diff --git a/src/backend/access/hash/hashfunc.c b/src/backend/access/hash/hashfunc.c index 96d5643..8a236b5 100644 --- a/src/backend/access/hash/hashfunc.c +++ b/src/backend/access/hash/hashfunc.c @@ -200,39 +200,94 @@ hashvarlena(PG_FUNCTION_ARGS) * hash function, see http://burtleburtle.net/bob/hash/doobs.html, * or Bob's article in Dr. Dobb's Journal, Sept. 1997. * - * In the current code, we have adopted an idea from Bob's 2006 update - * of his hash function, which is to fetch the data a word at a time when - * it is suitably aligned. This makes for a useful speedup, at the cost - * of having to maintain four code paths (aligned vs unaligned, and - * little-endian vs big-endian). Note that we have NOT adopted his newer - * mix() function, which is faster but may sacrifice some randomness. + * In the current code, we have adopted Bob's 2006 update of his hash + * which fetches the data a word at a time when it is suitably aligned. + * This makes for a useful speedup, at the cost of having to maintain + * four code paths (aligned vs unaligned, and little-endian vs big-endian). + * It also two separate mixing functions mix() and final(), instead + * of a slower multi-purpose function. */ /* Get a bit mask of the bits set in non-uint32 aligned addresses */ #define UINT32_ALIGN_MASK (sizeof(uint32) - 1) +#define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) /*---------- * mix -- mix 3 32-bit values reversibly. - * For every delta with one or two bits set, and the deltas of all three - * high bits or all three low bits, whether the original value of a,b,c - * is almost all zero or is uniformly distributed, - * - If mix() is run forward or backward, at least 32 bits in a,b,c - * have at least 1/4 probability of changing. - * - If mix() is run forward, every bit of c will change between 1/3 and - * 2/3 of the time. (Well, 22/100 and 78/100 for some 2-bit deltas.) + * + * This is reversible, so any information in (a,b,c) before mix() is + * still in (a,b,c) after mix(). + * + * If four pairs of (a,b,c) inputs are run through mix(), or through + * mix() in reverse, there are at least 32 bits of the output that + * are sometimes the same for one pair and different for another pair. + * This was tested for: + * * pairs that differed by one bit, by two bits, in any combination + * of top bits of (a,b,c), or in any combination of bottom bits of + * (a,b,c). + * * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed + * the output delta to a Gray code (a^(a>>1)) so a string of 1's (as + * is commonly produced by subtraction) look like a single 1-bit + * difference. + * * the base values were pseudorandom, all zero but one bit set, or + * all zero plus a counter that starts at zero. + * + * This does not achieve avalanche. There are input bits of (a,b,c) + * that fail to affect some output bits of (a,b,c), especially of a. The + * most thoroughly mixed value is c, but it doesn't really even achieve + * avalanche in c. + * + * This allows some parallelism. Read-after-writes are good at doubling + * the number of bits affected, so the goal of mixing pulls in the opposite + * direction as the goal of parallelism. I did what I could. Rotates + * seem to cost as much as shifts on every machine I could lay my hands + * on, and rotates are much kinder to the top and bottom bits, so I used + * rotates. *---------- */ #define mix(a,b,c) \ { \ - a -= b; a -= c; a ^= ((c)>>13); \ - b -= c; b -= a; b ^= ((a)<<8); \ - c -= a; c -= b; c ^= ((b)>>13); \ - a -= b; a -= c; a ^= ((c)>>12); \ - b -= c; b -= a; b ^= ((a)<<16); \ - c -= a; c -= b; c ^= ((b)>>5); \ - a -= b; a -= c; a ^= ((c)>>3); \ - b -= c; b -= a; b ^= ((a)<<10); \ - c -= a; c -= b; c ^= ((b)>>15); \ + a -= c; a ^= rot(c, 4); c += b; \ + b -= a; b ^= rot(a, 6); a += c; \ + c -= b; c ^= rot(b, 8); b += a; \ + a -= c; a ^= rot(c,16); c += b; \ + b -= a; b ^= rot(a,19); a += c; \ + c -= b; c ^= rot(b, 4); b += a; \ +} + +/*---------- + * final -- final mixing of 3 32-bit values (a,b,c) into c + * + * Pairs of (a,b,c) values differing in only a few bits will usually + * produce values of c that look totally different. This was tested for + * * pairs that differed by one bit, by two bits, in any combination + * of top bits of (a,b,c), or in any combination of bottom bits of + * (a,b,c). + * * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed + * the output delta to a Gray code (a^(a>>1)) so a string of 1's (as + * is commonly produced by subtraction) look like a single 1-bit + * difference. + * * the base values were pseudorandom, all zero but one bit set, or + * all zero plus a counter that starts at zero. + * + * The use of separate functions for mix() and final() allow for a + * substantial performance increase since final() does not need to + * do well in reverse, but is does need to affect all output bits. + * mix(), on the other hand, does not need to affect all output + * bits (affecting 32 bits is enough).The original hash function had + * a single mixing operation that had to satisfy both sets of requirements + * and was slower as a result. + *---------- + */ +#define final(a,b,c) \ +{ \ + c ^= b; c -= rot(b,14); \ + a ^= c; a -= rot(c,11); \ + b ^= a; b -= rot(a,25); \ + c ^= b; c -= rot(b,16); \ + a ^= c; a -= rot(c,4); \ + b ^= a; b -= rot(a,14); \ + c ^= b; c -= rot(b,24); \ } /* @@ -260,8 +315,7 @@ hash_any(register const unsigned char *k, register int keylen) /* Set up the internal state */ len = keylen; - a = b = 0x9e3779b9; /* the golden ratio; an arbitrary value */ - c = 3923095; /* initialize with an arbitrary value */ + a = b = c = 0x9e3779b9 + len + 3923095; /* If the source pointer is word-aligned, we use word-wide fetches */ if (((long) k & UINT32_ALIGN_MASK) == 0) @@ -445,7 +499,7 @@ hash_any(register const unsigned char *k, register int keylen) #endif /* WORDS_BIGENDIAN */ } - mix(a, b, c); + final(a, b, c); /* report the result */ return UInt32GetDatum(c); @@ -465,11 +519,10 @@ hash_uint32(uint32 k) b, c; - a = 0x9e3779b9 + k; - b = 0x9e3779b9; - c = 3923095 + (uint32) sizeof(uint32); + a = b = c = 0x9e3779b9 + (uint32) sizeof(uint32) + 3923095; + a += k; - mix(a, b, c); + final(a, b, c); /* report the result */ return UInt32GetDatum(c); diff --git a/src/test/regress/expected/union.out b/src/test/regress/expected/union.out index 295dace..be046a9 100644 --- a/src/test/regress/expected/union.out +++ b/src/test/regress/expected/union.out @@ -263,16 +263,16 @@ ORDER BY 1; SELECT q2 FROM int8_tbl INTERSECT SELECT q1 FROM int8_tbl; q2 ------------------ - 123 4567890123456789 + 123 (2 rows) SELECT q2 FROM int8_tbl INTERSECT ALL SELECT q1 FROM int8_tbl; q2 ------------------ - 123 4567890123456789 4567890123456789 + 123 (3 rows) SELECT q2 FROM int8_tbl EXCEPT SELECT q1 FROM int8_tbl ORDER BY 1; @@ -305,16 +305,16 @@ SELECT q1 FROM int8_tbl EXCEPT SELECT q2 FROM int8_tbl; SELECT q1 FROM int8_tbl EXCEPT ALL SELECT q2 FROM int8_tbl; q1 ------------------ - 123 4567890123456789 + 123 (2 rows) SELECT q1 FROM int8_tbl EXCEPT ALL SELECT DISTINCT q2 FROM int8_tbl; q1 ------------------ - 123 4567890123456789 4567890123456789 + 123 (3 rows) -- @@ -341,8 +341,8 @@ SELECT f1 FROM float8_tbl EXCEPT SELECT f1 FROM int4_tbl ORDER BY 1; SELECT q1 FROM int8_tbl INTERSECT SELECT q2 FROM int8_tbl UNION ALL SELECT q2 FROM int8_tbl; q1 ------------------- - 123 4567890123456789 + 123 456 4567890123456789 123 @@ -353,15 +353,15 @@ SELECT q1 FROM int8_tbl INTERSECT SELECT q2 FROM int8_tbl UNION ALL SELECT q2 FR SELECT q1 FROM int8_tbl INTERSECT (((SELECT q2 FROM int8_tbl UNION ALL SELECT q2 FROM int8_tbl))); q1 ------------------ - 123 4567890123456789 + 123 (2 rows) (((SELECT q1 FROM int8_tbl INTERSECT SELECT q2 FROM int8_tbl))) UNION ALL SELECT q2 FROM int8_tbl; q1 ------------------- - 123 4567890123456789 + 123 456 4567890123456789 123 @@ -416,8 +416,8 @@ LINE 1: ... int8_tbl EXCEPT SELECT q2 FROM int8_tbl ORDER BY q2 LIMIT 1... SELECT q1 FROM int8_tbl EXCEPT (((SELECT q2 FROM int8_tbl ORDER BY q2 LIMIT 1))); q1 ------------------ - 123 4567890123456789 + 123 (2 rows) --