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@ -8,7 +8,7 @@ |
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* |
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* |
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* IDENTIFICATION |
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* $PostgreSQL: pgsql/src/backend/access/hash/hashfunc.c,v 1.57 2009/01/01 17:23:35 momjian Exp $ |
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* $PostgreSQL: pgsql/src/backend/access/hash/hashfunc.c,v 1.58 2009/02/09 21:18:28 tgl Exp $ |
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* |
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* NOTES |
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* These functions are stored in pg_amproc. For each operator class |
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@ -200,39 +200,95 @@ hashvarlena(PG_FUNCTION_ARGS) |
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* hash function, see http://burtleburtle.net/bob/hash/doobs.html,
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* or Bob's article in Dr. Dobb's Journal, Sept. 1997. |
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* |
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* In the current code, we have adopted an idea from Bob's 2006 update |
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* of his hash function, which is to fetch the data a word at a time when |
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* it is suitably aligned. This makes for a useful speedup, at the cost |
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* of having to maintain four code paths (aligned vs unaligned, and |
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* little-endian vs big-endian). Note that we have NOT adopted his newer |
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* mix() function, which is faster but may sacrifice some randomness. |
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* In the current code, we have adopted Bob's 2006 update of his hash |
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* function to fetch the data a word at a time when it is suitably aligned. |
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* This makes for a useful speedup, at the cost of having to maintain |
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* four code paths (aligned vs unaligned, and little-endian vs big-endian). |
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* It also uses two separate mixing functions mix() and final(), instead |
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* of a slower multi-purpose function. |
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*/ |
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/* Get a bit mask of the bits set in non-uint32 aligned addresses */ |
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#define UINT32_ALIGN_MASK (sizeof(uint32) - 1) |
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/* Rotate a uint32 value left by k bits - note multiple evaluation! */ |
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#define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) |
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/*----------
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* mix -- mix 3 32-bit values reversibly. |
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* For every delta with one or two bits set, and the deltas of all three |
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* high bits or all three low bits, whether the original value of a,b,c |
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* is almost all zero or is uniformly distributed, |
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* - If mix() is run forward or backward, at least 32 bits in a,b,c |
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* have at least 1/4 probability of changing. |
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* - If mix() is run forward, every bit of c will change between 1/3 and |
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* 2/3 of the time. (Well, 22/100 and 78/100 for some 2-bit deltas.) |
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* |
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* This is reversible, so any information in (a,b,c) before mix() is |
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* still in (a,b,c) after mix(). |
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* |
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* If four pairs of (a,b,c) inputs are run through mix(), or through |
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* mix() in reverse, there are at least 32 bits of the output that |
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* are sometimes the same for one pair and different for another pair. |
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* This was tested for: |
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* * pairs that differed by one bit, by two bits, in any combination |
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* of top bits of (a,b,c), or in any combination of bottom bits of |
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* (a,b,c). |
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* * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed |
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* the output delta to a Gray code (a^(a>>1)) so a string of 1's (as |
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* is commonly produced by subtraction) look like a single 1-bit |
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* difference. |
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* * the base values were pseudorandom, all zero but one bit set, or |
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* all zero plus a counter that starts at zero. |
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*
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* This does not achieve avalanche. There are input bits of (a,b,c) |
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* that fail to affect some output bits of (a,b,c), especially of a. The |
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* most thoroughly mixed value is c, but it doesn't really even achieve |
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* avalanche in c.
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*
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* This allows some parallelism. Read-after-writes are good at doubling |
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* the number of bits affected, so the goal of mixing pulls in the opposite |
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* direction from the goal of parallelism. I did what I could. Rotates |
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* seem to cost as much as shifts on every machine I could lay my hands on, |
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* and rotates are much kinder to the top and bottom bits, so I used rotates. |
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*---------- |
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*/ |
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#define mix(a,b,c) \ |
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{ \
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a -= b; a -= c; a ^= ((c)>>13); \
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b -= c; b -= a; b ^= ((a)<<8); \
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c -= a; c -= b; c ^= ((b)>>13); \
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a -= b; a -= c; a ^= ((c)>>12); \
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b -= c; b -= a; b ^= ((a)<<16); \
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c -= a; c -= b; c ^= ((b)>>5); \
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a -= b; a -= c; a ^= ((c)>>3); \
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b -= c; b -= a; b ^= ((a)<<10); \
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c -= a; c -= b; c ^= ((b)>>15); \
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a -= c; a ^= rot(c, 4); c += b; \
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b -= a; b ^= rot(a, 6); a += c; \
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c -= b; c ^= rot(b, 8); b += a; \
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a -= c; a ^= rot(c,16); c += b; \
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b -= a; b ^= rot(a,19); a += c; \
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c -= b; c ^= rot(b, 4); b += a; \
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} |
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/*----------
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* final -- final mixing of 3 32-bit values (a,b,c) into c |
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* |
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* Pairs of (a,b,c) values differing in only a few bits will usually |
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* produce values of c that look totally different. This was tested for |
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* * pairs that differed by one bit, by two bits, in any combination |
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* of top bits of (a,b,c), or in any combination of bottom bits of |
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* (a,b,c). |
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* * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed |
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* the output delta to a Gray code (a^(a>>1)) so a string of 1's (as |
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* is commonly produced by subtraction) look like a single 1-bit |
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* difference. |
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* * the base values were pseudorandom, all zero but one bit set, or |
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* all zero plus a counter that starts at zero. |
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*
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* The use of separate functions for mix() and final() allow for a |
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* substantial performance increase since final() does not need to |
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* do well in reverse, but is does need to affect all output bits. |
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* mix(), on the other hand, does not need to affect all output |
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* bits (affecting 32 bits is enough). The original hash function had |
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* a single mixing operation that had to satisfy both sets of requirements |
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* and was slower as a result. |
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*---------- |
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*/ |
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#define final(a,b,c) \ |
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{ \
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c ^= b; c -= rot(b,14); \
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a ^= c; a -= rot(c,11); \
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b ^= a; b -= rot(a,25); \
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c ^= b; c -= rot(b,16); \
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a ^= c; a -= rot(c, 4); \
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b ^= a; b -= rot(a,14); \
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c ^= b; c -= rot(b,24); \
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} |
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/*
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@ -260,8 +316,7 @@ hash_any(register const unsigned char *k, register int keylen) |
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/* Set up the internal state */ |
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len = keylen; |
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a = b = 0x9e3779b9; /* the golden ratio; an arbitrary value */ |
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c = 3923095; /* initialize with an arbitrary value */ |
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a = b = c = 0x9e3779b9 + len + 3923095; |
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/* If the source pointer is word-aligned, we use word-wide fetches */ |
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if (((long) k & UINT32_ALIGN_MASK) == 0) |
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@ -282,7 +337,6 @@ hash_any(register const unsigned char *k, register int keylen) |
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/* handle the last 11 bytes */ |
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k = (const unsigned char *) ka; |
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c += keylen; |
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#ifdef WORDS_BIGENDIAN |
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switch (len) |
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{ |
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@ -385,7 +439,6 @@ hash_any(register const unsigned char *k, register int keylen) |
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} |
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/* handle the last 11 bytes */ |
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c += keylen; |
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#ifdef WORDS_BIGENDIAN |
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switch (len) /* all the case statements fall through */ |
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{ |
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@ -445,7 +498,7 @@ hash_any(register const unsigned char *k, register int keylen) |
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#endif /* WORDS_BIGENDIAN */ |
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} |
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mix(a, b, c); |
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final(a, b, c); |
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/* report the result */ |
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return UInt32GetDatum(c); |
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@ -465,11 +518,10 @@ hash_uint32(uint32 k) |
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b, |
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c; |
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a = 0x9e3779b9 + k; |
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b = 0x9e3779b9; |
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c = 3923095 + (uint32) sizeof(uint32); |
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a = b = c = 0x9e3779b9 + (uint32) sizeof(uint32) + 3923095; |
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a += k; |
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mix(a, b, c); |
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final(a, b, c); |
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/* report the result */ |
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return UInt32GetDatum(c); |
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