draft patch for strtof()

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..dce6ea31cf 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -104,13 +104,39 @@ 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 +161,7 @@ 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 +169,14 @@ 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)
 		{
@@ -196,7 +222,7 @@ float4in(PG_FUNCTION_ARGS)
 			 * detect whether it's a "real" out-of-range condition by checking
 			 * to see if the result is zero or huge.
 			 */
-			if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+			if (val == 0.0 || val >= HUGE_VALF || val <= -HUGE_VALF)
 				ereport(ERROR,
 						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
 						 errmsg("\"%s\" is out of range for type real",
@@ -232,13 +258,7 @@ 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);
 }
 
 /*
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/utils/float.h b/src/include/utils/float.h
index 0f82a25ede..5e11ab4aa9 100644
--- a/src/include/utils/float.h
+++ b/src/include/utils/float.h
@@ -17,6 +17,11 @@
 
 #include <math.h>
 
+/* this might not be needed */
+#ifndef HUGE_VALF
+#define HUGE_VALF ((float)HUGE_VAL)
+#endif
+
 #ifndef M_PI
 /* From my RH5.2 gcc math.h file - thomas 2000-04-03 */
 #define M_PI 3.14159265358979323846
diff --git a/src/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..75a41fbcfa
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,52 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ *	  src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+/*
+ * strtof() is part of C99; this file 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;
+}
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..b8795c6fdf
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,401 @@
+--
+-- 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');
+                                           ^
+-- 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
+      | 1.23457e+20
+      | 1.23457e-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
+(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
+       | 1.23457e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE  f.f1 < '1004.3';
+ three |     f1      
+-------+-------------
+       |           0
+       |      -34.84
+       | 1.23457e-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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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)
+
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..3aa7f257d5 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,19 +9,19 @@ 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');
                                            ^
 -- bad input
@@ -306,3 +306,96 @@ 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)
+
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/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..12421f7c75 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -95,3 +95,24 @@ 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);

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..b907613056 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -104,13 +104,39 @@ 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 +161,7 @@ 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 +169,14 @@ 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)
 		{
@@ -196,7 +222,14 @@ float4in(PG_FUNCTION_ARGS)
 			 * detect whether it's a "real" out-of-range condition by checking
 			 * to see if the result is zero or huge.
 			 */
-			if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+
+			if (val == 0.0 ||
+#ifdef HUGE_VALF
+				val >= HUGE_VALF || val <= -HUGE_VALF
+#else
+				isinf(val)
+#endif
+				)
 				ereport(ERROR,
 						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
 						 errmsg("\"%s\" is out of range for type real",
@@ -232,13 +265,7 @@ 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);
 }
 
 /*
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/port/strtof.c b/src/port/strtof.c
new file mode 100644
index 0000000000..75a41fbcfa
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,52 @@
+/*-------------------------------------------------------------------------
+ *
+ * strtof.c
+ *
+ * Portions Copyright (c) 2019, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ *	  src/port/strtof.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "c.h"
+
+#include <float.h>
+#include <math.h>
+
+/*
+ * strtof() is part of C99; this file 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;
+}
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..b8795c6fdf
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,401 @@
+--
+-- 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');
+                                           ^
+-- 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
+      | 1.23457e+20
+      | 1.23457e-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
+(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
+       | 1.23457e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE  f.f1 < '1004.3';
+ three |     f1      
+-------+-------------
+       |           0
+       |      -34.84
+       | 1.23457e-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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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)
+
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..3aa7f257d5 100644
--- a/src/test/regress/expected/float4.out
+++ b/src/test/regress/expected/float4.out
@@ -9,19 +9,19 @@ 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');
                                            ^
 -- bad input
@@ -306,3 +306,96 @@ 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)
+
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/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..12421f7c75 100644
--- a/src/test/regress/sql/float4.sql
+++ b/src/test/regress/sql/float4.sql
@@ -95,3 +95,24 @@ 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);

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..31f53878a2 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -104,13 +104,39 @@ 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 +161,7 @@ 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 +169,14 @@ 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 +221,17 @@ 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 +267,7 @@ 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);
 }
 
 /*
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/float4-misrounded-input.out b/src/test/regress/expected/float4-misrounded-input.out
new file mode 100644
index 0000000000..a554bd29bf
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,417 @@
+--
+-- 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
+      | 1.23457e+20
+      | 1.23457e-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
+(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
+       | 1.23457e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE  f.f1 < '1004.3';
+ three |     f1      
+-------+-------------
+       |           0
+       |      -34.84
+       | 1.23457e-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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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)
+
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..62b29648f0 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: ""
@@ -306,3 +322,96 @@ 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)
+
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/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..a6bce9710b 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 +100,24 @@ 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);
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..c930eafe89 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');

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/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 117ded8d1d..eb111ee2db 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -104,13 +104,39 @@ 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 +161,7 @@ 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 +169,14 @@ 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 +221,18 @@ 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 +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);
 }
 
 /*
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..7aca8e2e3d
--- /dev/null
+++ b/src/port/strtof.c
@@ -0,0 +1,123 @@
+/*-------------------------------------------------------------------------
+ *
+ * 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) || isnan(fresult) ||
+			 ((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. errno is already 0 here.
+		 */
+		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))
+		{
+			/* subnormal but nonzero value */
+			errno = caller_errno;
+			return (float) dresult;
+		}
+		else
+		{
+			errno = ERANGE;
+			return fresult;
+		}
+	}
+}
+
+#endif
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..9898d92928
--- /dev/null
+++ b/src/test/regress/expected/float4-misrounded-input.out
@@ -0,0 +1,436 @@
+--
+-- 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
+      | 1.23457e+20
+      | 1.23457e-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
+(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
+       | 1.23457e-20
+(3 rows)
+
+SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE  f.f1 < '1004.3';
+ three |     f1      
+-------+-------------
+       |           0
+       |      -34.84
+       | 1.23457e-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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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
+(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)
+
diff --git a/src/test/regress/expected/float4.out b/src/test/regress/expected/float4.out
index 2f47e1c202..9b8b4d4280 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: ""
@@ -306,3 +322,115 @@ 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)
+
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/float4.sql b/src/test/regress/sql/float4.sql
index 46a9166d13..1fc482e146 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 +100,35 @@ 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);
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 56192f1b20..c930eafe89 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');