40 | 7.34685e-40 | \x00080001 | t
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+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(278 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..51bf63817d 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -213,7 +213,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +230,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +314,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +451,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +531,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +632,355 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'),
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0000000000000001 | 5e-324 | 5e-324 | \x0000000000000001 | t
+ \x0000000000000002 | 1e-323 | 1e-323 | \x0000000000000002 | t
+ \x0000000000000003 | 1.5e-323 | 1.5e-323 | \x0000000000000003 | t
+ \x0000000000001000 | 2.0237e-320 | 2.0237e-320 | \x0000000000001000 | t
+ \x0000000100000000 | 2.121995791e-314 | 2.121995791e-314 | \x0000000100000000 | t
+ \x0000010000000000 | 5.43230922487e-312 | 5.43230922487e-312 | \x0000010000000000 | t
+ \x0000010100000000 | 5.45352918278e-312 | 5.45352918278e-312 | \x0000010100000000 | t
+ \x0000400000000000 | 3.4766779039175e-310 | 3.4766779039175e-310 | \x0000400000000000 | t
+ \x0000400100000000 | 3.4768901034966e-310 | 3.4768901034966e-310 | \x0000400100000000 | t
+ \x0000800000000000 | 6.953355807835e-310 | 6.953355807835e-310 | \x0000800000000000 | t
+ \x0000800000000001 | 6.95335580783505e-310 | 6.95335580783505e-310 | \x0000800000000001 | t
+ \x000ffffffffffff0 | 2.2250738585071935e-308 | 2.2250738585071935e-308 | \x000ffffffffffff0 | t
+ \x000ffffffffffff1 | 2.225073858507194e-308 | 2.225073858507194e-308 | \x000ffffffffffff1 | t
+ \x000ffffffffffffe | 2.2250738585072004e-308 | 2.2250738585072004e-308 | \x000ffffffffffffe | t
+ \x000fffffffffffff | 2.225073858507201e-308 | 2.225073858507201e-308 | \x000fffffffffffff | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 1e+23 | 1e+23 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.109808898695963e+16 | -2.109808898695963e+16 | \xc352bd2668e077c4 | t
+ \x00000000000f4240 | 4.940656e-318 | 4.940656e-318 | \x00000000000f4240 | t
+ \x00000000016e3600 | 1.18575755e-316 | 1.18575755e-316 | \x00000000016e3600 | t
+ \x0000008cdcdea440 | 2.989102097996e-312 | 2.989102097996e-312 | \x0000008cdcdea440 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(198 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..81c10c343d 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -209,7 +209,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +226,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +310,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +447,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +533,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +634,355 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'),
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0000000000000001 | 5e-324 | 5e-324 | \x0000000000000001 | t
+ \x0000000000000002 | 1e-323 | 1e-323 | \x0000000000000002 | t
+ \x0000000000000003 | 1.5e-323 | 1.5e-323 | \x0000000000000003 | t
+ \x0000000000001000 | 2.0237e-320 | 2.0237e-320 | \x0000000000001000 | t
+ \x0000000100000000 | 2.121995791e-314 | 2.121995791e-314 | \x0000000100000000 | t
+ \x0000010000000000 | 5.43230922487e-312 | 5.43230922487e-312 | \x0000010000000000 | t
+ \x0000010100000000 | 5.45352918278e-312 | 5.45352918278e-312 | \x0000010100000000 | t
+ \x0000400000000000 | 3.4766779039175e-310 | 3.4766779039175e-310 | \x0000400000000000 | t
+ \x0000400100000000 | 3.4768901034966e-310 | 3.4768901034966e-310 | \x0000400100000000 | t
+ \x0000800000000000 | 6.953355807835e-310 | 6.953355807835e-310 | \x0000800000000000 | t
+ \x0000800000000001 | 6.95335580783505e-310 | 6.95335580783505e-310 | \x0000800000000001 | t
+ \x000ffffffffffff0 | 2.2250738585071935e-308 | 2.2250738585071935e-308 | \x000ffffffffffff0 | t
+ \x000ffffffffffff1 | 2.225073858507194e-308 | 2.225073858507194e-308 | \x000ffffffffffff1 | t
+ \x000ffffffffffffe | 2.2250738585072004e-308 | 2.2250738585072004e-308 | \x000ffffffffffffe | t
+ \x000fffffffffffff | 2.225073858507201e-308 | 2.225073858507201e-308 | \x000fffffffffffff | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 1e+23 | 1e+23 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.109808898695963e+16 | -2.109808898695963e+16 | \xc352bd2668e077c4 | t
+ \x00000000000f4240 | 4.940656e-318 | 4.940656e-318 | \x00000000000f4240 | t
+ \x00000000016e3600 | 1.18575755e-316 | 1.18575755e-316 | \x00000000016e3600 | t
+ \x0000008cdcdea440 | 2.989102097996e-312 | 2.989102097996e-312 | \x0000008cdcdea440 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(198 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index e384cd2279..76cb82ca83 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 0ac08ca51d..cbd7fee7e4 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..c91de0fc14 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,222 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- small subnormals
+ (x'00000001'), (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'),
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'0053c4f4'), -- 7693e-42
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'006c85c4'), -- 996622e-44
+ (x'15ae43fd'), -- 7038531e-32
+ (x'0041ca76'), -- 60419369e-46
+ (x'2cf757ca'), -- 702990899e-20
+ (x'004b7678'), -- 6930161142e-48
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'00424fe2'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'00000007'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'00000001'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..f4db28c5a6 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -97,6 +97,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +151,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +194,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +236,156 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and rount-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'),
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
"Donald" == Donald Dong <xdong@csumb.edu> writes:
Donald> I attached my changes as a patch.
BTW, doing that in a thread about a commitfest patch confuses the
commitfest app and cfbot (both of which think it's a new version of the
patch under discussion), so best avoided.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> 4. Passes regression tests
Well, almost. I missed a contrib module, and there's some issues with
rounding and subnormal values on Windows that I need to track down.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> 4. Passes regression tests
Andrew> Well, almost. I missed a contrib module, and there's some
Andrew> issues with rounding and subnormal values on Windows that I
Andrew> need to track down.
This should fix all the known issues.
This does make one significant change to the algorithm: it will no
longer return the exact midpoint between two values (thereby relying on
the reader to get the correct rounding direction). This gains
portability without compromising the performance (which is not affected
by the change).
--
Andrew (irc:RhodiumToad)
Attachments:
ryu7.patchtext/x-patchDownload
diff --git a/configure b/configure
index 67ba8b677a..b8581493d8 100755
--- a/configure
+++ b/configure
@@ -15812,6 +15812,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 0fc0fb3cfe..f1ad753341 100644
--- a/configure.in
+++ b/configure.in
@@ -1704,6 +1704,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/contrib/btree_gist/expected/float4.out b/contrib/btree_gist/expected/float4.out
index abbd9eef4e..dfe732049e 100644
--- a/contrib/btree_gist/expected/float4.out
+++ b/contrib/btree_gist/expected/float4.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
(1 row)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
diff --git a/contrib/btree_gist/expected/float8.out b/contrib/btree_gist/expected/float8.out
index 5111dbdfae..ebd0ef3d68 100644
--- a/contrib/btree_gist/expected/float8.out
+++ b/contrib/btree_gist/expected/float8.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
(1 row)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out
index 1a65e6944a..5b89cb1a26 100644
--- a/contrib/cube/expected/cube.out
+++ b/contrib/cube/expected/cube.out
@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
(1 row)
SELECT '.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
- cube
-----------------------
- (-0.123456789012346)
+ cube
+-----------------------
+ (-0.1234567890123456)
(1 row)
-- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
(1 row)
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
- cube_distance
-------------------
- 140.762210837994
+ cube_distance
+--------------------
+ 140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
diff --git a/contrib/cube/expected/cube_sci.out b/contrib/cube/expected/cube_sci.out
index 1e8269cdf0..488499ac8e 100644
--- a/contrib/cube/expected/cube_sci.out
+++ b/contrib/cube/expected/cube_sci.out
@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
(1 row)
SELECT '1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
- cube
--------------------------
- (-1.23456789012346e+15)
+ cube
+--------------------------
+ (-1.234567890123456e+15)
(1 row)
diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql
index 59e7e4159d..7f8b2e3979 100644
--- a/contrib/cube/sql/cube.sql
+++ b/contrib/cube/sql/cube.sql
@@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
diff --git a/contrib/pg_trgm/expected/pg_strict_word_trgm.out b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
index 43898a3b98..1e1ee16ce9 100644
--- a/contrib/pg_trgm/expected/pg_strict_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
@@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
+-- reduce noise
+set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/expected/pg_trgm.out b/contrib/pg_trgm/expected/pg_trgm.out
index 6efc54356a..b3e709f496 100644
--- a/contrib/pg_trgm/expected/pg_trgm.out
+++ b/contrib/pg_trgm/expected/pg_trgm.out
@@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------
diff --git a/contrib/pg_trgm/expected/pg_word_trgm.out b/contrib/pg_trgm/expected/pg_word_trgm.out
index bed61c4922..936d489390 100644
--- a/contrib/pg_trgm/expected/pg_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_word_trgm.out
@@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
index 98e0d379f8..ce0791f29b 100644
--- a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
@@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;
diff --git a/contrib/pg_trgm/sql/pg_trgm.sql b/contrib/pg_trgm/sql/pg_trgm.sql
index 96ae542320..08459e64c3 100644
--- a/contrib/pg_trgm/sql/pg_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_trgm.sql
@@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
+
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');
diff --git a/contrib/pg_trgm/sql/pg_word_trgm.sql b/contrib/pg_trgm/sql/pg_word_trgm.sql
index 4b1db9706a..d9fa1c55e5 100644
--- a/contrib/pg_trgm/sql/pg_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_word_trgm.sql
@@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;
diff --git a/contrib/seg/expected/seg.out b/contrib/seg/expected/seg.out
index a289dbe5f9..80b0bca156 100644
--- a/contrib/seg/expected/seg.out
+++ b/contrib/seg/expected/seg.out
@@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
- 2.4 | 6.85 | 11.3
+ 2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
- 4.8 | 8.2 | 11.6
+ 4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
- 9.4 | 10.8 | 12.2
+ 9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..5c792c86f9 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -31,7 +32,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +105,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +162,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +170,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +222,17 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +268,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +282,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +504,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index c216ed0922..e792ae9922 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2653,11 +2653,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..bd3a506f9e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): override CFLAGS := $(filter-out -Wdeclaration-after-statement,$(CFLAGS))
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..555bda27ef
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,936 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..9fbbd8e86c
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,664 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..14639aff9c
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+/*
+ * Upstream Ryu's output is always the shortest possible. But we adjust that
+ * slightly to improve portability: we avoid outputting the exact midpoint
+ * value between two representable floats, since that relies on the reader
+ * getting the round-to-even rule correct, which seems to be the common
+ * failure mode.
+ *
+ * Defining this to 1 would restore the upstream behavior.
+ */
+#define STRICTLY_SHORTEST 0
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..ee602d7d9a
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+void double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+void float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 9d99816eae..84ca929439 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index 1a89a8c24e..793897271c 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index a55c473262..a6950c1526 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..34f85638c9
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,121 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs. Also, strtof() doesn't handle subnormal input
+ * well, so prefer to round the strtod() result in such cases. (Normally we'd
+ * just say "too bad" if strtof() doesn't support subnormals, but since we're
+ * already in here fixing stuff, we might as well do the best fix we can.)
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ ((fresult >= FLT_MIN || fresult <= -FLT_MIN) && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 non-subnormal
+ * finite value (or NaN) without error, then return that to the caller
+ * without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else if ((dresult > 0 && dresult <= FLT_MIN && (float)dresult != 0.0) ||
+ (dresult < 0 && dresult >= -FLT_MIN && (float)dresult != 0.0))
+ {
+ return (float) dresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..d7e66f00b8
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,927 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(256 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..38cb3a66cd 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,606 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(256 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..1689493373 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +237,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +639,401 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(194 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..00fd5fd673 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +233,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +641,401 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(194 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index e384cd2279..76cb82ca83 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 0ac08ca51d..cbd7fee7e4 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..5f146f414d 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,247 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+
+SELECT float4send('1.17549435e-38'::float4);
+SELECT float4send('1.1754944e-38'::float4);
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..62b904a442 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +239,187 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- round-trip tests
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
On Jan 18, 2019, at 2:05 AM, Andrew Gierth <andrew@tao11.riddles.org.uk> wrote:
BTW, doing that in a thread about a commitfest patch confuses the
commitfest app and cfbot (both of which think it's a new version of the
patch under discussion), so best avoided.
Oops. Thank you. Noted.
I think the previous additional digits behavior still exist
in the latest patch. For example:
=# set extra_float_digits = 0;
SET
=# select float4in('1.123456789');
float4in
----------
1.12346
(1 row)
=# set extra_float_digits = 1;
SET
=# select float4in('1.123456789');
float4in
-----------
1.1234568
(1 row)
The extra_float_digits is increased by 1, but two digits are
added. Without the patch, it will render ' 1.123457' instead.
Re: Ryu floating point output patch
"Donald" == Donald Dong <xdong@csumb.edu> writes:
Donald> I think the previous additional digits behavior still exist
Donald> in the latest patch. For example:
Donald> =# set extra_float_digits = 0;
Donald> SET
Donald> =# select float4in('1.123456789');
Donald> float4in
Donald> ----------
Donald> 1.12346
Donald> (1 row)
Donald> =# set extra_float_digits = 1;
Donald> SET
Donald> =# select float4in('1.123456789');
Donald> float4in
Donald> -----------
Donald> 1.1234568
Donald> (1 row)
Donald> The extra_float_digits is increased by 1, but two digits are
Donald> added.
That's intentional; this patch takes any value of extra_float_digits
greater than 0 to mean "generate the shortest precise output".
In practice setting extra_float_digits to 1 is rare to nonexistent;
almost all users of extra_float_digits set it to either 3 (to get
precise values), 2 (for historical reasons since we didn't allow more
than 2 in older versions), or less than 0 (to get rounded output for
more convenient display when precision is not required).
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On Jan 19, 2019, at 5:12 PM, Andrew Gierth <andrew@tao11.riddles.org.uk> wrote:
"Donald" == Donald Dong <xdong@csumb.edu> writes:
Donald> I think the previous additional digits behavior still exist
Donald> in the latest patch. For example:Donald> =# set extra_float_digits = 0;
Donald> SET
Donald> =# select float4in('1.123456789');
Donald> float4in
Donald> ----------
Donald> 1.12346
Donald> (1 row)Donald> =# set extra_float_digits = 1;
Donald> SET
Donald> =# select float4in('1.123456789');
Donald> float4in
Donald> -----------
Donald> 1.1234568
Donald> (1 row)Donald> The extra_float_digits is increased by 1, but two digits are
Donald> added.That's intentional; this patch takes any value of extra_float_digits
greater than 0 to mean "generate the shortest precise output".In practice setting extra_float_digits to 1 is rare to nonexistent;
almost all users of extra_float_digits set it to either 3 (to get
precise values), 2 (for historical reasons since we didn't allow more
than 2 in older versions), or less than 0 (to get rounded output for
more convenient display when precision is not required).
Makes sense! Thank you for explaining.
I wonder if it's necessary to update the doc accordingly? Such as
https://www.postgresql.org/docs/11/datatype-numeric.html#DATATYPE-FLOAT
and
https://www.postgresql.org/docs/11/runtime-config-client.html
.
Re: Ryu floating point output patch
"Donald" == Donald Dong <xdong@csumb.edu> writes:
Donald> I wonder if it's necessary to update the doc accordingly?
Yes, I specifically mentioned that doc updates were needed, and that
they were not included because they depend on final decisions on the
various questions that I have asked.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Latest patch.
No semantic changes; fixes postgresql.conf.sample and adds docs.
In the absence of feedback to the contrary, I've documented the current
behavior of extra_float_digits. I've also removed language from the docs
regarding non-IEEE float formats, and made it clear that all supported
platforms now use IEEE format (whether or not they implement the actual
arithmetic correctly).
I thought of what might be a good reason to leave float->numeric
conversions alone: since they're currently immutable (unlike float
output), they might appear in indexes, and pg_upgrade would have to cope
with that. I'm therefore going to consider float to numeric conversion
as being an issue for a separate patch if at all, rather than part of
this one.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu8.patchtext/x-patchDownload
diff --git a/configure b/configure
index ddb3c8b1ba..378860e9ce 100755
--- a/configure
+++ b/configure
@@ -15812,6 +15812,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 3d8888805c..08fc8fd1bf 100644
--- a/configure.in
+++ b/configure.in
@@ -1705,6 +1705,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/contrib/btree_gist/expected/float4.out b/contrib/btree_gist/expected/float4.out
index abbd9eef4e..dfe732049e 100644
--- a/contrib/btree_gist/expected/float4.out
+++ b/contrib/btree_gist/expected/float4.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
(1 row)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
diff --git a/contrib/btree_gist/expected/float8.out b/contrib/btree_gist/expected/float8.out
index 5111dbdfae..ebd0ef3d68 100644
--- a/contrib/btree_gist/expected/float8.out
+++ b/contrib/btree_gist/expected/float8.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
(1 row)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out
index 1a65e6944a..5b89cb1a26 100644
--- a/contrib/cube/expected/cube.out
+++ b/contrib/cube/expected/cube.out
@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
(1 row)
SELECT '.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
- cube
-----------------------
- (-0.123456789012346)
+ cube
+-----------------------
+ (-0.1234567890123456)
(1 row)
-- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
(1 row)
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
- cube_distance
-------------------
- 140.762210837994
+ cube_distance
+--------------------
+ 140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
diff --git a/contrib/cube/expected/cube_sci.out b/contrib/cube/expected/cube_sci.out
index 1e8269cdf0..488499ac8e 100644
--- a/contrib/cube/expected/cube_sci.out
+++ b/contrib/cube/expected/cube_sci.out
@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
(1 row)
SELECT '1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
- cube
--------------------------
- (-1.23456789012346e+15)
+ cube
+--------------------------
+ (-1.234567890123456e+15)
(1 row)
diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql
index 59e7e4159d..7f8b2e3979 100644
--- a/contrib/cube/sql/cube.sql
+++ b/contrib/cube/sql/cube.sql
@@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
diff --git a/contrib/pg_trgm/expected/pg_strict_word_trgm.out b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
index 43898a3b98..1e1ee16ce9 100644
--- a/contrib/pg_trgm/expected/pg_strict_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
@@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
+-- reduce noise
+set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/expected/pg_trgm.out b/contrib/pg_trgm/expected/pg_trgm.out
index 6efc54356a..b3e709f496 100644
--- a/contrib/pg_trgm/expected/pg_trgm.out
+++ b/contrib/pg_trgm/expected/pg_trgm.out
@@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------
diff --git a/contrib/pg_trgm/expected/pg_word_trgm.out b/contrib/pg_trgm/expected/pg_word_trgm.out
index bed61c4922..936d489390 100644
--- a/contrib/pg_trgm/expected/pg_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_word_trgm.out
@@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
index 98e0d379f8..ce0791f29b 100644
--- a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
@@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;
diff --git a/contrib/pg_trgm/sql/pg_trgm.sql b/contrib/pg_trgm/sql/pg_trgm.sql
index 96ae542320..08459e64c3 100644
--- a/contrib/pg_trgm/sql/pg_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_trgm.sql
@@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
+
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');
diff --git a/contrib/pg_trgm/sql/pg_word_trgm.sql b/contrib/pg_trgm/sql/pg_word_trgm.sql
index 4b1db9706a..d9fa1c55e5 100644
--- a/contrib/pg_trgm/sql/pg_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_word_trgm.sql
@@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;
diff --git a/contrib/seg/expected/seg.out b/contrib/seg/expected/seg.out
index a289dbe5f9..80b0bca156 100644
--- a/contrib/seg/expected/seg.out
+++ b/contrib/seg/expected/seg.out
@@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
- 2.4 | 6.85 | 11.3
+ 2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
- 4.8 | 8.2 | 11.6
+ 4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
- 9.4 | 10.8 | 12.2
+ 9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity
diff --git a/doc/src/sgml/config.sgml b/doc/src/sgml/config.sgml
index b6f5822b84..340b5ad478 100644
--- a/doc/src/sgml/config.sgml
+++ b/doc/src/sgml/config.sgml
@@ -7833,16 +7833,37 @@ SET XML OPTION { DOCUMENT | CONTENT };
</term>
<listitem>
<para>
- This parameter adjusts the number of digits displayed for
+ This parameter adjusts the number of digits used for textual output of
floating-point values, including <type>float4</type>, <type>float8</type>,
- and geometric data types. The parameter value is added to the
- standard number of digits (<literal>FLT_DIG</literal> or <literal>DBL_DIG</literal>
- as appropriate). The value can be set as high as 3, to include
- partially-significant digits; this is especially useful for dumping
- float data that needs to be restored exactly. Or it can be set
- negative to suppress unwanted digits.
- See also <xref linkend="datatype-float"/>.
+ and geometric data types.
</para>
+ <para>
+ If the value is 1 (the default) or above, float values are output in
+ shortest-precise format; see <xref linkend="datatype-float"/>. The
+ actual number of digits generated depends only on the value being
+ output, not on the value of this parameter. At most 17 digits are
+ required for <type>float8</type> values, and 9 for <type>float4</type>
+ values. This format is both fast and precise, preserving the original
+ binary float value exactly when correctly read. For historical
+ compatibility, values up to 3 are permitted.
+ </para>
+ <para>
+ If the value is zero or negative, then the output is rounded to a
+ given decimal precision. The precision used is the standard number of
+ digits for the type (<literal>FLT_DIG</literal>
+ or <literal>DBL_DIG</literal> as appropriate) reduced according to the
+ value of this parameter. (For example, specifying -1 will cause float4
+ values to be output rounded to 5 significant digits, and float8 values
+ rounded to 14 digits.) This format is slower and does not preserve all
+ the bits of the binary float value, but may be more human-readable.
+ </para>
+ <note>
+ <para>
+ The meaning of this parameter, and its default value, changed
+ in <productname>PostgreSQL</productname> 12;
+ see <xref linkend="datatype-float"/> for further discussion.
+ </para>
+ </note>
</listitem>
</varlistentry>
diff --git a/doc/src/sgml/datatype.sgml b/doc/src/sgml/datatype.sgml
index ed0ee584c9..da0d887623 100644
--- a/doc/src/sgml/datatype.sgml
+++ b/doc/src/sgml/datatype.sgml
@@ -671,13 +671,12 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</indexterm>
<para>
- The data types <type>real</type> and <type>double
- precision</type> are inexact, variable-precision numeric types.
- In practice, these types are usually implementations of
- <acronym>IEEE</acronym> Standard 754 for Binary Floating-Point
- Arithmetic (single and double precision, respectively), to the
- extent that the underlying processor, operating system, and
- compiler support it.
+ The data types <type>real</type> and <type>double precision</type> are
+ inexact, variable-precision numeric types. On all currently supported
+ platforms, these types are implementations of <acronym>IEEE</acronym>
+ Standard 754 for Binary Floating-Point Arithmetic (single and double
+ precision, respectively), to the extent that the underlying processor,
+ operating system, and compiler support it.
</para>
<para>
@@ -715,24 +714,57 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</para>
<para>
- On most platforms, the <type>real</type> type has a range of at least
- 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The
- <type>double precision</type> type typically has a range of around
- 1E-307 to 1E+308 with a precision of at least 15 digits. Values that
- are too large or too small will cause an error. Rounding might
- take place if the precision of an input number is too high.
- Numbers too close to zero that are not representable as distinct
- from zero will cause an underflow error.
+ On all currently supported platforms, the <type>real</type> type has a
+ range of around 1E-37 to 1E+37 with a precision of at least 6 decimal
+ digits. The <type>double precision</type> type has a range of around
+ 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are
+ too large or too small will cause an error. Rounding might take place if
+ the precision of an input number is too high. Numbers too close to zero
+ that are not representable as distinct from zero will cause an underflow
+ error.
+ </para>
+
+ <para>
+ By default, floating point values are output in text form in their
+ shortest precise decimal representation; the decimal value produced is
+ closer to the true stored binary value than to any other value
+ representable in the same binary precision. (However, the output value is
+ currently never <emphasis>exactly</emphasis> midway between two
+ representable values, in order to avoid a widespread bug where input
+ routines do not properly respect the round-to-even rule.) This value will
+ use at most 17 significant decimal digits for <type>float8</type>
+ values, and at most 9 digits for <type>float4</type> values.
</para>
<note>
<para>
- The <xref linkend="guc-extra-float-digits"/> setting controls the
- number of extra significant digits included when a floating point
- value is converted to text for output. With the default value of
- <literal>0</literal>, the output is the same on every platform
- supported by PostgreSQL. Increasing it will produce output that
- more accurately represents the stored value, but may be unportable.
+ This shortest-precise output format is much faster to generate than the
+ historical rounded format.
+ </para>
+ </note>
+
+ <para>
+ For compatibility with output generated by older versions
+ of <productname>PostgreSQL</productname>, and to allow the output
+ precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
+ parameter can be used to select rounded decimal output instead. Setting a
+ value of 0 restores the previous default of rounding the value to 6
+ (for <type>float4</type>) or 15 (for <type>float8</type>)
+ significant decimal digits. Setting a negative value reduces the number
+ of digits further; for example -2 would round output to 4 or 13 digits
+ respectively.
+ </para>
+
+ <para>
+ Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
+ selects the shortest-precise format.
+ </para>
+
+ <note>
+ <para>
+ Applications that wanted precise values have historically had to set
+ <xref linkend="guc-extra-float-digits"/> to 3 obtain them. For maximum
+ compatibility between versions, they should continue to do so.
</para>
</note>
@@ -751,9 +783,7 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</literallayout>
These represent the IEEE 754 special values
<quote>infinity</quote>, <quote>negative infinity</quote>, and
- <quote>not-a-number</quote>, respectively. (On a machine whose
- floating-point arithmetic does not follow IEEE 754, these values
- will probably not work as expected.) When writing these values
+ <quote>not-a-number</quote>, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example <literal>UPDATE table SET x = '-Infinity'</literal>. On input,
these strings are recognized in a case-insensitive manner.
@@ -786,17 +816,6 @@ FROM generate_series(-3.5, 3.5, 1) as x;
<type>double precision</type>.
</para>
- <note>
- <para>
- The assumption that <type>real</type> and
- <type>double precision</type> have exactly 24 and 53 bits in the
- mantissa respectively is correct for IEEE-standard floating point
- implementations. On non-IEEE platforms it might be off a little, but
- for simplicity the same ranges of <replaceable>p</replaceable> are used
- on all platforms.
- </para>
- </note>
-
</sect2>
<sect2 id="datatype-serial">
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..4e403d02cd 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -30,8 +31,15 @@
#include "utils/timestamp.h"
-/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+/*
+ * Configurable GUC parameter
+ *
+ * If >0, use shortest-decimal format for output; this is both the default and
+ * allows for compatibility with clients that explicitly set a value here to
+ * get round-trip-accurate results. If 0 or less, then use the old, slow,
+ * decimal rounding method.
+ */
+int extra_float_digits = 1;
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +112,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +169,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +177,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +229,17 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +275,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +289,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +511,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 98d75be292..56e7ceff46 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2654,11 +2654,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects precise output mode.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/backend/utils/misc/postgresql.conf.sample b/src/backend/utils/misc/postgresql.conf.sample
index a21865a77f..13d7436b42 100644
--- a/src/backend/utils/misc/postgresql.conf.sample
+++ b/src/backend/utils/misc/postgresql.conf.sample
@@ -649,7 +649,8 @@
# India
# You can create your own file in
# share/timezonesets/.
-#extra_float_digits = 0 # min -15, max 3
+#extra_float_digits = 1 # min -15, max 3; any value >0 actually
+ # selects precise output mode
#client_encoding = sql_ascii # actually, defaults to database
# encoding
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..bd3a506f9e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): override CFLAGS := $(filter-out -Wdeclaration-after-statement,$(CFLAGS))
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..555bda27ef
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,936 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ {
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ }
+
+ {
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..9fbbd8e86c
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,664 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result + 1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..14639aff9c
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+/*
+ * Upstream Ryu's output is always the shortest possible. But we adjust that
+ * slightly to improve portability: we avoid outputting the exact midpoint
+ * value between two representable floats, since that relies on the reader
+ * getting the round-to-even rule correct, which seems to be the common
+ * failure mode.
+ *
+ * Defining this to 1 would restore the upstream behavior.
+ */
+#define STRICTLY_SHORTEST 0
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..5e881c982f
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+void double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+void float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 82547f321f..b38b0ae189 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index a3c44f0fd8..160fa1279e 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index 485e771f99..436bc83fe3 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..34f85638c9
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,121 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs. Also, strtof() doesn't handle subnormal input
+ * well, so prefer to round the strtod() result in such cases. (Normally we'd
+ * just say "too bad" if strtof() doesn't support subnormals, but since we're
+ * already in here fixing stuff, we might as well do the best fix we can.)
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ ((fresult >= FLT_MIN || fresult <= -FLT_MIN) && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 non-subnormal
+ * finite value (or NaN) without error, then return that to the caller
+ * without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else if ((dresult > 0 && dresult <= FLT_MIN && (float)dresult != 0.0) ||
+ (dresult < 0 && dresult >= -FLT_MIN && (float)dresult != 0.0))
+ {
+ return (float) dresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..d7e66f00b8
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,927 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(256 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..38cb3a66cd 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,606 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(256 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..1689493373 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +237,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +639,401 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(194 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..00fd5fd673 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +233,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +641,401 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(194 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index 2c8e21baa7..b31594a7b5 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 420c5a54f2..8b13ef3a09 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..5f146f414d 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,247 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+
+SELECT float4send('1.17549435e-38'::float4);
+SELECT float4send('1.1754944e-38'::float4);
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..62b904a442 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +239,187 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- round-trip tests
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
And another version. (I should have checked upstream before posting the
last one, sigh)
This one incorporates (with heavy adaptations) a new optimization from
upstream, adding a fastpath for values that happen to be small nonzero
integers. The overhead is low enough for this to be worthwhile.
Additionally, I've now micro-optimized the fixed-point output format
code (which is not in upstream), so it no longer makes a noticable
difference to performance.
There probably isn't any need for more optimization here since it's now
measurably faster (sometimes almost 2x faster) than bigint output in all
my tests (which probably means we could improve on bigint's performance,
but that's a job for another day).
--
Andrew (irc:RhodiumToad)
Attachments:
ryu9.patchtext/x-patchDownload
diff --git a/configure b/configure
index ddb3c8b1ba..378860e9ce 100755
--- a/configure
+++ b/configure
@@ -15812,6 +15812,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 3d8888805c..08fc8fd1bf 100644
--- a/configure.in
+++ b/configure.in
@@ -1705,6 +1705,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/contrib/btree_gist/expected/float4.out b/contrib/btree_gist/expected/float4.out
index abbd9eef4e..dfe732049e 100644
--- a/contrib/btree_gist/expected/float4.out
+++ b/contrib/btree_gist/expected/float4.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
(1 row)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
diff --git a/contrib/btree_gist/expected/float8.out b/contrib/btree_gist/expected/float8.out
index 5111dbdfae..ebd0ef3d68 100644
--- a/contrib/btree_gist/expected/float8.out
+++ b/contrib/btree_gist/expected/float8.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
(1 row)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out
index 1a65e6944a..5b89cb1a26 100644
--- a/contrib/cube/expected/cube.out
+++ b/contrib/cube/expected/cube.out
@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
(1 row)
SELECT '.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
- cube
-----------------------
- (-0.123456789012346)
+ cube
+-----------------------
+ (-0.1234567890123456)
(1 row)
-- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
(1 row)
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
- cube_distance
-------------------
- 140.762210837994
+ cube_distance
+--------------------
+ 140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
diff --git a/contrib/cube/expected/cube_sci.out b/contrib/cube/expected/cube_sci.out
index 1e8269cdf0..488499ac8e 100644
--- a/contrib/cube/expected/cube_sci.out
+++ b/contrib/cube/expected/cube_sci.out
@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
(1 row)
SELECT '1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
- cube
--------------------------
- (-1.23456789012346e+15)
+ cube
+--------------------------
+ (-1.234567890123456e+15)
(1 row)
diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql
index 59e7e4159d..7f8b2e3979 100644
--- a/contrib/cube/sql/cube.sql
+++ b/contrib/cube/sql/cube.sql
@@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
diff --git a/contrib/pg_trgm/expected/pg_strict_word_trgm.out b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
index 43898a3b98..1e1ee16ce9 100644
--- a/contrib/pg_trgm/expected/pg_strict_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
@@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
+-- reduce noise
+set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/expected/pg_trgm.out b/contrib/pg_trgm/expected/pg_trgm.out
index 6efc54356a..b3e709f496 100644
--- a/contrib/pg_trgm/expected/pg_trgm.out
+++ b/contrib/pg_trgm/expected/pg_trgm.out
@@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------
diff --git a/contrib/pg_trgm/expected/pg_word_trgm.out b/contrib/pg_trgm/expected/pg_word_trgm.out
index bed61c4922..936d489390 100644
--- a/contrib/pg_trgm/expected/pg_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_word_trgm.out
@@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
index 98e0d379f8..ce0791f29b 100644
--- a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
@@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;
diff --git a/contrib/pg_trgm/sql/pg_trgm.sql b/contrib/pg_trgm/sql/pg_trgm.sql
index 96ae542320..08459e64c3 100644
--- a/contrib/pg_trgm/sql/pg_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_trgm.sql
@@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
+
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');
diff --git a/contrib/pg_trgm/sql/pg_word_trgm.sql b/contrib/pg_trgm/sql/pg_word_trgm.sql
index 4b1db9706a..d9fa1c55e5 100644
--- a/contrib/pg_trgm/sql/pg_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_word_trgm.sql
@@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;
diff --git a/contrib/seg/expected/seg.out b/contrib/seg/expected/seg.out
index a289dbe5f9..80b0bca156 100644
--- a/contrib/seg/expected/seg.out
+++ b/contrib/seg/expected/seg.out
@@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
- 2.4 | 6.85 | 11.3
+ 2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
- 4.8 | 8.2 | 11.6
+ 4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
- 9.4 | 10.8 | 12.2
+ 9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity
diff --git a/doc/src/sgml/config.sgml b/doc/src/sgml/config.sgml
index b6f5822b84..340b5ad478 100644
--- a/doc/src/sgml/config.sgml
+++ b/doc/src/sgml/config.sgml
@@ -7833,16 +7833,37 @@ SET XML OPTION { DOCUMENT | CONTENT };
</term>
<listitem>
<para>
- This parameter adjusts the number of digits displayed for
+ This parameter adjusts the number of digits used for textual output of
floating-point values, including <type>float4</type>, <type>float8</type>,
- and geometric data types. The parameter value is added to the
- standard number of digits (<literal>FLT_DIG</literal> or <literal>DBL_DIG</literal>
- as appropriate). The value can be set as high as 3, to include
- partially-significant digits; this is especially useful for dumping
- float data that needs to be restored exactly. Or it can be set
- negative to suppress unwanted digits.
- See also <xref linkend="datatype-float"/>.
+ and geometric data types.
</para>
+ <para>
+ If the value is 1 (the default) or above, float values are output in
+ shortest-precise format; see <xref linkend="datatype-float"/>. The
+ actual number of digits generated depends only on the value being
+ output, not on the value of this parameter. At most 17 digits are
+ required for <type>float8</type> values, and 9 for <type>float4</type>
+ values. This format is both fast and precise, preserving the original
+ binary float value exactly when correctly read. For historical
+ compatibility, values up to 3 are permitted.
+ </para>
+ <para>
+ If the value is zero or negative, then the output is rounded to a
+ given decimal precision. The precision used is the standard number of
+ digits for the type (<literal>FLT_DIG</literal>
+ or <literal>DBL_DIG</literal> as appropriate) reduced according to the
+ value of this parameter. (For example, specifying -1 will cause float4
+ values to be output rounded to 5 significant digits, and float8 values
+ rounded to 14 digits.) This format is slower and does not preserve all
+ the bits of the binary float value, but may be more human-readable.
+ </para>
+ <note>
+ <para>
+ The meaning of this parameter, and its default value, changed
+ in <productname>PostgreSQL</productname> 12;
+ see <xref linkend="datatype-float"/> for further discussion.
+ </para>
+ </note>
</listitem>
</varlistentry>
diff --git a/doc/src/sgml/datatype.sgml b/doc/src/sgml/datatype.sgml
index ed0ee584c9..da0d887623 100644
--- a/doc/src/sgml/datatype.sgml
+++ b/doc/src/sgml/datatype.sgml
@@ -671,13 +671,12 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</indexterm>
<para>
- The data types <type>real</type> and <type>double
- precision</type> are inexact, variable-precision numeric types.
- In practice, these types are usually implementations of
- <acronym>IEEE</acronym> Standard 754 for Binary Floating-Point
- Arithmetic (single and double precision, respectively), to the
- extent that the underlying processor, operating system, and
- compiler support it.
+ The data types <type>real</type> and <type>double precision</type> are
+ inexact, variable-precision numeric types. On all currently supported
+ platforms, these types are implementations of <acronym>IEEE</acronym>
+ Standard 754 for Binary Floating-Point Arithmetic (single and double
+ precision, respectively), to the extent that the underlying processor,
+ operating system, and compiler support it.
</para>
<para>
@@ -715,24 +714,57 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</para>
<para>
- On most platforms, the <type>real</type> type has a range of at least
- 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The
- <type>double precision</type> type typically has a range of around
- 1E-307 to 1E+308 with a precision of at least 15 digits. Values that
- are too large or too small will cause an error. Rounding might
- take place if the precision of an input number is too high.
- Numbers too close to zero that are not representable as distinct
- from zero will cause an underflow error.
+ On all currently supported platforms, the <type>real</type> type has a
+ range of around 1E-37 to 1E+37 with a precision of at least 6 decimal
+ digits. The <type>double precision</type> type has a range of around
+ 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are
+ too large or too small will cause an error. Rounding might take place if
+ the precision of an input number is too high. Numbers too close to zero
+ that are not representable as distinct from zero will cause an underflow
+ error.
+ </para>
+
+ <para>
+ By default, floating point values are output in text form in their
+ shortest precise decimal representation; the decimal value produced is
+ closer to the true stored binary value than to any other value
+ representable in the same binary precision. (However, the output value is
+ currently never <emphasis>exactly</emphasis> midway between two
+ representable values, in order to avoid a widespread bug where input
+ routines do not properly respect the round-to-even rule.) This value will
+ use at most 17 significant decimal digits for <type>float8</type>
+ values, and at most 9 digits for <type>float4</type> values.
</para>
<note>
<para>
- The <xref linkend="guc-extra-float-digits"/> setting controls the
- number of extra significant digits included when a floating point
- value is converted to text for output. With the default value of
- <literal>0</literal>, the output is the same on every platform
- supported by PostgreSQL. Increasing it will produce output that
- more accurately represents the stored value, but may be unportable.
+ This shortest-precise output format is much faster to generate than the
+ historical rounded format.
+ </para>
+ </note>
+
+ <para>
+ For compatibility with output generated by older versions
+ of <productname>PostgreSQL</productname>, and to allow the output
+ precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
+ parameter can be used to select rounded decimal output instead. Setting a
+ value of 0 restores the previous default of rounding the value to 6
+ (for <type>float4</type>) or 15 (for <type>float8</type>)
+ significant decimal digits. Setting a negative value reduces the number
+ of digits further; for example -2 would round output to 4 or 13 digits
+ respectively.
+ </para>
+
+ <para>
+ Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
+ selects the shortest-precise format.
+ </para>
+
+ <note>
+ <para>
+ Applications that wanted precise values have historically had to set
+ <xref linkend="guc-extra-float-digits"/> to 3 obtain them. For maximum
+ compatibility between versions, they should continue to do so.
</para>
</note>
@@ -751,9 +783,7 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</literallayout>
These represent the IEEE 754 special values
<quote>infinity</quote>, <quote>negative infinity</quote>, and
- <quote>not-a-number</quote>, respectively. (On a machine whose
- floating-point arithmetic does not follow IEEE 754, these values
- will probably not work as expected.) When writing these values
+ <quote>not-a-number</quote>, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example <literal>UPDATE table SET x = '-Infinity'</literal>. On input,
these strings are recognized in a case-insensitive manner.
@@ -786,17 +816,6 @@ FROM generate_series(-3.5, 3.5, 1) as x;
<type>double precision</type>.
</para>
- <note>
- <para>
- The assumption that <type>real</type> and
- <type>double precision</type> have exactly 24 and 53 bits in the
- mantissa respectively is correct for IEEE-standard floating point
- implementations. On non-IEEE platforms it might be off a little, but
- for simplicity the same ranges of <replaceable>p</replaceable> are used
- on all platforms.
- </para>
- </note>
-
</sect2>
<sect2 id="datatype-serial">
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..4e403d02cd 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -30,8 +31,15 @@
#include "utils/timestamp.h"
-/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+/*
+ * Configurable GUC parameter
+ *
+ * If >0, use shortest-decimal format for output; this is both the default and
+ * allows for compatibility with clients that explicitly set a value here to
+ * get round-trip-accurate results. If 0 or less, then use the old, slow,
+ * decimal rounding method.
+ */
+int extra_float_digits = 1;
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +112,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +169,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +177,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +229,17 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +275,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +289,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +511,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 98d75be292..56e7ceff46 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2654,11 +2654,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects precise output mode.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/backend/utils/misc/postgresql.conf.sample b/src/backend/utils/misc/postgresql.conf.sample
index a21865a77f..13d7436b42 100644
--- a/src/backend/utils/misc/postgresql.conf.sample
+++ b/src/backend/utils/misc/postgresql.conf.sample
@@ -649,7 +649,8 @@
# India
# You can create your own file in
# share/timezonesets/.
-#extra_float_digits = 0 # min -15, max 3
+#extra_float_digits = 1 # min -15, max 3; any value >0 actually
+ # selects precise output mode
#client_encoding = sql_ascii # actually, defaults to database
# encoding
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..bd3a506f9e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): override CFLAGS := $(filter-out -Wdeclaration-after-statement,$(CFLAGS))
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..58f91523e7
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,1041 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ if (index == 1)
+ {
+ /* nexp is 1..16 */
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp >= 16)
+ {
+ memmove(result, result + 1, 16);
+ }
+ else
+ {
+ if (nexp & 8)
+ {
+ memmove(result + index - 1, result + index, 8);
+ index += 8;
+ }
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ for (int i = 0; i < exp; ++i)
+ result[olength + i] = '0';
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint64 q = div10(output);
+ const uint32 r = (uint32) (output - 10 * q);
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+static inline bool
+d2d_small_int(const uint64 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_64 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of d2s, which is undesirable.
+ */
+
+ if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
+ * 1 <= f = m2 / 2^-e2 < 2^53.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
+ */
+ const uint64 mask = (UINT64CONST(1) << -e2) - 1;
+ const uint64 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^53).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^53 < 10^16, there is no need to adjust
+ * decimalLength().
+ */
+ const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_64 v;
+ const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = d2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..59fc5267a0
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,768 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ /* nexp is 1..8 */
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp >= 8)
+ {
+ memmove(result, result + 1, 8);
+ }
+ else
+ {
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint32 q = output / 10;
+ const uint32 r = output - 10 * q;
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+static inline bool
+f2d_small_int(const uint32 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_32 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of f2s, which is undesirable.
+ */
+
+ if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
+ * 1 <= f = m2 / 2^-e2 < 2^24.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
+ */
+ const uint32 mask = (1U << -e2) - 1;
+ const uint32 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^24).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^24 < 10^9, there is no need to adjust
+ * decimalLength().
+ */
+ const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_32 v;
+ const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = f2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..14639aff9c
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+/*
+ * Upstream Ryu's output is always the shortest possible. But we adjust that
+ * slightly to improve portability: we avoid outputting the exact midpoint
+ * value between two representable floats, since that relies on the reader
+ * getting the round-to-even rule correct, which seems to be the common
+ * failure mode.
+ *
+ * Defining this to 1 would restore the upstream behavior.
+ */
+#define STRICTLY_SHORTEST 0
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..5e881c982f
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+void double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+void float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 82547f321f..b38b0ae189 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index a3c44f0fd8..160fa1279e 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index 485e771f99..436bc83fe3 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..34f85638c9
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,121 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs. Also, strtof() doesn't handle subnormal input
+ * well, so prefer to round the strtod() result in such cases. (Normally we'd
+ * just say "too bad" if strtof() doesn't support subnormals, but since we're
+ * already in here fixing stuff, we might as well do the best fix we can.)
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ ((fresult >= FLT_MIN || fresult <= -FLT_MIN) && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 non-subnormal
+ * finite value (or NaN) without error, then return that to the caller
+ * without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else if ((dresult > 0 && dresult <= FLT_MIN && (float)dresult != 0.0) ||
+ (dresult < 0 && dresult >= -FLT_MIN && (float)dresult != 0.0))
+ {
+ return (float) dresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..54de939a6e
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,940 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..dff1921944 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,619 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..f67c22e9fa 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +237,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +639,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..c3a6f5331f 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +233,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +641,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index 2c8e21baa7..b31594a7b5 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 420c5a54f2..8b13ef3a09 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..d606e7787b 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,254 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+
+SELECT float4send('1.17549435e-38'::float4);
+SELECT float4send('1.1754944e-38'::float4);
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..a33321811d 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +239,203 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- round-trip tests
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
[ ryu9.patch ]
I recall having tried some earlier version on my old HPUX dinosaur,
and it worked, but this one doesn't compile:
float.c: In function `float4in':
float.c:240: error: `HUGE_VALF' undeclared (first use in this function)
float.c:240: error: (Each undeclared identifier is reported only once
float.c:240: error: for each function it appears in.)
As far as I can find, that symbol doesn't appear anywhere in the
system headers on this platform.
FWIW, I did get a successful build and core regression test run on
NetBSD 8.99/aarch64.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
[ ryu9.patch ]
Tom> I recall having tried some earlier version on my old HPUX dinosaur,
Tom> and it worked, but this one doesn't compile:
Tom> float.c: In function `float4in':
Tom> float.c:240: error: `HUGE_VALF' undeclared (first use in this function)
(mutter mutter)
Try this one.
--
Andrew (irc:RhodiumToad)
Attachments:
ryu10.patchtext/x-patchDownload
diff --git a/configure b/configure
index ddb3c8b1ba..378860e9ce 100755
--- a/configure
+++ b/configure
@@ -15812,6 +15812,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 3d8888805c..08fc8fd1bf 100644
--- a/configure.in
+++ b/configure.in
@@ -1705,6 +1705,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/contrib/btree_gist/expected/float4.out b/contrib/btree_gist/expected/float4.out
index abbd9eef4e..dfe732049e 100644
--- a/contrib/btree_gist/expected/float4.out
+++ b/contrib/btree_gist/expected/float4.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
(1 row)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
diff --git a/contrib/btree_gist/expected/float8.out b/contrib/btree_gist/expected/float8.out
index 5111dbdfae..ebd0ef3d68 100644
--- a/contrib/btree_gist/expected/float8.out
+++ b/contrib/btree_gist/expected/float8.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
(1 row)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out
index 1a65e6944a..5b89cb1a26 100644
--- a/contrib/cube/expected/cube.out
+++ b/contrib/cube/expected/cube.out
@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
(1 row)
SELECT '.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
- cube
-----------------------
- (-0.123456789012346)
+ cube
+-----------------------
+ (-0.1234567890123456)
(1 row)
-- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
(1 row)
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
- cube_distance
-------------------
- 140.762210837994
+ cube_distance
+--------------------
+ 140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
diff --git a/contrib/cube/expected/cube_sci.out b/contrib/cube/expected/cube_sci.out
index 1e8269cdf0..488499ac8e 100644
--- a/contrib/cube/expected/cube_sci.out
+++ b/contrib/cube/expected/cube_sci.out
@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
(1 row)
SELECT '1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
- cube
--------------------------
- (-1.23456789012346e+15)
+ cube
+--------------------------
+ (-1.234567890123456e+15)
(1 row)
diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql
index 59e7e4159d..7f8b2e3979 100644
--- a/contrib/cube/sql/cube.sql
+++ b/contrib/cube/sql/cube.sql
@@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
diff --git a/contrib/pg_trgm/expected/pg_strict_word_trgm.out b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
index 43898a3b98..1e1ee16ce9 100644
--- a/contrib/pg_trgm/expected/pg_strict_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
@@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
+-- reduce noise
+set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/expected/pg_trgm.out b/contrib/pg_trgm/expected/pg_trgm.out
index 6efc54356a..b3e709f496 100644
--- a/contrib/pg_trgm/expected/pg_trgm.out
+++ b/contrib/pg_trgm/expected/pg_trgm.out
@@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------
diff --git a/contrib/pg_trgm/expected/pg_word_trgm.out b/contrib/pg_trgm/expected/pg_word_trgm.out
index bed61c4922..936d489390 100644
--- a/contrib/pg_trgm/expected/pg_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_word_trgm.out
@@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
index 98e0d379f8..ce0791f29b 100644
--- a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
@@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;
diff --git a/contrib/pg_trgm/sql/pg_trgm.sql b/contrib/pg_trgm/sql/pg_trgm.sql
index 96ae542320..08459e64c3 100644
--- a/contrib/pg_trgm/sql/pg_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_trgm.sql
@@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
+
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');
diff --git a/contrib/pg_trgm/sql/pg_word_trgm.sql b/contrib/pg_trgm/sql/pg_word_trgm.sql
index 4b1db9706a..d9fa1c55e5 100644
--- a/contrib/pg_trgm/sql/pg_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_word_trgm.sql
@@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;
diff --git a/contrib/seg/expected/seg.out b/contrib/seg/expected/seg.out
index a289dbe5f9..80b0bca156 100644
--- a/contrib/seg/expected/seg.out
+++ b/contrib/seg/expected/seg.out
@@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
- 2.4 | 6.85 | 11.3
+ 2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
- 4.8 | 8.2 | 11.6
+ 4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
- 9.4 | 10.8 | 12.2
+ 9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity
diff --git a/doc/src/sgml/config.sgml b/doc/src/sgml/config.sgml
index b6f5822b84..340b5ad478 100644
--- a/doc/src/sgml/config.sgml
+++ b/doc/src/sgml/config.sgml
@@ -7833,16 +7833,37 @@ SET XML OPTION { DOCUMENT | CONTENT };
</term>
<listitem>
<para>
- This parameter adjusts the number of digits displayed for
+ This parameter adjusts the number of digits used for textual output of
floating-point values, including <type>float4</type>, <type>float8</type>,
- and geometric data types. The parameter value is added to the
- standard number of digits (<literal>FLT_DIG</literal> or <literal>DBL_DIG</literal>
- as appropriate). The value can be set as high as 3, to include
- partially-significant digits; this is especially useful for dumping
- float data that needs to be restored exactly. Or it can be set
- negative to suppress unwanted digits.
- See also <xref linkend="datatype-float"/>.
+ and geometric data types.
</para>
+ <para>
+ If the value is 1 (the default) or above, float values are output in
+ shortest-precise format; see <xref linkend="datatype-float"/>. The
+ actual number of digits generated depends only on the value being
+ output, not on the value of this parameter. At most 17 digits are
+ required for <type>float8</type> values, and 9 for <type>float4</type>
+ values. This format is both fast and precise, preserving the original
+ binary float value exactly when correctly read. For historical
+ compatibility, values up to 3 are permitted.
+ </para>
+ <para>
+ If the value is zero or negative, then the output is rounded to a
+ given decimal precision. The precision used is the standard number of
+ digits for the type (<literal>FLT_DIG</literal>
+ or <literal>DBL_DIG</literal> as appropriate) reduced according to the
+ value of this parameter. (For example, specifying -1 will cause float4
+ values to be output rounded to 5 significant digits, and float8 values
+ rounded to 14 digits.) This format is slower and does not preserve all
+ the bits of the binary float value, but may be more human-readable.
+ </para>
+ <note>
+ <para>
+ The meaning of this parameter, and its default value, changed
+ in <productname>PostgreSQL</productname> 12;
+ see <xref linkend="datatype-float"/> for further discussion.
+ </para>
+ </note>
</listitem>
</varlistentry>
diff --git a/doc/src/sgml/datatype.sgml b/doc/src/sgml/datatype.sgml
index ed0ee584c9..da0d887623 100644
--- a/doc/src/sgml/datatype.sgml
+++ b/doc/src/sgml/datatype.sgml
@@ -671,13 +671,12 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</indexterm>
<para>
- The data types <type>real</type> and <type>double
- precision</type> are inexact, variable-precision numeric types.
- In practice, these types are usually implementations of
- <acronym>IEEE</acronym> Standard 754 for Binary Floating-Point
- Arithmetic (single and double precision, respectively), to the
- extent that the underlying processor, operating system, and
- compiler support it.
+ The data types <type>real</type> and <type>double precision</type> are
+ inexact, variable-precision numeric types. On all currently supported
+ platforms, these types are implementations of <acronym>IEEE</acronym>
+ Standard 754 for Binary Floating-Point Arithmetic (single and double
+ precision, respectively), to the extent that the underlying processor,
+ operating system, and compiler support it.
</para>
<para>
@@ -715,24 +714,57 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</para>
<para>
- On most platforms, the <type>real</type> type has a range of at least
- 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The
- <type>double precision</type> type typically has a range of around
- 1E-307 to 1E+308 with a precision of at least 15 digits. Values that
- are too large or too small will cause an error. Rounding might
- take place if the precision of an input number is too high.
- Numbers too close to zero that are not representable as distinct
- from zero will cause an underflow error.
+ On all currently supported platforms, the <type>real</type> type has a
+ range of around 1E-37 to 1E+37 with a precision of at least 6 decimal
+ digits. The <type>double precision</type> type has a range of around
+ 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are
+ too large or too small will cause an error. Rounding might take place if
+ the precision of an input number is too high. Numbers too close to zero
+ that are not representable as distinct from zero will cause an underflow
+ error.
+ </para>
+
+ <para>
+ By default, floating point values are output in text form in their
+ shortest precise decimal representation; the decimal value produced is
+ closer to the true stored binary value than to any other value
+ representable in the same binary precision. (However, the output value is
+ currently never <emphasis>exactly</emphasis> midway between two
+ representable values, in order to avoid a widespread bug where input
+ routines do not properly respect the round-to-even rule.) This value will
+ use at most 17 significant decimal digits for <type>float8</type>
+ values, and at most 9 digits for <type>float4</type> values.
</para>
<note>
<para>
- The <xref linkend="guc-extra-float-digits"/> setting controls the
- number of extra significant digits included when a floating point
- value is converted to text for output. With the default value of
- <literal>0</literal>, the output is the same on every platform
- supported by PostgreSQL. Increasing it will produce output that
- more accurately represents the stored value, but may be unportable.
+ This shortest-precise output format is much faster to generate than the
+ historical rounded format.
+ </para>
+ </note>
+
+ <para>
+ For compatibility with output generated by older versions
+ of <productname>PostgreSQL</productname>, and to allow the output
+ precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
+ parameter can be used to select rounded decimal output instead. Setting a
+ value of 0 restores the previous default of rounding the value to 6
+ (for <type>float4</type>) or 15 (for <type>float8</type>)
+ significant decimal digits. Setting a negative value reduces the number
+ of digits further; for example -2 would round output to 4 or 13 digits
+ respectively.
+ </para>
+
+ <para>
+ Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
+ selects the shortest-precise format.
+ </para>
+
+ <note>
+ <para>
+ Applications that wanted precise values have historically had to set
+ <xref linkend="guc-extra-float-digits"/> to 3 obtain them. For maximum
+ compatibility between versions, they should continue to do so.
</para>
</note>
@@ -751,9 +783,7 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</literallayout>
These represent the IEEE 754 special values
<quote>infinity</quote>, <quote>negative infinity</quote>, and
- <quote>not-a-number</quote>, respectively. (On a machine whose
- floating-point arithmetic does not follow IEEE 754, these values
- will probably not work as expected.) When writing these values
+ <quote>not-a-number</quote>, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example <literal>UPDATE table SET x = '-Infinity'</literal>. On input,
these strings are recognized in a case-insensitive manner.
@@ -786,17 +816,6 @@ FROM generate_series(-3.5, 3.5, 1) as x;
<type>double precision</type>.
</para>
- <note>
- <para>
- The assumption that <type>real</type> and
- <type>double precision</type> have exactly 24 and 53 bits in the
- mantissa respectively is correct for IEEE-standard floating point
- implementations. On non-IEEE platforms it might be off a little, but
- for simplicity the same ranges of <replaceable>p</replaceable> are used
- on all platforms.
- </para>
- </note>
-
</sect2>
<sect2 id="datatype-serial">
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..37c202d21c 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -30,8 +31,15 @@
#include "utils/timestamp.h"
-/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+/*
+ * Configurable GUC parameter
+ *
+ * If >0, use shortest-decimal format for output; this is both the default and
+ * allows for compatibility with clients that explicitly set a value here to
+ * get round-trip-accurate results. If 0 or less, then use the old, slow,
+ * decimal rounding method.
+ */
+int extra_float_digits = 1;
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +112,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +169,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +177,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +229,18 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF. Also use isinf() if
+ * HUGE_VALF is missing.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if !defined(HUGE_VALF) || (defined(_MSC_VER) && (_MSC_VER < 1900))
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +276,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +290,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +512,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 98d75be292..56e7ceff46 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2654,11 +2654,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects precise output mode.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/backend/utils/misc/postgresql.conf.sample b/src/backend/utils/misc/postgresql.conf.sample
index a21865a77f..13d7436b42 100644
--- a/src/backend/utils/misc/postgresql.conf.sample
+++ b/src/backend/utils/misc/postgresql.conf.sample
@@ -649,7 +649,8 @@
# India
# You can create your own file in
# share/timezonesets/.
-#extra_float_digits = 0 # min -15, max 3
+#extra_float_digits = 1 # min -15, max 3; any value >0 actually
+ # selects precise output mode
#client_encoding = sql_ascii # actually, defaults to database
# encoding
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..bd3a506f9e 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): override CFLAGS := $(filter-out -Wdeclaration-after-statement,$(CFLAGS))
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..58f91523e7
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,1041 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ if (index == 1)
+ {
+ /* nexp is 1..16 */
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp >= 16)
+ {
+ memmove(result, result + 1, 16);
+ }
+ else
+ {
+ if (nexp & 8)
+ {
+ memmove(result + index - 1, result + index, 8);
+ index += 8;
+ }
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ for (int i = 0; i < exp; ++i)
+ result[olength + i] = '0';
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint64 q = div10(output);
+ const uint32 r = (uint32) (output - 10 * q);
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+static inline bool
+d2d_small_int(const uint64 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_64 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of d2s, which is undesirable.
+ */
+
+ if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
+ * 1 <= f = m2 / 2^-e2 < 2^53.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
+ */
+ const uint64 mask = (UINT64CONST(1) << -e2) - 1;
+ const uint64 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^53).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^53 < 10^16, there is no need to adjust
+ * decimalLength().
+ */
+ const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_64 v;
+ const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = d2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(25);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..59fc5267a0
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,768 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ *
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ /* nexp is 1..8 */
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp >= 8)
+ {
+ memmove(result, result + 1, 8);
+ }
+ else
+ {
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint32 q = output / 10;
+ const uint32 r = output - 10 * q;
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+static inline bool
+f2d_small_int(const uint32 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_32 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of f2s, which is undesirable.
+ */
+
+ if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
+ * 1 <= f = m2 / 2^-e2 < 2^24.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
+ */
+ const uint32 mask = (1U << -e2) - 1;
+ const uint32 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^24).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^24 < 10^9, there is no need to adjust
+ * decimalLength().
+ */
+ const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_32 v;
+ const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = f2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(16);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..14639aff9c
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+/*
+ * Upstream Ryu's output is always the shortest possible. But we adjust that
+ * slightly to improve portability: we avoid outputting the exact midpoint
+ * value between two representable floats, since that relies on the reader
+ * getting the round-to-even rule correct, which seems to be the common
+ * failure mode.
+ *
+ * Defining this to 1 would restore the upstream behavior.
+ */
+#define STRICTLY_SHORTEST 0
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..5e881c982f
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+void double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+void float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 82547f321f..b38b0ae189 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index a3c44f0fd8..160fa1279e 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index 485e771f99..436bc83fe3 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..34f85638c9
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,121 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs. Also, strtof() doesn't handle subnormal input
+ * well, so prefer to round the strtod() result in such cases. (Normally we'd
+ * just say "too bad" if strtof() doesn't support subnormals, but since we're
+ * already in here fixing stuff, we might as well do the best fix we can.)
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ ((fresult >= FLT_MIN || fresult <= -FLT_MIN) && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 non-subnormal
+ * finite value (or NaN) without error, then return that to the caller
+ * without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else if ((dresult > 0 && dresult <= FLT_MIN && (float)dresult != 0.0) ||
+ (dresult < 0 && dresult >= -FLT_MIN && (float)dresult != 0.0))
+ {
+ return (float) dresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..54de939a6e
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,940 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..dff1921944 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,619 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..f67c22e9fa 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +237,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +639,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..c3a6f5331f 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +233,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +641,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index 2c8e21baa7..b31594a7b5 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 420c5a54f2..8b13ef3a09 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..d606e7787b 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,254 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+
+SELECT float4send('1.17549435e-38'::float4);
+SELECT float4send('1.1754944e-38'::float4);
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..a33321811d 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +239,203 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- round-trip tests
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
Some final (I hope) updates:
- adopt Noah's configure code for -Wno-declaration-after-statement
- remove some code that proved to be dead, replaced by comments and
asserts
- add header comments for the public entry points
- move definition of buffer lengths to public header and comment them
- comment some assumptions that might otherwise be overlooked
- simplify some of the fixed-point optimizations slightly
- clarify some comments
- change _buf variants to return the string length, just because they can
--
Andrew (irc:RhodiumToad)
Attachments:
ryu11.patchtext/x-patchDownload
diff --git a/configure b/configure
index ddb3c8b1ba..708157a683 100755
--- a/configure
+++ b/configure
@@ -732,6 +732,7 @@ CPP
BITCODE_CXXFLAGS
BITCODE_CFLAGS
CFLAGS_VECTOR
+PERMIT_DECLARATION_AFTER_STATEMENT
LLVM_BINPATH
LLVM_CXXFLAGS
LLVM_CFLAGS
@@ -5262,6 +5263,7 @@ if test "$GCC" = yes -a "$ICC" = no; then
CFLAGS="-Wall -Wmissing-prototypes -Wpointer-arith"
CXXFLAGS="-Wall -Wpointer-arith"
# These work in some but not all gcc versions
+ save_CFLAGS=$CFLAGS
{ $as_echo "$as_me:${as_lineno-$LINENO}: checking whether ${CC} supports -Wdeclaration-after-statement, for CFLAGS" >&5
$as_echo_n "checking whether ${CC} supports -Wdeclaration-after-statement, for CFLAGS... " >&6; }
@@ -5302,7 +5304,13 @@ if test x"$pgac_cv_prog_CC_cflags__Wdeclaration_after_statement" = x"yes"; then
fi
- # -Wdeclaration-after-statement isn't applicable for C++
+ # -Wdeclaration-after-statement isn't applicable for C++. Specific C files
+ # disable it, so AC_SUBST the negative form.
+ PERMIT_DECLARATION_AFTER_STATEMENT=
+ if test x"save_$CFLAGS" != x"$CFLAGS"; then
+ PERMIT_DECLARATION_AFTER_STATEMENT=-Wno-declaration-after-statement
+ fi
+
# Really don't want VLAs to be used in our dialect of C
{ $as_echo "$as_me:${as_lineno-$LINENO}: checking whether ${CC} supports -Werror=vla, for CFLAGS" >&5
@@ -15812,6 +15820,19 @@ esac
fi
+ac_fn_c_check_func "$LINENO" "strtof" "ac_cv_func_strtof"
+if test "x$ac_cv_func_strtof" = xyes; then :
+ $as_echo "#define HAVE_STRTOF 1" >>confdefs.h
+
+else
+ case " $LIBOBJS " in
+ *" strtof.$ac_objext "* ) ;;
+ *) LIBOBJS="$LIBOBJS strtof.$ac_objext"
+ ;;
+esac
+
+fi
+
case $host_os in
diff --git a/configure.in b/configure.in
index 3d8888805c..1e732e46d7 100644
--- a/configure.in
+++ b/configure.in
@@ -476,8 +476,15 @@ if test "$GCC" = yes -a "$ICC" = no; then
CFLAGS="-Wall -Wmissing-prototypes -Wpointer-arith"
CXXFLAGS="-Wall -Wpointer-arith"
# These work in some but not all gcc versions
+ save_CFLAGS=$CFLAGS
PGAC_PROG_CC_CFLAGS_OPT([-Wdeclaration-after-statement])
- # -Wdeclaration-after-statement isn't applicable for C++
+ # -Wdeclaration-after-statement isn't applicable for C++. Specific C files
+ # disable it, so AC_SUBST the negative form.
+ PERMIT_DECLARATION_AFTER_STATEMENT=
+ if test x"save_$CFLAGS" != x"$CFLAGS"; then
+ PERMIT_DECLARATION_AFTER_STATEMENT=-Wno-declaration-after-statement
+ fi
+ AC_SUBST(PERMIT_DECLARATION_AFTER_STATEMENT)
# Really don't want VLAs to be used in our dialect of C
PGAC_PROG_CC_CFLAGS_OPT([-Werror=vla])
# -Wvla is not applicable for C++
@@ -1705,6 +1712,7 @@ AC_REPLACE_FUNCS(m4_normalize([
strlcat
strlcpy
strnlen
+ strtof
]))
case $host_os in
diff --git a/contrib/btree_gist/expected/float4.out b/contrib/btree_gist/expected/float4.out
index abbd9eef4e..dfe732049e 100644
--- a/contrib/btree_gist/expected/float4.out
+++ b/contrib/btree_gist/expected/float4.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
(1 row)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
- a | ?column?
-----------+----------
- -179 | 0
- -189.024 | 10.0239
- -158.177 | 20.8226
+ a | ?column?
+------------+-----------
+ -179 | 0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
(3 rows)
diff --git a/contrib/btree_gist/expected/float8.out b/contrib/btree_gist/expected/float8.out
index 5111dbdfae..ebd0ef3d68 100644
--- a/contrib/btree_gist/expected/float8.out
+++ b/contrib/btree_gist/expected/float8.out
@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
(1 row)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
(3 rows)
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
- a | ?column?
---------------+------------
- -1890 | 0
- -2003.634512 | 113.634512
- -1769.73634 | 120.26366
+ a | ?column?
+--------------+--------------------
+ -1890 | 0
+ -2003.634512 | 113.63451200000009
+ -1769.73634 | 120.26366000000007
(3 rows)
diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out
index 1a65e6944a..5b89cb1a26 100644
--- a/contrib/cube/expected/cube.out
+++ b/contrib/cube/expected/cube.out
@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
(1 row)
SELECT '.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
- cube
----------------------
- (0.123456789012346)
+ cube
+----------------------
+ (0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
- cube
-----------------------
- (-0.123456789012346)
+ cube
+-----------------------
+ (-0.1234567890123456)
(1 row)
-- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
(1 row)
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
- cube_distance
-------------------
- 140.762210837994
+ cube_distance
+--------------------
+ 140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
diff --git a/contrib/cube/expected/cube_sci.out b/contrib/cube/expected/cube_sci.out
index 1e8269cdf0..488499ac8e 100644
--- a/contrib/cube/expected/cube_sci.out
+++ b/contrib/cube/expected/cube_sci.out
@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
(1 row)
SELECT '1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
- cube
-------------------------
- (1.23456789012346e+15)
+ cube
+-------------------------
+ (1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
- cube
--------------------------
- (-1.23456789012346e+15)
+ cube
+--------------------------
+ (-1.234567890123456e+15)
(1 row)
diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql
index 59e7e4159d..7f8b2e3979 100644
--- a/contrib/cube/sql/cube.sql
+++ b/contrib/cube/sql/cube.sql
@@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
--- Test of distances
+-- Test of distances (euclidean distance may not be bit-exact)
--
+SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
+RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
+SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
+RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
diff --git a/contrib/pg_trgm/expected/pg_strict_word_trgm.out b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
index 43898a3b98..1e1ee16ce9 100644
--- a/contrib/pg_trgm/expected/pg_strict_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_strict_word_trgm.out
@@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
+-- reduce noise
+set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/expected/pg_trgm.out b/contrib/pg_trgm/expected/pg_trgm.out
index 6efc54356a..b3e709f496 100644
--- a/contrib/pg_trgm/expected/pg_trgm.out
+++ b/contrib/pg_trgm/expected/pg_trgm.out
@@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------
diff --git a/contrib/pg_trgm/expected/pg_word_trgm.out b/contrib/pg_trgm/expected/pg_word_trgm.out
index bed61c4922..936d489390 100644
--- a/contrib/pg_trgm/expected/pg_word_trgm.out
+++ b/contrib/pg_trgm/expected/pg_word_trgm.out
@@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------
diff --git a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
index 98e0d379f8..ce0791f29b 100644
--- a/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_strict_word_trgm.sql
@@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;
diff --git a/contrib/pg_trgm/sql/pg_trgm.sql b/contrib/pg_trgm/sql/pg_trgm.sql
index 96ae542320..08459e64c3 100644
--- a/contrib/pg_trgm/sql/pg_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_trgm.sql
@@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
+-- reduce noise
+set extra_float_digits = 0;
+
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');
diff --git a/contrib/pg_trgm/sql/pg_word_trgm.sql b/contrib/pg_trgm/sql/pg_word_trgm.sql
index 4b1db9706a..d9fa1c55e5 100644
--- a/contrib/pg_trgm/sql/pg_word_trgm.sql
+++ b/contrib/pg_trgm/sql/pg_word_trgm.sql
@@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
+-- reduce noise
+set extra_float_digits = 0;
+
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;
diff --git a/contrib/seg/expected/seg.out b/contrib/seg/expected/seg.out
index a289dbe5f9..80b0bca156 100644
--- a/contrib/seg/expected/seg.out
+++ b/contrib/seg/expected/seg.out
@@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
- 2.4 | 6.85 | 11.3
+ 2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
- 4.8 | 8.2 | 11.6
+ 4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
- 9.4 | 10.8 | 12.2
+ 9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity
diff --git a/doc/src/sgml/config.sgml b/doc/src/sgml/config.sgml
index b6f5822b84..340b5ad478 100644
--- a/doc/src/sgml/config.sgml
+++ b/doc/src/sgml/config.sgml
@@ -7833,16 +7833,37 @@ SET XML OPTION { DOCUMENT | CONTENT };
</term>
<listitem>
<para>
- This parameter adjusts the number of digits displayed for
+ This parameter adjusts the number of digits used for textual output of
floating-point values, including <type>float4</type>, <type>float8</type>,
- and geometric data types. The parameter value is added to the
- standard number of digits (<literal>FLT_DIG</literal> or <literal>DBL_DIG</literal>
- as appropriate). The value can be set as high as 3, to include
- partially-significant digits; this is especially useful for dumping
- float data that needs to be restored exactly. Or it can be set
- negative to suppress unwanted digits.
- See also <xref linkend="datatype-float"/>.
+ and geometric data types.
</para>
+ <para>
+ If the value is 1 (the default) or above, float values are output in
+ shortest-precise format; see <xref linkend="datatype-float"/>. The
+ actual number of digits generated depends only on the value being
+ output, not on the value of this parameter. At most 17 digits are
+ required for <type>float8</type> values, and 9 for <type>float4</type>
+ values. This format is both fast and precise, preserving the original
+ binary float value exactly when correctly read. For historical
+ compatibility, values up to 3 are permitted.
+ </para>
+ <para>
+ If the value is zero or negative, then the output is rounded to a
+ given decimal precision. The precision used is the standard number of
+ digits for the type (<literal>FLT_DIG</literal>
+ or <literal>DBL_DIG</literal> as appropriate) reduced according to the
+ value of this parameter. (For example, specifying -1 will cause float4
+ values to be output rounded to 5 significant digits, and float8 values
+ rounded to 14 digits.) This format is slower and does not preserve all
+ the bits of the binary float value, but may be more human-readable.
+ </para>
+ <note>
+ <para>
+ The meaning of this parameter, and its default value, changed
+ in <productname>PostgreSQL</productname> 12;
+ see <xref linkend="datatype-float"/> for further discussion.
+ </para>
+ </note>
</listitem>
</varlistentry>
diff --git a/doc/src/sgml/datatype.sgml b/doc/src/sgml/datatype.sgml
index ed0ee584c9..da0d887623 100644
--- a/doc/src/sgml/datatype.sgml
+++ b/doc/src/sgml/datatype.sgml
@@ -671,13 +671,12 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</indexterm>
<para>
- The data types <type>real</type> and <type>double
- precision</type> are inexact, variable-precision numeric types.
- In practice, these types are usually implementations of
- <acronym>IEEE</acronym> Standard 754 for Binary Floating-Point
- Arithmetic (single and double precision, respectively), to the
- extent that the underlying processor, operating system, and
- compiler support it.
+ The data types <type>real</type> and <type>double precision</type> are
+ inexact, variable-precision numeric types. On all currently supported
+ platforms, these types are implementations of <acronym>IEEE</acronym>
+ Standard 754 for Binary Floating-Point Arithmetic (single and double
+ precision, respectively), to the extent that the underlying processor,
+ operating system, and compiler support it.
</para>
<para>
@@ -715,24 +714,57 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</para>
<para>
- On most platforms, the <type>real</type> type has a range of at least
- 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The
- <type>double precision</type> type typically has a range of around
- 1E-307 to 1E+308 with a precision of at least 15 digits. Values that
- are too large or too small will cause an error. Rounding might
- take place if the precision of an input number is too high.
- Numbers too close to zero that are not representable as distinct
- from zero will cause an underflow error.
+ On all currently supported platforms, the <type>real</type> type has a
+ range of around 1E-37 to 1E+37 with a precision of at least 6 decimal
+ digits. The <type>double precision</type> type has a range of around
+ 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are
+ too large or too small will cause an error. Rounding might take place if
+ the precision of an input number is too high. Numbers too close to zero
+ that are not representable as distinct from zero will cause an underflow
+ error.
+ </para>
+
+ <para>
+ By default, floating point values are output in text form in their
+ shortest precise decimal representation; the decimal value produced is
+ closer to the true stored binary value than to any other value
+ representable in the same binary precision. (However, the output value is
+ currently never <emphasis>exactly</emphasis> midway between two
+ representable values, in order to avoid a widespread bug where input
+ routines do not properly respect the round-to-even rule.) This value will
+ use at most 17 significant decimal digits for <type>float8</type>
+ values, and at most 9 digits for <type>float4</type> values.
</para>
<note>
<para>
- The <xref linkend="guc-extra-float-digits"/> setting controls the
- number of extra significant digits included when a floating point
- value is converted to text for output. With the default value of
- <literal>0</literal>, the output is the same on every platform
- supported by PostgreSQL. Increasing it will produce output that
- more accurately represents the stored value, but may be unportable.
+ This shortest-precise output format is much faster to generate than the
+ historical rounded format.
+ </para>
+ </note>
+
+ <para>
+ For compatibility with output generated by older versions
+ of <productname>PostgreSQL</productname>, and to allow the output
+ precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
+ parameter can be used to select rounded decimal output instead. Setting a
+ value of 0 restores the previous default of rounding the value to 6
+ (for <type>float4</type>) or 15 (for <type>float8</type>)
+ significant decimal digits. Setting a negative value reduces the number
+ of digits further; for example -2 would round output to 4 or 13 digits
+ respectively.
+ </para>
+
+ <para>
+ Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
+ selects the shortest-precise format.
+ </para>
+
+ <note>
+ <para>
+ Applications that wanted precise values have historically had to set
+ <xref linkend="guc-extra-float-digits"/> to 3 obtain them. For maximum
+ compatibility between versions, they should continue to do so.
</para>
</note>
@@ -751,9 +783,7 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</literallayout>
These represent the IEEE 754 special values
<quote>infinity</quote>, <quote>negative infinity</quote>, and
- <quote>not-a-number</quote>, respectively. (On a machine whose
- floating-point arithmetic does not follow IEEE 754, these values
- will probably not work as expected.) When writing these values
+ <quote>not-a-number</quote>, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example <literal>UPDATE table SET x = '-Infinity'</literal>. On input,
these strings are recognized in a case-insensitive manner.
@@ -786,17 +816,6 @@ FROM generate_series(-3.5, 3.5, 1) as x;
<type>double precision</type>.
</para>
- <note>
- <para>
- The assumption that <type>real</type> and
- <type>double precision</type> have exactly 24 and 53 bits in the
- mantissa respectively is correct for IEEE-standard floating point
- implementations. On non-IEEE platforms it might be off a little, but
- for simplicity the same ranges of <replaceable>p</replaceable> are used
- on all platforms.
- </para>
- </note>
-
</sect2>
<sect2 id="datatype-serial">
diff --git a/src/Makefile.global.in b/src/Makefile.global.in
index 6852853041..eda3ac3aa3 100644
--- a/src/Makefile.global.in
+++ b/src/Makefile.global.in
@@ -261,6 +261,7 @@ CFLAGS = @CFLAGS@
CFLAGS_VECTOR = @CFLAGS_VECTOR@
CFLAGS_SSE42 = @CFLAGS_SSE42@
CFLAGS_ARMV8_CRC32C = @CFLAGS_ARMV8_CRC32C@
+PERMIT_DECLARATION_AFTER_STATEMENT = @PERMIT_DECLARATION_AFTER_STATEMENT@
CXXFLAGS = @CXXFLAGS@
LLVM_CPPFLAGS = @LLVM_CPPFLAGS@
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..37c202d21c 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@@ -30,8 +31,15 @@
#include "utils/timestamp.h"
-/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+/*
+ * Configurable GUC parameter
+ *
+ * If >0, use shortest-decimal format for output; this is both the default and
+ * allows for compatibility with clients that explicitly set a value here to
+ * get round-trip-accurate results. If 0 or less, then use the old, slow,
+ * decimal rounding method.
+ */
+int extra_float_digits = 1;
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -104,13 +112,39 @@ is_infinite(double val)
/*
* float4in - converts "num" to float4
+ *
+ * Note that this code now uses strtof(), where it used to use strtod().
+ *
+ * The motivation for using strtof() is to avoid a double-rounding problem:
+ * for certain decimal inputs, if you round the input correctly to a double,
+ * and then round the double to a float, the result is incorrect in that it
+ * does not match the result of rounding the decimal value to float directly.
+ *
+ * One of the best examples is 7.038531e-26:
+ *
+ * 0xAE43FDp-107 = 7.03853069185120912085...e-26
+ * midpoint 7.03853100000000022281...e-26
+ * 0xAE43FEp-107 = 7.03853130814879132477...e-26
+ *
+ * making 0xAE43FDp-107 the correct float result, but if you do the conversion
+ * via a double, you get
+ *
+ * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
+ * midpoint 7.03853099999999964884...e-26
+ * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
+ * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
+ *
+ * so the value rounds to the double exactly on the midpoint between the two
+ * nearest floats, and then rounding again to a float gives the incorrect
+ * result of 0xAE43FEp-107.
+ *
*/
Datum
float4in(PG_FUNCTION_ARGS)
{
char *num = PG_GETARG_CSTRING(0);
char *orig_num;
- double val;
+ float val;
char *endptr;
/*
@@ -135,7 +169,7 @@ float4in(PG_FUNCTION_ARGS)
"real", orig_num)));
errno = 0;
- val = strtod(num, &endptr);
+ val = strtof(num, &endptr);
/* did we not see anything that looks like a double? */
if (endptr == num || errno != 0)
@@ -143,14 +177,14 @@ float4in(PG_FUNCTION_ARGS)
int save_errno = errno;
/*
- * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
+ * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
* but not all platforms support all of these (and some accept them
* but set ERANGE anyway...) Therefore, we check for these inputs
- * ourselves if strtod() fails.
+ * ourselves if strtof() fails.
*
* Note: C99 also requires hexadecimal input as well as some extended
* forms of NaN, but we consider these forms unportable and don't try
- * to support them. You can use 'em if your strtod() takes 'em.
+ * to support them. You can use 'em if your strtof() takes 'em.
*/
if (pg_strncasecmp(num, "NaN", 3) == 0)
{
@@ -195,8 +229,18 @@ float4in(PG_FUNCTION_ARGS)
* precision). We'd prefer not to throw error for that, so try to
* detect whether it's a "real" out-of-range condition by checking
* to see if the result is zero or huge.
+ *
+ * Use isinf() rather than HUGE_VALF on VS2013 because it generates
+ * a spurious overflow warning for -HUGE_VALF. Also use isinf() if
+ * HUGE_VALF is missing.
*/
- if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+ if (val == 0.0 ||
+#if !defined(HUGE_VALF) || (defined(_MSC_VER) && (_MSC_VER < 1900))
+ isinf(val)
+#else
+ (val >= HUGE_VALF || val <= -HUGE_VALF)
+#endif
+ )
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("\"%s\" is out of range for type real",
@@ -232,13 +276,7 @@ float4in(PG_FUNCTION_ARGS)
errmsg("invalid input syntax for type %s: \"%s\"",
"real", orig_num)));
- /*
- * if we get here, we have a legal double, still need to check to see if
- * it's a legal float4
- */
- check_float4_val((float4) val, isinf(val), val == 0);
-
- PG_RETURN_FLOAT4((float4) val);
+ PG_RETURN_FLOAT4(val);
}
/*
@@ -252,6 +290,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ float_to_shortest_decimal_buf(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -468,6 +512,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ double_to_shortest_decimal_buf(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 98d75be292..56e7ceff46 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2654,11 +2654,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects precise output mode.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/backend/utils/misc/postgresql.conf.sample b/src/backend/utils/misc/postgresql.conf.sample
index a21865a77f..13d7436b42 100644
--- a/src/backend/utils/misc/postgresql.conf.sample
+++ b/src/backend/utils/misc/postgresql.conf.sample
@@ -649,7 +649,8 @@
# India
# You can create your own file in
# share/timezonesets/.
-#extra_float_digits = 0 # min -15, max 3
+#extra_float_digits = 1 # min -15, max 3; any value >0 actually
+ # selects precise output mode
#client_encoding = sql_ascii # actually, defaults to database
# encoding
diff --git a/src/common/Makefile b/src/common/Makefile
index d0c2b970eb..d84c7b6e6a 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
- pgfnames.o psprintf.o relpath.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
+ pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
+# The code imported from Ryu gets a pass on declaration-after-statement,
+# in order to keep it more closely aligned with its upstream.
+RYU_FILES = d2s.o f2s.o
+RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
+
+$(RYU_OBJS): CFLAGS += $(PERMIT_DECLARATION_AFTER_STATEMENT)
+
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..e79457d962
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,1076 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_UINT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_UINT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere depending on the output length
+ * and exponent, which might mean adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* -nexp is number of 0s to add after '.' */
+ Assert(nexp >= -3);
+ /* 0.000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+ else
+ {
+ /*
+ * We can save some code later by pre-filling with zeros. We know
+ * that there can be no more than 16 output digits in this form,
+ * otherwise we would not choose fixed-point output.
+ */
+ Assert(exp < 16 && exp + olength <= 16);
+ memset(result, '0', 16);
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ if (index == 1)
+ {
+ /*
+ * nexp is 1..15 here, representing the number of digits before the
+ * point. A value of 16 is not possible because we switch to
+ * scientific notation when the display exponent reaches 15.
+ */
+ Assert(nexp < 16);
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp & 8)
+ {
+ memmove(result + index - 1, result + index, 8);
+ index += 8;
+ }
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ /* we supplied the trailing zeros earlier, now just set the length. */
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ /*
+ * The thresholds for fixed-point output are chosen to match printf
+ * defaults. Beware that both the code of to_chars_df and the value
+ * of DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
+ */
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint64 q = div10(output);
+ const uint32 r = (uint32) (output - 10 * q);
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+static inline bool
+d2d_small_int(const uint64 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_64 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of d2d, which is undesirable.
+ */
+
+ if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
+ * 1 <= f = m2 / 2^-e2 < 2^53.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
+ */
+ const uint64 mask = (UINT64CONST(1) << -e2) - 1;
+ const uint64 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^53).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^53 < 10^16, there is no need to adjust
+ * decimalLength().
+ */
+ const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+/*
+ * Store the shortest decimal representation of the given double as an
+ * UNTERMINATED string in the caller's supplied buffer (which must be at least
+ * DOUBLE_SHORTEST_DECIMAL_LEN-1 bytes long).
+ *
+ * Returns the number of bytes stored.
+ */
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_64 v;
+ const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = d2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+/*
+ * Store the shortest decimal representation of the given double as a
+ * null-terminated string in the caller's supplied buffer (which must be at
+ * least DOUBLE_SHORTEST_DECIMAL_LEN bytes long).
+ *
+ * Returns the string length.
+ */
+int
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
+ result[index] = '\0';
+ return index;
+}
+
+/*
+ * Return the shortest decimal representation as a null-terminated palloc'd
+ * string (outside the backend, uses malloc() instead).
+ *
+ * Caller is responsible for freeing the result.
+ */
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..d6520b437b
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,358 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated (by the upstream) using PrintDoubleLookupTable
+ * from the upstream sources at github.com/ulfjack/ryu, and then modified (by
+ * us) by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..248889e649
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..4f36e1a596
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,804 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/*
+ * This table is generated (by the upstream) by PrintFloatLookupTable,
+ * and modified (by us) to add UINT64CONST.
+ */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint32 q = value / 5;
+ const uint32 r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ const int32 s = shift - 32;
+
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+
+#else /* RYU_32_BIT_PLATFORM */
+
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8 lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+
+ e10 = q;
+
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going to
+ * loop below. We could use q = X - 1 above, except that would
+ * require 33 bits for the result, and we've found that 32-bit
+ * arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
+ * seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+
+ e10 = q + e2;
+
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~96.0%). Percentages below are
+ * relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
+ * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere depending on the output length
+ * and exponent, which might mean adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* -nexp is number of 0s to add after '.' */
+ Assert(nexp >= -3);
+ /* 0.000ddddd */
+ index = 2 - nexp;
+ /* copy 8 bytes rather than 5 to let compiler optimize */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+ else
+ {
+ /*
+ * We can save some code later by pre-filling with zeros. We know
+ * that there can be no more than 6 output digits in this form,
+ * otherwise we would not choose fixed-point output. memset 8
+ * rather than 6 bytes to let the compiler optimize it.
+ */
+ Assert(exp < 6 && exp + olength <= 6);
+ memset(result, '0', 8);
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ /*
+ * nexp is 1..6 here, representing the number of digits before the
+ * point. A value of 7+ is not possible because we switch to
+ * scientific notation when the display exponent reaches 6.
+ */
+ Assert(nexp < 7);
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ /* we supplied the trailing zeros earlier, now just set the length. */
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ result[index++] = '-';
+
+ /*
+ * The thresholds for fixed-point output are chosen to match printf
+ * defaults. Beware that both the code of to_chars_f and the value
+ * of FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
+ */
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint32 q = output / 10;
+ const uint32 r = output - 10 * q;
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ */
+ uint32 i = 0;
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+
+ return index;
+}
+
+static inline bool
+f2d_small_int(const uint32 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_32 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of f2d, which is undesirable.
+ */
+
+ if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
+ * 1 <= f = m2 / 2^-e2 < 2^24.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
+ */
+ const uint32 mask = (1U << -e2) - 1;
+ const uint32 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^24).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^24 < 10^9, there is no need to adjust
+ * decimalLength().
+ */
+ const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+/*
+ * Store the shortest decimal representation of the given float as an
+ * UNTERMINATED string in the caller's supplied buffer (which must be at least
+ * FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long).
+ *
+ * Returns the number of bytes stored.
+ */
+int
+float_to_shortest_decimal_bufn(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_32 v;
+ const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = f2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+/*
+ * Store the shortest decimal representation of the given float as a
+ * null-terminated string in the caller's supplied buffer (which must be at
+ * least FLOAT_SHORTEST_DECIMAL_LEN bytes long).
+ *
+ * Returns the string length.
+ */
+int
+float_to_shortest_decimal_buf(float f, char *result)
+{
+ const int index = float_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ Assert(index < FLOAT_SHORTEST_DECIMAL_LEN);
+ result[index] = '\0';
+ return index;
+}
+
+/*
+ * Return the shortest decimal representation as a null-terminated palloc'd
+ * string (outside the backend, uses malloc() instead).
+ *
+ * Caller is responsible for freeing the result.
+ */
+char *
+float_to_shortest_decimal(float f)
+{
+ char *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN);
+
+ float_to_shortest_decimal_buf(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..14639aff9c
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+/*
+ * Upstream Ryu's output is always the shortest possible. But we adjust that
+ * slightly to improve portability: we avoid outputting the exact midpoint
+ * value between two representable floats, since that relies on the reader
+ * getting the round-to-even rule correct, which seems to be the common
+ * failure mode.
+ *
+ * Defining this to 1 would restore the upstream behavior.
+ */
+#define STRICTLY_SHORTEST 0
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/shortest_dec.h b/src/include/common/shortest_dec.h
new file mode 100644
index 0000000000..4c3dcd37cf
--- /dev/null
+++ b/src/include/common/shortest_dec.h
@@ -0,0 +1,63 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/shortest_dec.h
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef SHORTEST_DEC_H
+#define SHORTEST_DEC_H
+
+/*----
+ * The length of 25 comes from:
+ *
+ * Case 1: -9.9999999999999999e-299 = 24 bytes, plus 1 for null
+ *
+ * Case 2: -0.00099999999999999999 = 23 bytes, plus 1 for null
+ */
+#define DOUBLE_SHORTEST_DECIMAL_LEN 25
+
+int double_to_shortest_decimal_bufn(double f, char *result);
+int double_to_shortest_decimal_buf(double f, char *result);
+char *double_to_shortest_decimal(double f);
+
+/*
+ * The length of 16 comes from:
+ *
+ * Case 1: -9.99999999e+29 = 15 bytes, plus 1 for null
+ *
+ * Case 2: -0.000999999999 = 15 bytes, plus 1 for null
+ */
+#define FLOAT_SHORTEST_DECIMAL_LEN 16
+
+int float_to_shortest_decimal_bufn(float f, char *result);
+int float_to_shortest_decimal_buf(float f, char *result);
+char *float_to_shortest_decimal(float f);
+
+#endif /* SHORTEST_DEC_H */
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 82547f321f..b38b0ae189 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -555,6 +555,9 @@
/* Define to 1 if you have the `strsignal' function. */
#undef HAVE_STRSIGNAL
+/* Define to 1 if you have the `strtof' function. */
+#undef HAVE_STRTOF
+
/* Define to 1 if you have the `strtoll' function. */
#undef HAVE_STRTOLL
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index a3c44f0fd8..160fa1279e 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -139,6 +139,9 @@
don't. */
#define HAVE_DECL_STRNLEN 1
+/* Define to 1 if you have the `strtof' function. */
+#define HAVE_STRTOF 1
+
/* Define to 1 if you have the declaration of `strtoll', and to 0 if you
don't. */
#define HAVE_DECL_STRTOLL 1
diff --git a/src/include/port.h b/src/include/port.h
index 485e771f99..436bc83fe3 100644
--- a/src/include/port.h
+++ b/src/include/port.h
@@ -381,6 +381,10 @@ extern int isinf(double x);
#endif /* __clang__ && !__cplusplus */
#endif /* !HAVE_ISINF */
+#ifndef HAVE_STRTOF
+extern float strtof(const char *nptr, char **endptr);
+#endif
+
#ifndef HAVE_MKDTEMP
extern char *mkdtemp(char *path);
#endif
diff --git a/src/include/port/win32_port.h b/src/include/port/win32_port.h
index fdd8b2d3b1..9bab75d5da 100644
--- a/src/include/port/win32_port.h
+++ b/src/include/port/win32_port.h
@@ -510,6 +510,18 @@ typedef unsigned short mode_t;
#define isnan(x) _isnan(x)
#endif
+#if defined(_MSC_VER) && (_MSC_VER < 1900)
+/*
+ * VS2013 has a strtof() that seems to give correct answers for valid input,
+ * even on the rounding edge cases, but which doesn't handle out-of-range
+ * input correctly. Work around that.
+ */
+#define HAVE_BUGGY_WINDOWS_STRTOF 1
+extern float pg_strtof(const char *nptr, char **endptr);
+#define strtof(a,b) (pg_strtof((a),(b)))
+
+#endif
+
/* Pulled from Makefile.port in MinGW */
#define DLSUFFIX ".dll"
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..34f85638c9
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,121 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+#ifndef HAVE_STRTOF
+/*
+ * strtof() is part of C99; this version is only for the benefit of obsolete
+ * platforms. As such, it is known to return incorrect values for edge cases,
+ * which have to be allowed for in variant files for regression test results
+ * for any such platform.
+ */
+
+float
+strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ double dresult;
+ float fresult;
+
+ errno = 0;
+ dresult = strtod(nptr, endptr);
+ fresult = (float) dresult;
+
+ if (errno == 0)
+ {
+ /*
+ * Value might be in-range for double but not float.
+ */
+ if (dresult != 0 && fresult == 0)
+ caller_errno = ERANGE; /* underflow */
+ if (!isinf(dresult) && isinf(fresult))
+ caller_errno = ERANGE; /* overflow */
+ }
+ else
+ caller_errno = errno;
+
+ errno = caller_errno;
+ return fresult;
+}
+
+#elif HAVE_BUGGY_WINDOWS_STRTOF
+/*
+ * On Windows, there's a slightly different problem: VS2013 has a strtof()
+ * that returns the correct results for valid input, but may fail to report an
+ * error for underflow or overflow, returning 0 instead. Work around that by
+ * trying strtod() when strtof() returns 0.0 or [+-]Inf, and calling it an
+ * error if the result differs. Also, strtof() doesn't handle subnormal input
+ * well, so prefer to round the strtod() result in such cases. (Normally we'd
+ * just say "too bad" if strtof() doesn't support subnormals, but since we're
+ * already in here fixing stuff, we might as well do the best fix we can.)
+ */
+float
+pg_strtof(const char *nptr, char **endptr)
+{
+ int caller_errno = errno;
+ float fresult;
+
+ errno = 0;
+ fresult = (strtof)(nptr, endptr);
+ if (errno)
+ {
+ /* On error, just return the error to the caller. */
+ return fresult;
+ }
+ else if ((*endptr == nptr) ||
+ ((fresult >= FLT_MIN || fresult <= -FLT_MIN) && !isinf(fresult)))
+ {
+ /*
+ * If we got nothing parseable, or if we got a non-0 non-subnormal
+ * finite value (or NaN) without error, then return that to the caller
+ * without error.
+ */
+ errno = caller_errno;
+ return fresult;
+ }
+ else
+ {
+ /*
+ * Try again.
+ */
+ double dresult = strtod(nptr, NULL);
+ if (errno)
+ {
+ /* On error, just return the error */
+ return fresult;
+ }
+ else if ((dresult == 0.0 && fresult == 0.0) ||
+ (isinf(dresult) && isinf(fresult) && (fresult == dresult)))
+ {
+ /* both values are 0 or infinities of the same sign */
+ errno = caller_errno;
+ return fresult;
+ }
+ else if ((dresult > 0 && dresult <= FLT_MIN && (float)dresult != 0.0) ||
+ (dresult < 0 && dresult >= -FLT_MIN && (float)dresult != 0.0))
+ {
+ return (float) dresult;
+ }
+ else
+ {
+ errno = ERANGE;
+ return fresult;
+ }
+ }
+}
+
+#endif
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 918db6cb67..129c1e5075 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -1,6 +1,8 @@
--
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------
diff --git a/src/test/regress/expected/circle.out b/src/test/regress/expected/circle.out
index 2ed74cc6aa..756c7e37ef 100644
--- a/src/test/regress/expected/circle.out
+++ b/src/test/regress/expected/circle.out
@@ -1,6 +1,8 @@
--
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
diff --git a/src/test/regress/expected/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..54de939a6e
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,940 @@
+--
+-- FLOAT4
+--
+CREATE TABLE FLOAT4_TBL (f1 float4);
+INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
+-- test for over and under flow
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ERROR: "10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ERROR: "-10e70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ERROR: "10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ERROR: "-10e-70" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
+-- bad input
+INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ERROR: invalid input syntax for type real: ""
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ERROR: invalid input syntax for type real: " "
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ERROR: invalid input syntax for type real: "xyz"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ERROR: invalid input syntax for type real: "5.0.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ERROR: invalid input syntax for type real: "5 . 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ERROR: invalid input syntax for type real: "5. 0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ERROR: invalid input syntax for type real: " - 3.0"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ERROR: invalid input syntax for type real: "123 5"
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
+ ^
+-- special inputs
+SELECT 'NaN'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT ' NAN '::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT 'infinity'::float4;
+ float4
+----------
+ Infinity
+(1 row)
+
+SELECT ' -INFINiTY '::float4;
+ float4
+-----------
+ -Infinity
+(1 row)
+
+-- bad special inputs
+SELECT 'N A N'::float4;
+ERROR: invalid input syntax for type real: "N A N"
+LINE 1: SELECT 'N A N'::float4;
+ ^
+SELECT 'NaN x'::float4;
+ERROR: invalid input syntax for type real: "NaN x"
+LINE 1: SELECT 'NaN x'::float4;
+ ^
+SELECT ' INFINITY x'::float4;
+ERROR: invalid input syntax for type real: " INFINITY x"
+LINE 1: SELECT ' INFINITY x'::float4;
+ ^
+SELECT 'Infinity'::float4 + 100.0;
+ ?column?
+----------
+ Infinity
+(1 row)
+
+SELECT 'Infinity'::float4 / 'Infinity'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::float4 / 'nan'::float4;
+ ?column?
+----------
+ NaN
+(1 row)
+
+SELECT 'nan'::numeric::float4;
+ float4
+--------
+ NaN
+(1 row)
+
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
+ one | f1
+-----+--------
+ | 1004.3
+(1 row)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
+(3 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
+(4 rows)
+
+SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
+(3 rows)
+
+SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
+ WHERE f.f1 > '0.0';
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
+(3 rows)
+
+-- test divide by zero
+SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
+ERROR: division by zero
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
+(5 rows)
+
+-- test the unary float4abs operator
+SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
+(5 rows)
+
+UPDATE FLOAT4_TBL
+ SET f1 = FLOAT4_TBL.f1 * '-1'
+ WHERE FLOAT4_TBL.f1 > '0.0';
+SELECT '' AS five, * FROM FLOAT4_TBL;
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
+(5 rows)
+
+-- test edge-case coercions to integer
+SELECT '32767.4'::float4::int2;
+ int2
+-------
+ 32767
+(1 row)
+
+SELECT '32767.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '-32768.4'::float4::int2;
+ int2
+--------
+ -32768
+(1 row)
+
+SELECT '-32768.6'::float4::int2;
+ERROR: smallint out of range
+SELECT '2147483520'::float4::int4;
+ int4
+------------
+ 2147483520
+(1 row)
+
+SELECT '2147483647'::float4::int4;
+ERROR: integer out of range
+SELECT '-2147483648.5'::float4::int4;
+ int4
+-------------
+ -2147483648
+(1 row)
+
+SELECT '-2147483900'::float4::int4;
+ERROR: integer out of range
+SELECT '9223369837831520256'::float4::int8;
+ int8
+---------------------
+ 9223369837831520256
+(1 row)
+
+SELECT '9223372036854775807'::float4::int8;
+ERROR: bigint out of range
+SELECT '-9223372036854775808.5'::float4::int8;
+ int8
+----------------------
+ -9223372036854775808
+(1 row)
+
+SELECT '-9223380000000000000'::float4::int8;
+ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fe
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d0
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..dff1921944 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,21 +9,37 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
-ERROR: value out of range: overflow
+ERROR: "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
-ERROR: value out of range: overflow
+ERROR: "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
-ERROR: value out of range: underflow
+ERROR: "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
-ERROR: value out of range: underflow
+ERROR: "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ERROR: "10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ERROR: "-10e400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ERROR: "10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+ ^
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ERROR: "-10e-400" is out of range for type real
+LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+ ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type real: ""
@@ -126,22 +142,22 @@ SELECT 'nan'::numeric::float4;
(1 row)
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
- four | f1
-------+-------------
- | 0
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@@ -151,110 +167,110 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
(1 row)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
- three | f1
--------+-------------
- | 0
- | -34.84
- | 1.23457e-20
+ three | f1
+-------+---------------
+ | 0
+ | -34.84
+ | 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
- four | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e-20
+ four | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -10043
- | 1.23457e+20 | -1.23457e+21
- | 1.23457e-20 | -1.23457e-19
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -10043
+ | 1.2345679e+20 | -1.2345678e+21
+ | 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 994.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | -10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 994.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+--------------
- | 1004.3 | -100.43
- | 1.23457e+20 | -1.23457e+19
- | 1.23457e-20 | -1.23457e-21
+ three | f1 | x
+-------+---------------+----------------
+ | 1004.3 | -100.43
+ | 1.2345679e+20 | -1.2345679e+19
+ | 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
- three | f1 | x
--------+-------------+-------------
- | 1004.3 | 1014.3
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 10
+ three | f1 | x
+-------+---------------+---------------
+ | 1004.3 | 1014.3
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+-------------
- | 0
- | 1004.3
- | -34.84
- | 1.23457e+20
- | 1.23457e-20
+ five | f1
+------+---------------
+ | 0
+ | 1004.3
+ | -34.84
+ | 1.2345679e+20
+ | 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
- five | f1 | abs_f1
-------+-------------+-------------
- | 0 | 0
- | 1004.3 | 1004.3
- | -34.84 | 34.84
- | 1.23457e+20 | 1.23457e+20
- | 1.23457e-20 | 1.23457e-20
+ five | f1 | abs_f1
+------+---------------+---------------
+ | 0 | 0
+ | 1004.3 | 1004.3
+ | -34.84 | 34.84
+ | 1.2345679e+20 | 1.2345679e+20
+ | 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
- five | f1
-------+--------------
- | 0
- | -34.84
- | -1004.3
- | -1.23457e+20
- | -1.23457e-20
+ five | f1
+------+----------------
+ | 0
+ | -34.84
+ | -1004.3
+ | -1.2345679e+20
+ | -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@@ -306,3 +322,619 @@ SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
ERROR: bigint out of range
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+SELECT float4send('5e-20'::float4);
+ float4send
+------------
+ \x1f6c1e4a
+(1 row)
+
+SELECT float4send('67e14'::float4);
+ float4send
+------------
+ \x59be6cea
+(1 row)
+
+SELECT float4send('985e15'::float4);
+ float4send
+------------
+ \x5d5ab6c4
+(1 row)
+
+SELECT float4send('55895e-16'::float4);
+ float4send
+------------
+ \x2cc4a9bd
+(1 row)
+
+SELECT float4send('7038531e-32'::float4);
+ float4send
+------------
+ \x15ae43fd
+(1 row)
+
+SELECT float4send('702990899e-20'::float4);
+ float4send
+------------
+ \x2cf757ca
+(1 row)
+
+SELECT float4send('3e-23'::float4);
+ float4send
+------------
+ \x1a111234
+(1 row)
+
+SELECT float4send('57e18'::float4);
+ float4send
+------------
+ \x6045c22c
+(1 row)
+
+SELECT float4send('789e-35'::float4);
+ float4send
+------------
+ \x0a23de70
+(1 row)
+
+SELECT float4send('2539e-18'::float4);
+ float4send
+------------
+ \x2736f449
+(1 row)
+
+SELECT float4send('76173e28'::float4);
+ float4send
+------------
+ \x7616398a
+(1 row)
+
+SELECT float4send('887745e-11'::float4);
+ float4send
+------------
+ \x3714f05c
+(1 row)
+
+SELECT float4send('5382571e-37'::float4);
+ float4send
+------------
+ \x0d2eaca7
+(1 row)
+
+SELECT float4send('82381273e-35'::float4);
+ float4send
+------------
+ \x128289d1
+(1 row)
+
+SELECT float4send('750486563e-38'::float4);
+ float4send
+------------
+ \x0f18377e
+(1 row)
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+SELECT float4send('1.17549435e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+SELECT float4send('1.1754944e-38'::float4);
+ float4send
+------------
+ \x00800000
+(1 row)
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+NOTICE: return type xfloat4 is only a shell
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+NOTICE: argument type xfloat4 is only a shell
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+------------+---------------
+ \x00000001 | 1e-45
+ \x00000002 | 3e-45
+ \x00000003 | 4e-45
+ \x00000010 | 2.2e-44
+ \x00000011 | 2.4e-44
+ \x00000100 | 3.59e-43
+ \x00000101 | 3.6e-43
+ \x00004000 | 2.2959e-41
+ \x00004001 | 2.296e-41
+ \x00080000 | 7.34684e-40
+ \x00080001 | 7.34685e-40
+ \x0053c4f4 | 7.693e-39
+ \x006c85c4 | 9.96622e-39
+ \x0041ca76 | 6.041937e-39
+ \x004b7678 | 6.930161e-39
+ \x00000007 | 1e-44
+ \x00424fe2 | 6.0898e-39
+ \x007ffff0 | 1.1754921e-38
+ \x007ffff1 | 1.1754922e-38
+ \x007ffffe | 1.1754941e-38
+ \x007fffff | 1.1754942e-38
+(21 rows)
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+------------+----------------+----------------+------------+---------
+ \x00000000 | 0 | 0 | \x00000000 | t
+ \x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
+ \x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
+ \x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
+ \x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
+ \x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
+ \x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
+ \x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
+ \x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
+ \x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
+ \x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
+ \x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
+ \x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
+ \x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
+ \x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
+ \x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
+ \x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
+ \x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
+ \x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
+ \x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
+ \x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
+ \x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
+ \x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
+ \x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
+ \x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
+ \x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
+ \x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
+ \x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
+ \x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
+ \x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
+ \x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
+ \x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
+ \x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
+ \x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
+ \x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
+ \x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
+ \x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
+ \x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
+ \x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
+ \x350637bd | 5e-07 | 5e-07 | \x350637bd | t
+ \x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
+ \x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
+ \x35719787 | 9e-07 | 9e-07 | \x35719787 | t
+ \x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
+ \x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
+ \x358637bd | 1e-06 | 1e-06 | \x358637bd | t
+ \x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
+ \x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
+ \x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
+ \x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
+ \x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
+ \x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
+ \x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
+ \x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
+ \x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
+ \x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
+ \x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
+ \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
+ \x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
+ \x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
+ \x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
+ \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
+ \x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
+ \x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
+ \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
+ \x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
+ \x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
+ \x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
+ \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
+ \x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
+ \x3a83126f | 0.001 | 0.001 | \x3a83126f | t
+ \x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
+ \x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
+ \x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
+ \x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
+ \x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
+ \x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
+ \x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
+ \x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
+ \x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
+ \x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
+ \x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
+ \x3f000000 | 0.5 | 0.5 | \x3f000000 | t
+ \x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
+ \x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
+ \x3f333333 | 0.7 | 0.7 | \x3f333333 | t
+ \x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
+ \x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
+ \x3f666666 | 0.9 | 0.9 | \x3f666666 | t
+ \x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
+ \x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
+ \x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
+ \x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
+ \x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
+ \x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
+ \x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
+ \x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
+ \x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
+ \x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
+ \x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
+ \x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
+ \x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
+ \x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
+ \x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
+ \x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
+ \x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
+ \x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
+ \x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
+ \x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
+ \x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
+ \x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
+ \x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
+ \x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
+ \x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
+ \x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
+ \x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
+ \x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
+ \x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
+ \x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
+ \x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
+ \x3f800000 | 1 | 1 | \x3f800000 | t
+ \x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
+ \x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
+ \x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
+ \x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
+ \x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
+ \x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
+ \x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
+ \x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
+ \x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
+ \x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
+ \x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
+ \x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
+ \x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
+ \x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
+ \x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
+ \x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
+ \x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
+ \x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
+ \x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
+ \x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
+ \x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
+ \x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
+ \x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
+ \x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
+ \x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
+ \x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
+ \x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
+ \x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
+ \x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
+ \x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
+ \x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
+ \x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
+ \x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
+ \x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
+ \x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
+ \x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
+ \x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
+ \x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
+ \x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
+ \x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
+ \x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
+ \x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
+ \x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
+ \x40a00000 | 5 | 5 | \x40a00000 | t
+ \x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
+ \x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
+ \x40b00000 | 5.5 | 5.5 | \x40b00000 | t
+ \x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
+ \x411fffff | 9.999999 | 9.999999 | \x411fffff | t
+ \x41200000 | 10 | 10 | \x41200000 | t
+ \x41200001 | 10.000001 | 10.000001 | \x41200001 | t
+ \x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
+ \x42c80000 | 100 | 100 | \x42c80000 | t
+ \x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
+ \x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
+ \x447a0000 | 1000 | 1000 | \x447a0000 | t
+ \x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
+ \x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
+ \x461c4000 | 10000 | 10000 | \x461c4000 | t
+ \x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
+ \x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
+ \x47c35000 | 100000 | 100000 | \x47c35000 | t
+ \x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
+ \x497423ff | 999999.94 | 999999.94 | \x497423ff | t
+ \x49742400 | 1e+06 | 1e+06 | \x49742400 | t
+ \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
+ \x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
+ \x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
+ \x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
+ \x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
+ \x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
+ \x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
+ \x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
+ \x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
+ \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
+ \x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
+ \x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
+ \x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
+ \x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
+ \x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
+ \x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
+ \x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
+ \x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
+ \x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
+ \x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
+ \x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
+ \x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
+ \x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
+ \x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
+ \x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
+ \x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
+ \x414587dd | 12.34567 | 12.34567 | \x414587dd | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
+ \x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
+ \x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
+ \x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
+ \x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
+ \x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
+ \x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
+ \x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
+ \x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
+ \x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
+ \x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
+ \x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
+ \x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
+ \x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
+ \x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
+ \x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
+ \x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
+ \x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
+ \x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
+ \x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
+ \x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
+ \x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
+ \x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
+ \x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
+ \x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
+ \x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
+ \x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
+ \x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
+ \x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
+ \x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
+ \x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
+ \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
+ \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
+ \x43480000 | 200 | 200 | \x43480000 | t
+ \x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
+ \x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
+ \x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
+ \x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
+ \x3f99999a | 1.2 | 1.2 | \x3f99999a | t
+ \x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
+ \x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
+ \x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
+ \x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
+ \x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
+ \x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
+ \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
+(262 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8-small-is-zero.out b/src/test/regress/expected/float8-small-is-zero.out
index 1c3bbae6b8..f67c22e9fa 100644
--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -230,9 +237,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -630,4 +639,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
index 75c0bf389b..c3a6f5331f 100644
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+ float8send
+--------------------
+ \x0010000000000000
+(1 row)
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
- | 1004.3 | -100.43
+ | 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@@ -226,9 +233,9 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
- one | square_f1
------+------------
- | 1008618.49
+ one | square_f1
+-----+--------------------
+ | 1008618.4899999999
(1 row)
-- absolute value
@@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@@ -632,4 +641,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+NOTICE: return type xfloat8 is only a shell
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+NOTICE: argument type xfloat8 is only a shell
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt
+--------------------+-------------------------
+ \x0000000000000001 | 5e-324
+ \x0000000000000002 | 1e-323
+ \x0000000000000003 | 1.5e-323
+ \x0000000000001000 | 2.0237e-320
+ \x0000000100000000 | 2.121995791e-314
+ \x0000010000000000 | 5.43230922487e-312
+ \x0000010100000000 | 5.45352918278e-312
+ \x0000400000000000 | 3.4766779039175e-310
+ \x0000400100000000 | 3.4768901034966e-310
+ \x0000800000000000 | 6.953355807835e-310
+ \x0000800000000001 | 6.95335580783505e-310
+ \x00000000000f4240 | 4.940656e-318
+ \x00000000016e3600 | 1.18575755e-316
+ \x0000008cdcdea440 | 2.989102097996e-312
+ \x000ffffffffffff0 | 2.2250738585071935e-308
+ \x000ffffffffffff1 | 2.225073858507194e-308
+ \x000ffffffffffffe | 2.2250738585072004e-308
+ \x000fffffffffffff | 2.225073858507201e-308
+(18 rows)
+
+-- round-trip tests
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+ ibits | flt | r_flt | obits | correct
+--------------------+-------------------------+-------------------------+--------------------+---------
+ \x0000000000000000 | 0 | 0 | \x0000000000000000 | t
+ \x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
+ \x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
+ \x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
+ \x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
+ \x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
+ \x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
+ \x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
+ \x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
+ \x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
+ \x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
+ \x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
+ \x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
+ \x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
+ \x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
+ \x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
+ \x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
+ \x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
+ \x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
+ \x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
+ \x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
+ \x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
+ \x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
+ \x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
+ \x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
+ \x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
+ \x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
+ \x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
+ \x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
+ \x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
+ \x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
+ \x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
+ \x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
+ \x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
+ \x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
+ \x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
+ \x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
+ \x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
+ \x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
+ \x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
+ \x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
+ \x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
+ \x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
+ \x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
+ \x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
+ \x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
+ \x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
+ \x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
+ \x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
+ \x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
+ \x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
+ \x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
+ \x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
+ \x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
+ \x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
+ \x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
+ \x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
+ \x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
+ \x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
+ \x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
+ \x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
+ \x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
+ \x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
+ \x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
+ \x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
+ \x4024000000000000 | 10 | 10 | \x4024000000000000 | t
+ \x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
+ \x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
+ \x4059000000000000 | 100 | 100 | \x4059000000000000 | t
+ \x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
+ \x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
+ \x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
+ \x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
+ \x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
+ \x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
+ \x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
+ \x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
+ \x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
+ \x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
+ \x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
+ \x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
+ \x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
+ \x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
+ \x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
+ \x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
+ \x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
+ \x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
+ \x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
+ \x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
+ \x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
+ \x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
+ \x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
+ \x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
+ \x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
+ \x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
+ \x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
+ \x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
+ \x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
+ \x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
+ \x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
+ \x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
+ \x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
+ \x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
+ \x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
+ \x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
+ \x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
+ \x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
+ \x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
+ \x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
+ \x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
+ \x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
+ \x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
+ \x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
+ \x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
+ \x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
+ \x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
+ \x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
+ \x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
+ \x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
+ \x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
+ \x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
+ \x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
+ \x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
+ \x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
+ \x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
+ \x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
+ \x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
+ \x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
+ \x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
+ \x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
+ \x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
+ \x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
+ \x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
+ \x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
+ \x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
+ \x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
+ \x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
+ \x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
+ \x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
+ \x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
+ \x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
+ \x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
+ \x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
+ \x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
+ \x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
+ \x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
+ \x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
+ \x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
+ \xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
+ \xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
+ \xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
+ \xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
+ \xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
+ \xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
+ \xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
+ \x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
+ \x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
+ \x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
+ \x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
+ \x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
+ \x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
+ \x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
+ \x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
+ \x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
+ \x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
+ \x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
+ \x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
+ \x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
+ \x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
+ \xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
+ \x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
+ \x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
+ \x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
+ \x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
+ \x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
+ \x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
+ \x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
+ \x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
+ \x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
+ \x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
+ \x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
+ \x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
+ \x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
+ \x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
+ \x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
+ \x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
+ \x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
+ \x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
+ \x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
+ \x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
+ \x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
+ \x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
+ \x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
+ \x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
+ \x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
+ \x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
+ \x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
+ \x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
+ \x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
+ \x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
+ \x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
+ \x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
+ \x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
+ \x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
+ \x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
+(209 rows)
+
+-- clean up, lest opr_sanity complain
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+NOTICE: drop cascades to 6 other objects
+\set VERBOSITY default
+--
diff --git a/src/test/regress/expected/int8.out b/src/test/regress/expected/int8.out
index 35e3b3ff81..8447a28c3d 100644
--- a/src/test/regress/expected/int8.out
+++ b/src/test/regress/expected/int8.out
@@ -329,23 +329,23 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
(5 rows)
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
- five | q1 | float8
-------+------------------+----------------------
- | 123 | 123
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
- | 4567890123456789 | 4.56789012345679e+15
+ five | q1 | float8
+------+------------------+-----------------------
+ | 123 | 123
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
+ | 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
- five | q2 | float8
-------+-------------------+-----------------------
- | 456 | 456
- | 4567890123456789 | 4.56789012345679e+15
- | 123 | 123
- | 4567890123456789 | 4.56789012345679e+15
- | -4567890123456789 | -4.56789012345679e+15
+ five | q2 | float8
+------+-------------------+------------------------
+ | 456 | 456
+ | 4567890123456789 | 4.567890123456789e+15
+ | 123 | 123
+ | 4567890123456789 | 4.567890123456789e+15
+ | -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@@ -726,13 +726,13 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
(1 row)
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
- q1 | q2
--------------+-----------------------
- 123 | 456
- 123 | 4.56789012345679e+15
- 4.56789e+15 | 123
- 4.56789e+15 | 4.56789012345679e+15
- 4.56789e+15 | -4.56789012345679e+15
+ q1 | q2
+-------------+------------------------
+ 123 | 456
+ 123 | 4.567890123456789e+15
+ 4.56789e+15 | 123
+ 4.56789e+15 | 4.567890123456789e+15
+ 4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);
diff --git a/src/test/regress/expected/jsonb.out b/src/test/regress/expected/jsonb.out
index 0ac47fcaee..8dcdaf5602 100644
--- a/src/test/regress/expected/jsonb.out
+++ b/src/test/regress/expected/jsonb.out
@@ -4376,9 +4376,9 @@ select '12345.05'::jsonb::numeric;
(1 row)
select '12345.05'::jsonb::float4;
- float4
---------
- 12345
+ float4
+----------
+ 12345.05
(1 row)
select '12345.05'::jsonb::float8;
diff --git a/src/test/regress/expected/line.out b/src/test/regress/expected/line.out
index bf780daa2c..fe106589c6 100644
--- a/src/test/regress/expected/line.out
+++ b/src/test/regress/expected/line.out
@@ -64,14 +64,14 @@ LINE 1: INSERT INTO LINE_TBL VALUES ('[(1,2),(1,2)]');
INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
- s
----------------------------------------------
+ s
+------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
- {-0.000184615384615385,-1,15.3846153846154}
+ {-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}
diff --git a/src/test/regress/expected/point.out b/src/test/regress/expected/point.out
index c18e865370..15e3b83b37 100644
--- a/src/test/regress/expected/point.out
+++ b/src/test/regress/expected/point.out
@@ -1,6 +1,8 @@
--
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');
diff --git a/src/test/regress/expected/rules.out b/src/test/regress/expected/rules.out
index 2c8e21baa7..b31594a7b5 100644
--- a/src/test/regress/expected/rules.out
+++ b/src/test/regress/expected/rules.out
@@ -910,24 +910,24 @@ insert into rtest_comp values ('p4', 'cm', 15.0);
insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p3 | 5
- p4 | 15
- p5 | 17.78
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p3 | 5
+ p4 | 15
+ p5 | 17.78
+ p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
- part | size_in_cm
-------+------------
- p1 | 500
- p2 | 300
- p5 | 17.78
- p4 | 15
- p6 | 11.176
+ part | size_in_cm
+------+--------------------
+ p1 | 500
+ p2 | 300
+ p5 | 17.78
+ p4 | 15
+ p6 | 11.176000000000002
(5 rows)
--
diff --git a/src/test/regress/expected/tsearch.out b/src/test/regress/expected/tsearch.out
index b088ff0d4f..6f61acc1ed 100644
--- a/src/test/regress/expected/tsearch.out
+++ b/src/test/regress/expected/tsearch.out
@@ -970,9 +970,9 @@ Water, water, every where,
Nor any drop to drink.
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
- ts_rank_cd
-------------
- 0.00833333
+ ts_rank_cd
+-------------
+ 0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '
diff --git a/src/test/regress/expected/tstypes.out b/src/test/regress/expected/tstypes.out
index 6272e70e09..87a36ca329 100644
--- a/src/test/regress/expected/tstypes.out
+++ b/src/test/regress/expected/tstypes.out
@@ -787,57 +787,57 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0303964
+ ts_rank
+-------------
+ 0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
- ts_rank
------------
- 0.0911891
+ ts_rank
+-------------
+ 0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
- ts_rank
-----------
- 0.151982
+ ts_rank
+------------
+ 0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
- ts_rank
------------
- 0.0607927
+ ts_rank
+------------
+ 0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.140153
+ ts_rank
+------------
+ 0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
- ts_rank
-----------
- 0.198206
+ ts_rank
+------------
+ 0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
- ts_rank
------------
- 0.0991032
+ ts_rank
+------------
+ 0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.181818
+ 0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
- 0.133333
+ 0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
- 0.0909091
+ 0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');
diff --git a/src/test/regress/expected/updatable_views.out b/src/test/regress/expected/updatable_views.out
index 420c5a54f2..8b13ef3a09 100644
--- a/src/test/regress/expected/updatable_views.out
+++ b/src/test/regress/expected/updatable_views.out
@@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');
diff --git a/src/test/regress/expected/window.out b/src/test/regress/expected/window.out
index 662d348653..edc93d5729 100644
--- a/src/test/regress/expected/window.out
+++ b/src/test/regress/expected/window.out
@@ -204,33 +204,33 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
(10 rows)
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- percent_rank | ten | four
--------------------+-----+------
- 0 | 0 | 0
- 0 | 0 | 0
- 1 | 4 | 0
- 0 | 1 | 1
- 0 | 1 | 1
- 0.666666666666667 | 7 | 1
- 1 | 9 | 1
- 0 | 0 | 2
- 0 | 1 | 3
- 1 | 3 | 3
+ percent_rank | ten | four
+--------------------+-----+------
+ 0 | 0 | 0
+ 0 | 0 | 0
+ 1 | 4 | 0
+ 0 | 1 | 1
+ 0 | 1 | 1
+ 0.6666666666666666 | 7 | 1
+ 1 | 9 | 1
+ 0 | 0 | 2
+ 0 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
- cume_dist | ten | four
--------------------+-----+------
- 0.666666666666667 | 0 | 0
- 0.666666666666667 | 0 | 0
- 1 | 4 | 0
- 0.5 | 1 | 1
- 0.5 | 1 | 1
- 0.75 | 7 | 1
- 1 | 9 | 1
- 1 | 0 | 2
- 0.5 | 1 | 3
- 1 | 3 | 3
+ cume_dist | ten | four
+--------------------+-----+------
+ 0.6666666666666666 | 0 | 0
+ 0.6666666666666666 | 0 | 0
+ 1 | 4 | 0
+ 0.5 | 1 | 1
+ 0.5 | 1 | 1
+ 0.75 | 7 | 1
+ 1 | 9 | 1
+ 1 | 0 | 2
+ 0.5 | 1 | 3
+ 1 | 3 | 3
(10 rows)
SELECT ntile(3) OVER (ORDER BY ten, four), ten, four FROM tenk1 WHERE unique2 < 10;
diff --git a/src/test/regress/resultmap b/src/test/regress/resultmap
index 46ca5639c2..3bd1585a35 100644
--- a/src/test/regress/resultmap
+++ b/src/test/regress/resultmap
@@ -3,3 +3,4 @@ float8:out:i.86-.*-openbsd=float8-small-is-zero.out
float8:out:i.86-.*-netbsd=float8-small-is-zero.out
float8:out:m68k-.*-netbsd=float8-small-is-zero.out
float8:out:i.86-pc-cygwin=float8-small-is-zero.out
+float4:out:hppa.*-hp-hpux10.*=float4-misrounded-input.out
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index a09fa47ae4..d4fd657188 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -2,6 +2,9 @@
-- AGGREGATES
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;
diff --git a/src/test/regress/sql/circle.sql b/src/test/regress/sql/circle.sql
index 46c96e1400..10e51d780e 100644
--- a/src/test/regress/sql/circle.sql
+++ b/src/test/regress/sql/circle.sql
@@ -2,6 +2,9 @@
-- CIRCLE
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
diff --git a/src/test/regress/sql/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..d606e7787b 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -16,6 +16,11 @@ INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
+INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
+
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
@@ -95,3 +100,254 @@ SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
+
+-- Test for correct input rounding in edge cases.
+-- These lists are from Paxson 1991, excluding subnormals and
+-- inputs of over 9 sig. digits.
+
+SELECT float4send('5e-20'::float4);
+SELECT float4send('67e14'::float4);
+SELECT float4send('985e15'::float4);
+SELECT float4send('55895e-16'::float4);
+SELECT float4send('7038531e-32'::float4);
+SELECT float4send('702990899e-20'::float4);
+
+SELECT float4send('3e-23'::float4);
+SELECT float4send('57e18'::float4);
+SELECT float4send('789e-35'::float4);
+SELECT float4send('2539e-18'::float4);
+SELECT float4send('76173e28'::float4);
+SELECT float4send('887745e-11'::float4);
+SELECT float4send('5382571e-37'::float4);
+SELECT float4send('82381273e-35'::float4);
+SELECT float4send('750486563e-38'::float4);
+
+-- Test that the smallest possible normalized input value inputs
+-- correctly, either in 9-significant-digit or shortest-decimal
+-- format.
+--
+-- exact val is 1.1754943508...
+-- shortest val is 1.1754944000
+-- midpoint to next val is 1.1754944208...
+
+SELECT float4send('1.17549435e-38'::float4);
+SELECT float4send('1.1754944e-38'::float4);
+
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat4;
+create function xfloat4in(cstring) returns xfloat4 immutable strict
+ language internal as 'int4in';
+create function xfloat4out(xfloat4) returns cstring immutable strict
+ language internal as 'int4out';
+create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
+create cast (xfloat4 as float4) without function;
+create cast (float4 as xfloat4) without function;
+create cast (xfloat4 as integer) without function;
+create cast (integer as xfloat4) without function;
+
+-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'00000001'),
+ (x'00000002'), (x'00000003'),
+ (x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
+ (x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
+ -- stress values
+ (x'0053c4f4'), -- 7693e-42
+ (x'006c85c4'), -- 996622e-44
+ (x'0041ca76'), -- 60419369e-46
+ (x'004b7678'), -- 6930161142e-48
+ -- taken from upstream testsuite
+ (x'00000007'),
+ (x'00424fe2'),
+ -- borderline between subnormal and normal
+ (x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
+select float4send(flt) as ibits,
+ flt
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+with testdata(bits) as (values
+ (x'00000000'),
+ -- smallest normal values
+ (x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
+ (x'00800006'),
+ -- small normal values chosen for short vs. long output
+ (x'008002f1'), (x'008002f2'), (x'008002f3'),
+ (x'00800e17'), (x'00800e18'), (x'00800e19'),
+ -- assorted values (random mantissae)
+ (x'01000001'), (x'01102843'), (x'01a52c98'),
+ (x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
+ (x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
+ (x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
+ (x'1f850283'), (x'2874a9d6'),
+ -- values around 5e-08
+ (x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
+ -- around 1e-07
+ (x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
+ -- around 3e-07 .. 1e-04
+ (x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
+ (x'350637bc'), (x'350637bd'), (x'350637be'),
+ (x'35719786'), (x'35719787'), (x'35719788'),
+ (x'358637bc'), (x'358637bd'), (x'358637be'),
+ (x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
+ (x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
+ -- format crossover at 1e-04
+ (x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
+ (x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
+ (x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
+ (x'38d1b71d'),
+ --
+ (x'38dffffe'), (x'38dfffff'), (x'38e00000'),
+ (x'38efffff'), (x'38f00000'), (x'38f00001'),
+ (x'3a83126e'), (x'3a83126f'), (x'3a831270'),
+ (x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
+ (x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
+ -- chosen to need 9 digits for 3dcccd70
+ (x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
+ --
+ (x'3effffff'), (x'3f000000'), (x'3f000001'),
+ (x'3f333332'), (x'3f333333'), (x'3f333334'),
+ -- approach 1.0 with increasing numbers of 9s
+ (x'3f666665'), (x'3f666666'), (x'3f666667'),
+ (x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
+ (x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
+ (x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
+ (x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
+ (x'3f7fffee'), (x'3f7fffef'),
+ -- values very close to 1
+ (x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
+ (x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
+ (x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
+ (x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
+ (x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
+ (x'3f7fffff'),
+ (x'3f800000'),
+ (x'3f800001'), (x'3f800002'), (x'3f800003'),
+ (x'3f800004'), (x'3f800005'), (x'3f800006'),
+ (x'3f800007'), (x'3f800008'), (x'3f800009'),
+ -- values 1 to 1.1
+ (x'3f80000f'), (x'3f800010'), (x'3f800011'),
+ (x'3f800012'), (x'3f800013'), (x'3f800014'),
+ (x'3f800017'), (x'3f800018'), (x'3f800019'),
+ (x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
+ (x'3f800029'), (x'3f80002a'), (x'3f80002b'),
+ (x'3f800053'), (x'3f800054'), (x'3f800055'),
+ (x'3f800346'), (x'3f800347'), (x'3f800348'),
+ (x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
+ (x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
+ (x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
+ --
+ (x'3fc90fdb'), -- pi/2
+ (x'402df854'), -- e
+ (x'40490fdb'), -- pi
+ --
+ (x'409fffff'), (x'40a00000'), (x'40a00001'),
+ (x'40afffff'), (x'40b00000'), (x'40b00001'),
+ (x'411fffff'), (x'41200000'), (x'41200001'),
+ (x'42c7ffff'), (x'42c80000'), (x'42c80001'),
+ (x'4479ffff'), (x'447a0000'), (x'447a0001'),
+ (x'461c3fff'), (x'461c4000'), (x'461c4001'),
+ (x'47c34fff'), (x'47c35000'), (x'47c35001'),
+ (x'497423ff'), (x'49742400'), (x'49742401'),
+ (x'4b18967f'), (x'4b189680'), (x'4b189681'),
+ (x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
+ (x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
+ (x'501502f8'), (x'501502f9'), (x'501502fa'),
+ (x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
+ -- stress values
+ (x'1f6c1e4a'), -- 5e-20
+ (x'59be6cea'), -- 67e14
+ (x'5d5ab6c4'), -- 985e15
+ (x'2cc4a9bd'), -- 55895e-16
+ (x'15ae43fd'), -- 7038531e-32
+ (x'2cf757ca'), -- 702990899e-20
+ (x'665ba998'), -- 25933168707e13
+ (x'743c3324'), -- 596428896559e20
+ -- exercise fixed-point memmoves
+ (x'47f1205a'),
+ (x'4640e6ae'),
+ (x'449a5225'),
+ (x'42f6e9d5'),
+ (x'414587dd'),
+ (x'3f9e064b'),
+ -- these cases come from the upstream's testsuite
+ -- BoundaryRoundEven
+ (x'4c000004'),
+ (x'50061c46'),
+ (x'510006a8'),
+ -- ExactValueRoundEven
+ (x'48951f84'),
+ (x'45fd1840'),
+ -- LotsOfTrailingZeros
+ (x'39800000'),
+ (x'3b200000'),
+ (x'3b900000'),
+ (x'3bd00000'),
+ -- Regression
+ (x'63800000'),
+ (x'4b000000'),
+ (x'4b800000'),
+ (x'4c000001'),
+ (x'4c800b0d'),
+ (x'00d24584'),
+ (x'800000b0'),
+ (x'00d90b88'),
+ (x'45803f34'),
+ (x'4f9f24f7'),
+ (x'3a8722c3'),
+ (x'5c800041'),
+ (x'15ae43fd'),
+ (x'5d4cccfb'),
+ (x'4c800001'),
+ (x'57800ed8'),
+ (x'5f000000'),
+ (x'700000f0'),
+ (x'5f23e9ac'),
+ (x'5e9502f9'),
+ (x'5e8012b1'),
+ (x'3c000028'),
+ (x'60cde861'),
+ (x'03aa2a50'),
+ (x'43480000'),
+ (x'4c000000'),
+ -- LooksLikePow5
+ (x'5D1502F9'),
+ (x'5D9502F9'),
+ (x'5E1502F9'),
+ -- OutputLength
+ (x'3f99999a'),
+ (x'3f9d70a4'),
+ (x'3f9df3b6'),
+ (x'3f9e0419'),
+ (x'3f9e0610'),
+ (x'3f9e064b'),
+ (x'3f9e0651'),
+ (x'03d20cfe')
+)
+select float4send(flt) as ibits,
+ flt,
+ flt::text::float4 as r_flt,
+ float4send(flt::text::float4) as obits,
+ float4send(flt::text::float4) = float4send(flt) as correct
+ from (select bits::integer::xfloat4::float4 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat4 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
index 6595fd2b95..a33321811d 100644
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
+-- test smallest normalized input
+SELECT float8send('2.2250738585072014E-308'::float8);
+
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- square root
SELECT sqrt(float8 '64') AS eight;
@@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
-SET extra_float_digits = 3;
SELECT x,
sind(x),
@@ -232,4 +239,203 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
-RESET extra_float_digits;
+--
+-- test output (and round-trip safety) of various values.
+-- To ensure we're testing what we think we're testing, start with
+-- float values specified by bit patterns (as a useful side effect,
+-- this means we'll fail on non-IEEE platforms).
+
+create type xfloat8;
+create function xfloat8in(cstring) returns xfloat8 immutable strict
+ language internal as 'int8in';
+create function xfloat8out(xfloat8) returns cstring immutable strict
+ language internal as 'int8out';
+create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
+create cast (xfloat8 as float8) without function;
+create cast (float8 as xfloat8) without function;
+create cast (xfloat8 as bigint) without function;
+create cast (bigint as xfloat8) without function;
+
+-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
+
+-- we don't care to assume the platform's strtod() handles subnormals
+-- correctly; those are "use at your own risk". However we do test
+-- subnormal outputs, since those are under our control.
+
+with testdata(bits) as (values
+ -- small subnormals
+ (x'0000000000000001'),
+ (x'0000000000000002'), (x'0000000000000003'),
+ (x'0000000000001000'), (x'0000000100000000'),
+ (x'0000010000000000'), (x'0000010100000000'),
+ (x'0000400000000000'), (x'0000400100000000'),
+ (x'0000800000000000'), (x'0000800000000001'),
+ -- these values taken from upstream testsuite
+ (x'00000000000f4240'),
+ (x'00000000016e3600'),
+ (x'0000008cdcdea440'),
+ -- borderline between subnormal and normal
+ (x'000ffffffffffff0'), (x'000ffffffffffff1'),
+ (x'000ffffffffffffe'), (x'000fffffffffffff'))
+select float8send(flt) as ibits,
+ flt
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- round-trip tests
+
+with testdata(bits) as (values
+ (x'0000000000000000'),
+ -- smallest normal values
+ (x'0010000000000000'), (x'0010000000000001'),
+ (x'0010000000000002'), (x'0018000000000000'),
+ --
+ (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
+ (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
+ (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
+ (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
+ (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
+ (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
+ (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
+ (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
+ (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
+ (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
+ -- values very close to 1
+ (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
+ (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
+ (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
+ (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
+ (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
+ (x'3fefffffffffffff'),
+ (x'3ff0000000000000'),
+ (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
+ (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
+ (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
+ --
+ (x'3ff921fb54442d18'),
+ (x'4005bf0a8b14576a'),
+ (x'400921fb54442d18'),
+ --
+ (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
+ (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
+ (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
+ (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
+ (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
+ (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
+ (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
+ (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
+ (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
+ (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
+ (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
+ (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
+ (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
+ (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
+ (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
+ (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
+ (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
+ (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
+ (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
+ (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
+ (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
+ (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
+ (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
+ (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
+ (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
+ --
+ (x'7feffffffffffffe'), (x'7fefffffffffffff'),
+ -- round to even tests (+ve)
+ (x'4350000000000002'),
+ (x'4350000000002e06'),
+ (x'4352000000000003'),
+ (x'4352000000000004'),
+ (x'4358000000000003'),
+ (x'4358000000000004'),
+ (x'435f000000000020'),
+ -- round to even tests (-ve)
+ (x'c350000000000002'),
+ (x'c350000000002e06'),
+ (x'c352000000000003'),
+ (x'c352000000000004'),
+ (x'c358000000000003'),
+ (x'c358000000000004'),
+ (x'c35f000000000020'),
+ -- exercise fixed-point memmoves
+ (x'42dc12218377de66'),
+ (x'42a674e79c5fe51f'),
+ (x'4271f71fb04cb74c'),
+ (x'423cbe991a145879'),
+ (x'4206fee0e1a9e061'),
+ (x'41d26580b487e6b4'),
+ (x'419d6f34540ca453'),
+ (x'41678c29dcd6e9dc'),
+ (x'4132d687e3df217d'),
+ (x'40fe240c9fcb68c8'),
+ (x'40c81cd6e63c53d3'),
+ (x'40934a4584fd0fdc'),
+ (x'405edd3c07fb4c93'),
+ (x'4028b0fcd32f7076'),
+ (x'3ff3c0ca428c59f8'),
+ -- these cases come from the upstream's testsuite
+ -- LotsOfTrailingZeros)
+ (x'3e60000000000000'),
+ -- Regression
+ (x'c352bd2668e077c4'),
+ (x'434018601510c000'),
+ (x'43d055dc36f24000'),
+ (x'43e052961c6f8000'),
+ (x'3ff3c0ca2a5b1d5d'),
+ -- LooksLikePow5
+ (x'4830f0cf064dd592'),
+ (x'4840f0cf064dd592'),
+ (x'4850f0cf064dd592'),
+ -- OutputLength
+ (x'3ff3333333333333'),
+ (x'3ff3ae147ae147ae'),
+ (x'3ff3be76c8b43958'),
+ (x'3ff3c083126e978d'),
+ (x'3ff3c0c1fc8f3238'),
+ (x'3ff3c0c9539b8887'),
+ (x'3ff3c0ca2a5b1d5d'),
+ (x'3ff3c0ca4283de1b'),
+ (x'3ff3c0ca43db770a'),
+ (x'3ff3c0ca428abd53'),
+ (x'3ff3c0ca428c1d2b'),
+ (x'3ff3c0ca428c51f2'),
+ (x'3ff3c0ca428c58fc'),
+ (x'3ff3c0ca428c59dd'),
+ (x'3ff3c0ca428c59f8'),
+ (x'3ff3c0ca428c59fb'),
+ -- 32-bit chunking
+ (x'40112e0be8047a7d'),
+ (x'40112e0be815a889'),
+ (x'40112e0be826d695'),
+ (x'40112e0be83804a1'),
+ (x'40112e0be84932ad'),
+ -- MinMaxShift
+ (x'0040000000000000'),
+ (x'007fffffffffffff'),
+ (x'0290000000000000'),
+ (x'029fffffffffffff'),
+ (x'4350000000000000'),
+ (x'435fffffffffffff'),
+ (x'1330000000000000'),
+ (x'133fffffffffffff'),
+ (x'3a6fa7161a4d6e0c')
+)
+select float8send(flt) as ibits,
+ flt,
+ flt::text::float8 as r_flt,
+ float8send(flt::text::float8) as obits,
+ float8send(flt::text::float8) = float8send(flt) as correct
+ from (select bits::bigint::xfloat8::float8 as flt
+ from testdata
+ offset 0) s;
+
+-- clean up, lest opr_sanity complain
+
+\set VERBOSITY terse
+drop type xfloat8 cascade;
+\set VERBOSITY default
+
+--
diff --git a/src/test/regress/sql/point.sql b/src/test/regress/sql/point.sql
index a209f3bfeb..7f8504dbd1 100644
--- a/src/test/regress/sql/point.sql
+++ b/src/test/regress/sql/point.sql
@@ -2,6 +2,9 @@
-- POINT
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
diff --git a/src/test/regress/sql/updatable_views.sql b/src/test/regress/sql/updatable_views.sql
index dc6d5cbe35..2ecc386238 100644
--- a/src/test/regress/sql/updatable_views.sql
+++ b/src/test/regress/sql/updatable_views.sql
@@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
+-- avoid bit-exact output here because operations may not be bit-exact.
+SET extra_float_digits = 0;
+
-- check that non-updatable views and columns are rejected with useful error
-- messages
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..5251a21d34 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -105,6 +105,8 @@ sub mkvcbuild
push(@pgportfiles, 'rint.c') if ($vsVersion < '12.00');
+ push(@pgportfiles, 'strtof.c') if ($vsVersion < '14.00');
+
if ($vsVersion >= '9.00')
{
push(@pgportfiles, 'pg_crc32c_sse42_choose.c');
@@ -117,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
[ ryu11.patch ]
I can confirm this compiles and passes core regression tests on
my HPPA dinosaur.
regards, tom lane
Re: Ryu floating point output patch
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> 2. How far do we need to go to support existing uses of
Andrew> extra_float_digits? For example, do we need a way for clients to
Andrew> request that they get the exact same output as previously for
Andrew> extra_float_digits=2 or 3, rather than just assuming that any
Andrew> round-trip-exact value will do?
Andrew> (this would likely mean adding a new GUC, rather than basing
Andrew> everything off extra_float_digits as the patch does now)
So it turns out, for reasons that should have been obvious in advance,
that _of course_ we need this, because otherwise there's no way to do
the cross-version upgrade regression check.
So we need something like exact_float_output='on' (default) that can be
selectively set to 'off' to restore the previous behavior of
extra_float_digits.
Thoughts?
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On 2/13/19 12:09 PM, Andrew Gierth wrote:
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> 2. How far do we need to go to support existing uses of
Andrew> extra_float_digits? For example, do we need a way for clients to
Andrew> request that they get the exact same output as previously for
Andrew> extra_float_digits=2 or 3, rather than just assuming that any
Andrew> round-trip-exact value will do?Andrew> (this would likely mean adding a new GUC, rather than basing
Andrew> everything off extra_float_digits as the patch does now)So it turns out, for reasons that should have been obvious in advance,
that _of course_ we need this, because otherwise there's no way to do
the cross-version upgrade regression check.So we need something like exact_float_output='on' (default) that can be
selectively set to 'off' to restore the previous behavior of
extra_float_digits.Thoughts?
I applied this:
diff --git a/src/bin/pg_dump/pg_dump.c b/src/bin/pg_dump/pg_dump.c
index 9edc7b9a02..a6b804ad2c 100644
--- a/src/bin/pg_dump/pg_dump.c
+++ b/src/bin/pg_dump/pg_dump.c
@@ -1062,7 +1062,15 @@ setup_connection(Archive *AH, const char
*dumpencoding,
* Set extra_float_digits so that we can dump float data exactly (given
* correctly implemented float I/O code, anyway)
*/
- if (AH->remoteVersion >= 90000)
+ if (getenv("PGDUMP_EXTRA_FLOAT_DIGITS"))
+ {
+ PQExpBuffer q = createPQExpBuffer();
+ appendPQExpBuffer(q, "SET extra_float_digits TO %s",
+ getenv("PGDUMP_EXTRA_FLOAT_DIGITS"));
+ ExecuteSqlStatement(AH, q->data);
+ destroyPQExpBuffer(q);
+ }
+ else if (AH->remoteVersion >= 90000)
ExecuteSqlStatement(AH, "SET extra_float_digits TO 3");
else
ExecuteSqlStatement(AH, "SET extra_float_digits TO 2");Then I got the buildfarm cross-version-upgrade module to set the
environment value to 0 in the appropriate cases. All the tests passed,
as far back as 9.2, no new GUC needed.
We might not want to use that in more real-world cases of pg_dump use,
but I think for this purpose it should be fine.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
Andrew,
Is there any chance you can get me the regress/results/float[48].out
files from lorikeet and jacana? It would help a lot.
Seeing the diffs isn't enough, because I want to know if the float8 test
(which passes, so there's no diff) is matching the standard file or the
-small-is-zero file.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On 2/14/19 12:24 PM, Andrew Gierth wrote:
Andrew,
Is there any chance you can get me the regress/results/float[48].out
files from lorikeet and jacana? It would help a lot.Seeing the diffs isn't enough, because I want to know if the float8 test
(which passes, so there's no diff) is matching the standard file or the
-small-is-zero file.
Yeah, later on today or tomorrow.
Maybe we should have pg_regress report on the files it matches ...
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
On 2/14/19 12:42 PM, Andrew Dunstan wrote:
On 2/14/19 12:24 PM, Andrew Gierth wrote:
Andrew,
Is there any chance you can get me the regress/results/float[48].out
files from lorikeet and jacana? It would help a lot.Seeing the diffs isn't enough, because I want to know if the float8 test
(which passes, so there's no diff) is matching the standard file or the
-small-is-zero file.Yeah, later on today or tomorrow.
Maybe we should have pg_regress report on the files it matches ...
Rather than give you the files, I will just tell you, in both cases it
is matching float8.out, not the small-is-zero file. As you can see in
the buildfarm web, the float4 tests are failing and being compared
against float4.out
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Andrew> Rather than give you the files, I will just tell you, in both
Andrew> cases it is matching float8.out, not the small-is-zero file.
OK, thanks. That lets me fix the float4 failures in a reasonably
straightforward way.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On 2/14/19 10:14 AM, Andrew Dunstan wrote:
On 2/13/19 12:09 PM, Andrew Gierth wrote:
"Andrew" == Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Andrew> 2. How far do we need to go to support existing uses of
Andrew> extra_float_digits? For example, do we need a way for clients to
Andrew> request that they get the exact same output as previously for
Andrew> extra_float_digits=2 or 3, rather than just assuming that any
Andrew> round-trip-exact value will do?Andrew> (this would likely mean adding a new GUC, rather than basing
Andrew> everything off extra_float_digits as the patch does now)So it turns out, for reasons that should have been obvious in advance,
that _of course_ we need this, because otherwise there's no way to do
the cross-version upgrade regression check.So we need something like exact_float_output='on' (default) that can be
selectively set to 'off' to restore the previous behavior of
extra_float_digits.Thoughts?
I applied this:
diff --git a/src/bin/pg_dump/pg_dump.c b/src/bin/pg_dump/pg_dump.c index 9edc7b9a02..a6b804ad2c 100644 --- a/src/bin/pg_dump/pg_dump.c +++ b/src/bin/pg_dump/pg_dump.c @@ -1062,7 +1062,15 @@ setup_connection(Archive *AH, const char *dumpencoding, * Set extra_float_digits so that we can dump float data exactly (given * correctly implemented float I/O code, anyway) */ - if (AH->remoteVersion >= 90000) + if (getenv("PGDUMP_EXTRA_FLOAT_DIGITS")) + { + PQExpBuffer q = createPQExpBuffer(); + appendPQExpBuffer(q, "SET extra_float_digits TO %s", + getenv("PGDUMP_EXTRA_FLOAT_DIGITS")); + ExecuteSqlStatement(AH, q->data); + destroyPQExpBuffer(q); + } + else if (AH->remoteVersion >= 90000) ExecuteSqlStatement(AH, "SET extra_float_digits TO 3"); else ExecuteSqlStatement(AH, "SET extra_float_digits TO 2");Then I got the buildfarm cross-version-upgrade module to set the
environment value to 0 in the appropriate cases. All the tests passed,
as far back as 9.2, no new GUC needed.We might not want to use that in more real-world cases of pg_dump use,
but I think for this purpose it should be fine.
I haven't seen a response to this. Cross version upgrade testing is
still broken. I don't think we need a GUC to fix it, but we do need this
or a new switch to tell pg_dump what to set extra_float_digits to,
unless someone has a better idea.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
[horrible environment variable hack]
We might not want to use that in more real-world cases of pg_dump use,
but I think for this purpose it should be fine.
Andrew> I haven't seen a response to this. Cross version upgrade
Andrew> testing is still broken. I don't think we need a GUC to fix it,
Andrew> but we do need this or a new switch to tell pg_dump what to set
Andrew> extra_float_digits to, unless someone has a better idea.
I'd been holding off responding in the hope of other opinions, but for
what it's worth, I *really* dislike having pg_dump depend magically on
some new environment variable. I would suggest instead:
a) pg_dump could check if PGOPTIONS or the connect string contained an
extra_float_digits setting and defer to that if so.
Downside of this is that if someone is already using that in the
environment and pg_dump suddenly starts respecting it, they could get
imprecise values in their dumps unexpectedly. Option (a2) would be to
honour extra_float_digits only if it showed up in a connect string and
not in PGOPTIONS, which would be more explicit.
b) new command-line option, e.g. pg_dump --extra-float-digits=0
This is probably the safest option, IMO. Any preferences as to the
option name?
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
I'd been holding off responding in the hope of other opinions, but for
what it's worth, I *really* dislike having pg_dump depend magically on
some new environment variable.
Likewise.
b) new command-line option, e.g. pg_dump --extra-float-digits=0
This is probably the safest option, IMO. Any preferences as to the
option name?
I like that too, assuming that it can be made to fit into the
structure of the cross-version-upgrade tests (which would have
to know to use it only with >= v12 pg_dump).
--extra-float-digits seems fine as a name.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
b) new command-line option, e.g. pg_dump --extra-float-digits=0
This is probably the safest option, IMO. Any preferences as to the
option name?
Tom> I like that too, assuming that it can be made to fit into the
Tom> structure of the cross-version-upgrade tests (which would have
Tom> to know to use it only with >= v12 pg_dump).
Tom> --extra-float-digits seems fine as a name.
As far as I can tell, test.sh only uses the new version's pg_dump (in
fact the only binaries directly used from the old version are initdb and
pg_ctl).
... wait, this initdb in test.sh is using an option that doesn't exist
before pg11? Is the cross-version test actually using some different
script? Andrew?
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On 2/17/19 10:56 AM, Tom Lane wrote:
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
I'd been holding off responding in the hope of other opinions, but for
what it's worth, I *really* dislike having pg_dump depend magically on
some new environment variable.Likewise.
Sure, no problem here - that was just a POC. I did it that way to
minimize the code involved.
b) new command-line option, e.g. pg_dump --extra-float-digits=0
This is probably the safest option, IMO. Any preferences as to the
option name?I like that too, assuming that it can be made to fit into the
structure of the cross-version-upgrade tests (which would have
to know to use it only with >= v12 pg_dump).--extra-float-digits seems fine as a name.
There are all sorts of version-specific things done there. The code will
be pretty minimal. We'll only invoke it if the target version is >= 12
and the source version is <= 11.
I can do this if we're agreed.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
On 2/17/19 11:19 AM, Andrew Gierth wrote:
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
b) new command-line option, e.g. pg_dump --extra-float-digits=0
This is probably the safest option, IMO. Any preferences as to the
option name?Tom> I like that too, assuming that it can be made to fit into the
Tom> structure of the cross-version-upgrade tests (which would have
Tom> to know to use it only with >= v12 pg_dump).Tom> --extra-float-digits seems fine as a name.
As far as I can tell, test.sh only uses the new version's pg_dump (in
fact the only binaries directly used from the old version are initdb and
pg_ctl).... wait, this initdb in test.sh is using an option that doesn't exist
before pg11? Is the cross-version test actually using some different
script? Andrew?
The buildfarm cross-version upgrade tests do not run test.sh. See
<https://github.com/PGBuildFarm/client-code/blob/master/PGBuild/Modules/TestUpgradeXversion.pm>
Essentially it takes the result of a previous buildfarm run on the
source branch, dumps it, upgrades it, and dumps again, then compares the
two dumps. It doesn't itself run the regression tests.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Andrew> There are all sorts of version-specific things done there. The
Andrew> code will be pretty minimal. We'll only invoke it if the target
Andrew> version is >= 12 and the source version is <= 11.
Andrew> I can do this if we're agreed.
Sure, go ahead.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
BTW, another minor problem with this patch: various buildfarm members
are whining that
prairiedog | 2019-02-17 14:25:15 | ryu_common.h:111: warning: array subscript has type 'char'
This evidently is from the next-to-last line in
static inline int
copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
{
if (mantissa)
{
memcpy(result, "NaN", 3);
return 3;
}
if (sign)
{
result[0] = '-';
}
if (exponent)
{
memcpy(result + sign, "Infinity", 8);
return sign + 8;
}
result[sign] = '0';
return sign + 1;
}
IMO, this is just awful coding, using a "bool" argument in
just one place as a boolean and in four other ones as an integer.
Aside from being cowboy coding, this has very serious risks of
misbehaving on platforms where "bool" isn't C99-like, so that
"sign" could potentially have values other than 0 and 1.
Please clean up that type-punning.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Tom> result[sign] = '0';
Tom> IMO, this is just awful coding, using a "bool" argument in just
Tom> one place as a boolean and in four other ones as an integer. Aside
Tom> from being cowboy coding, this has very serious risks of
Tom> misbehaving on platforms where "bool" isn't C99-like, so that
Tom> "sign" could potentially have values other than 0 and 1.
Elsewhere in the code it relies fairly heavily on the result of boolean
expressions being exactly 0 or 1 (which I'm pretty sure is required in
C89, not just C99); the only two places in the upstream that actually
required C99-specific boolean semantics were fixed in da6520be7.
Obviously I'll fix the warning, but how strict do you want to be about
the rest of the code? There are a lot of examples of things like,
const uint32 q = log10Pow5(-e2) - (-e2 > 1);
output = vr + (vr == vm || roundUp);
The code as it stands now follows the rule that nothing is ever assigned
to a "bool" variable, parameter, or result except the result of a
logical expression; and given that, that the value of any "bool"
variable interpreted as an integer is 0 or 1 and no other value.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
Tom> IMO, this is just awful coding, using a "bool" argument in just
Tom> one place as a boolean and in four other ones as an integer. Aside
Tom> from being cowboy coding, this has very serious risks of
Tom> misbehaving on platforms where "bool" isn't C99-like, so that
Tom> "sign" could potentially have values other than 0 and 1.
Elsewhere in the code it relies fairly heavily on the result of boolean
expressions being exactly 0 or 1
Ugh.
(which I'm pretty sure is required in C89, not just C99);
For truth-valued expressions, yes. The question here is what can be
assumed about the integer value of a variable declared to be type "bool",
a question C89 does not address.
Obviously I'll fix the warning, but how strict do you want to be about
the rest of the code?
Well, given that we're now requiring C99 compilers, you'd think that
assuming stdbool semantics would be all right. The problem on prairiedog
and locust (which seem to be the only complainants) is that stdbool
provides a _Bool type that has size 4, so c.h decides not to use stdbool:
#if defined(HAVE_STDBOOL_H) && SIZEOF_BOOL == 1
#include <stdbool.h>
#define USE_STDBOOL 1
#else
#ifndef bool
typedef char bool;
#endif
I believe that we could suppress these warnings by changing that last
to be
typedef unsigned char bool;
since what these warnings are really on about is the uncertain signedness
of the type "char". Perhaps that's a reasonable way to deal with it.
If 0/1 assumptions are all over the place in the Ryu code, avoiding them
in this one place isn't going to move the goalposts for portability.
regards, tom lane
Re: Ryu floating point output patch
On 2/17/19 12:09 PM, Andrew Gierth wrote:
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Andrew> There are all sorts of version-specific things done there. The
Andrew> code will be pretty minimal. We'll only invoke it if the target
Andrew> version is >= 12 and the source version is <= 11.Andrew> I can do this if we're agreed.
Sure, go ahead.
Here's a patch without docco. How much do we actually want to document
this? I'm not sure it has any great value outside of cross-version
upgrade testing.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Attachments:
pg_dump_extra_float_digits.patchtext/x-patch; name=pg_dump_extra_float_digits.patchDownload
diff --git a/src/bin/pg_dump/pg_dump.c b/src/bin/pg_dump/pg_dump.c
index 9edc7b9a02..d2d7de0fc2 100644
--- a/src/bin/pg_dump/pg_dump.c
+++ b/src/bin/pg_dump/pg_dump.c
@@ -134,6 +134,10 @@ char g_comment_end[10];
static const CatalogId nilCatalogId = {0, 0};
+/* override for standard extra_float_digits setting */
+static bool have_extra_float_digits = false;
+static int extra_float_digits;
+
/*
* Macro for producing quoted, schema-qualified name of a dumpable object.
*/
@@ -357,6 +361,7 @@ main(int argc, char **argv)
{"disable-triggers", no_argument, &dopt.disable_triggers, 1},
{"enable-row-security", no_argument, &dopt.enable_row_security, 1},
{"exclude-table-data", required_argument, NULL, 4},
+ {"extra-float-digits", required_argument, NULL, 8},
{"if-exists", no_argument, &dopt.if_exists, 1},
{"inserts", no_argument, &dopt.dump_inserts, 1},
{"lock-wait-timeout", required_argument, NULL, 2},
@@ -557,6 +562,16 @@ main(int argc, char **argv)
dosync = false;
break;
+ case 8:
+ have_extra_float_digits = true;
+ extra_float_digits = atoi(optarg);
+ if (extra_float_digits < -15 || extra_float_digits > 3)
+ {
+ write_msg(NULL, "extra_float_digits must be in range -15..3\n");
+ exit_nicely(1);
+ }
+ break;
+
default:
fprintf(stderr, _("Try \"%s --help\" for more information.\n"), progname);
exit_nicely(1);
@@ -965,6 +980,7 @@ help(const char *progname)
printf(_(" --enable-row-security enable row security (dump only content user has\n"
" access to)\n"));
printf(_(" --exclude-table-data=TABLE do NOT dump data for the named table(s)\n"));
+ printf(_(" --extra-float-digits=NUM override default setting for extra_float_digits\n"));
printf(_(" --if-exists use IF EXISTS when dropping objects\n"));
printf(_(" --inserts dump data as INSERT commands, rather than COPY\n"));
printf(_(" --load-via-partition-root load partitions via the root table\n"));
@@ -1062,7 +1078,14 @@ setup_connection(Archive *AH, const char *dumpencoding,
* Set extra_float_digits so that we can dump float data exactly (given
* correctly implemented float I/O code, anyway)
*/
- if (AH->remoteVersion >= 90000)
+ if (have_extra_float_digits)
+ {
+ PQExpBuffer q = createPQExpBuffer();
+ appendPQExpBuffer(q, "SET extra_float_digits TO %d",extra_float_digits);
+ ExecuteSqlStatement(AH, q->data);
+ destroyPQExpBuffer(q);
+ }
+ else if (AH->remoteVersion >= 90000)
ExecuteSqlStatement(AH, "SET extra_float_digits TO 3");
else
ExecuteSqlStatement(AH, "SET extra_float_digits TO 2");
diff --git a/src/bin/pg_dump/pg_dumpall.c b/src/bin/pg_dump/pg_dumpall.c
index 5d40d19596..44c3350887 100644
--- a/src/bin/pg_dump/pg_dumpall.c
+++ b/src/bin/pg_dump/pg_dumpall.c
@@ -123,6 +123,7 @@ main(int argc, char *argv[])
{"column-inserts", no_argument, &column_inserts, 1},
{"disable-dollar-quoting", no_argument, &disable_dollar_quoting, 1},
{"disable-triggers", no_argument, &disable_triggers, 1},
+ {"extra-float-digits", required_argument, NULL, 5},
{"if-exists", no_argument, &if_exists, 1},
{"inserts", no_argument, &inserts, 1},
{"lock-wait-timeout", required_argument, NULL, 2},
@@ -318,6 +319,11 @@ main(int argc, char *argv[])
appendPQExpBufferStr(pgdumpopts, " --no-sync");
break;
+ case 5:
+ appendPQExpBufferStr(pgdumpopts, " --extra-float-digits ");
+ appendShellString(pgdumpopts, optarg);
+ break;
+
default:
fprintf(stderr, _("Try \"%s --help\" for more information.\n"), progname);
exit_nicely(1);
@@ -614,6 +620,7 @@ help(void)
printf(_(" --column-inserts dump data as INSERT commands with column names\n"));
printf(_(" --disable-dollar-quoting disable dollar quoting, use SQL standard quoting\n"));
printf(_(" --disable-triggers disable triggers during data-only restore\n"));
+ printf(_(" --extra-float-digits=NUM override default setting for extra_float_digits\n"));
printf(_(" --if-exists use IF EXISTS when dropping objects\n"));
printf(_(" --inserts dump data as INSERT commands, rather than COPY\n"));
printf(_(" --load-via-partition-root load partitions via the root table\n"));
Re: Ryu floating point output patch
Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Here's a patch without docco. How much do we actually want to document
this? I'm not sure it has any great value outside of cross-version
upgrade testing.
I think we have to document it, but it can be fairly terse perhaps.
Use the specified value of extra_float_digits when dumping
floating-point data, rather than pg_dump's default.
I don't think we need to go into detail about when/why you might want
to use it; I can see people thinking of their own reasons.
regards, tom lane
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Obviously I'll fix the warning, but how strict do you want to be
about the rest of the code?
Tom> Well, given that we're now requiring C99 compilers, you'd think
Tom> that assuming stdbool semantics would be all right. The problem on
Tom> prairiedog and locust (which seem to be the only complainants) is
Tom> that stdbool provides a _Bool type that has size 4, so c.h decides
Tom> not to use stdbool:
Yes, this was the cause of the earlier regression test failures that
were fixed by da6520be7; I realized exactly what was going on after
writing that commit message (otherwise I'd have been more explicit).
Tom> typedef char bool;
Tom> #endif
Tom> I believe that we could suppress these warnings by changing that
Tom> last to be
Tom> typedef unsigned char bool;
*squint* I _think_, going through the integer promotion rules, that that
should be safe.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Here's a patch without docco. How much do we actually want to
document this? I'm not sure it has any great value outside of
cross-version upgrade testing.
Tom> I think we have to document it, but it can be fairly terse perhaps.
Tom> Use the specified value of extra_float_digits when dumping
Tom> floating-point data, rather than pg_dump's default.
Tom> I don't think we need to go into detail about when/why you might
Tom> want to use it; I can see people thinking of their own reasons.
It should probably at least say that (a) the default is to dump with the
maximum available precision, and at least hint at (b) that ordinary use
doesn't require the option. We shouldn't mislead people into thinking
they need it when they don't.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
On 2/17/19 6:15 PM, Andrew Gierth wrote:
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Here's a patch without docco. How much do we actually want to
document this? I'm not sure it has any great value outside of
cross-version upgrade testing.Tom> I think we have to document it, but it can be fairly terse perhaps.
Tom> Use the specified value of extra_float_digits when dumping
Tom> floating-point data, rather than pg_dump's default.Tom> I don't think we need to go into detail about when/why you might
Tom> want to use it; I can see people thinking of their own reasons.It should probably at least say that (a) the default is to dump with the
maximum available precision, and at least hint at (b) that ordinary use
doesn't require the option. We shouldn't mislead people into thinking
they need it when they don't.
Would you like to reformulate this, then?
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Tom> I think we have to document it, but it can be fairly terse perhaps.
Tom> Use the specified value of extra_float_digits when dumping
Tom> floating-point data, rather than pg_dump's default.
Tom> I don't think we need to go into detail about when/why you might
Tom> want to use it; I can see people thinking of their own reasons.
It should probably at least say that (a) the default is to dump with the
maximum available precision, and at least hint at (b) that ordinary use
doesn't require the option. We shouldn't mislead people into thinking
they need it when they don't.
Andrew> Would you like to reformulate this, then?
How about:
Use the specified value of extra_float_digits when dumping
floating-point data, instead of the maximum available precision.
Routine dumps made for backup purposes should not use this option.
--
Andrew (irc:RhodiumToad)
Re: Ryu floating point output patch
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Andrew> Would you like to reformulate this, then?
How about:
Use the specified value of extra_float_digits when dumping
floating-point data, instead of the maximum available precision.
Routine dumps made for backup purposes should not use this option.
OK by me.
regards, tom lane
Re: Ryu floating point output patch
On 2/17/19 6:49 PM, Tom Lane wrote:
Andrew Gierth <andrew@tao11.riddles.org.uk> writes:
"Andrew" == Andrew Dunstan <andrew.dunstan@2ndquadrant.com> writes:
Andrew> Would you like to reformulate this, then?
How about:
Use the specified value of extra_float_digits when dumping
floating-point data, instead of the maximum available precision.
Routine dumps made for backup purposes should not use this option.OK by me.
Done.
cheers
andrew
--
Andrew Dunstan https://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services
Re: Ryu floating point output patch
"Tom" == Tom Lane <tgl@sss.pgh.pa.us> writes:
Tom> typedef char bool;
Tom> #endif
Tom> I believe that we could suppress these warnings by changing that
Tom> last to be
Tom> typedef unsigned char bool;
After testing this locally with a hand-tweaked configure result (since I
don't have hardware that triggers it) it all looked ok, so I've pushed
it and at least locust seems to be happy with the result.
--
Andrew (irc:RhodiumToad)