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+/*-------------------------------------------------------------------------
+ *
+ * hashfn.c
+ * Generic hashing functions, and hash functions for use in dynahash.c
+ * hashtables
+ *
+ *
+ * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ *
+ * IDENTIFICATION
+ * src/common/hashfn.c
+ *
+ * NOTES
+ * It is expected that every bit of a hash function's 32-bit result is
+ * as random as every other; failure to ensure this is likely to lead
+ * to poor performance of hash tables. In most cases a hash
+ * function should use hash_bytes() or its variant hash_bytes_uint32(),
+ * or the wrappers hash_any() and hash_uint32 defined in hashfn.h.
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include "common/hashfn.h"
+#include "port/pg_bitutils.h"
+
+
+/*
+ * This hash function was written by Bob Jenkins
+ * (bob_jenkins@burtleburtle.net), and superficially adapted
+ * for PostgreSQL by Neil Conway. For more information on this
+ * 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 Bob's 2006 update of his hash
+ * function 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).
+ * It also uses 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) pg_rotate_left32(x, k)
+
+/*----------
+ * mix -- mix 3 32-bit values reversibly.
+ *
+ * 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 from 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 -= 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); \
+}
+
+/*
+ * hash_bytes() -- hash a variable-length key into a 32-bit value
+ * k : the key (the unaligned variable-length array of bytes)
+ * len : the length of the key, counting by bytes
+ *
+ * Returns a uint32 value. Every bit of the key affects every bit of
+ * the return value. Every 1-bit and 2-bit delta achieves avalanche.
+ * About 6*len+35 instructions. The best hash table sizes are powers
+ * of 2. There is no need to do mod a prime (mod is sooo slow!).
+ * If you need less than 32 bits, use a bitmask.
+ *
+ * This procedure must never throw elog(ERROR); the ResourceOwner code
+ * relies on this not to fail.
+ *
+ * Note: we could easily change this function to return a 64-bit hash value
+ * by using the final values of both b and c. b is perhaps a little less
+ * well mixed than c, however.
+ */
+uint32
+hash_bytes(const unsigned char *k, int keylen)
+{
+ uint32 a,
+ b,
+ c,
+ len;
+
+ /* Set up the internal state */
+ len = keylen;
+ a = b = c = 0x9e3779b9 + len + 3923095;
+
+ /* If the source pointer is word-aligned, we use word-wide fetches */
+ if (((uintptr_t) k & UINT32_ALIGN_MASK) == 0)
+ {
+ /* Code path for aligned source data */
+ const uint32 *ka = (const uint32 *) k;
+
+ /* handle most of the key */
+ while (len >= 12)
+ {
+ a += ka[0];
+ b += ka[1];
+ c += ka[2];
+ mix(a, b, c);
+ ka += 3;
+ len -= 12;
+ }
+
+ /* handle the last 11 bytes */
+ k = (const unsigned char *) ka;
+#ifdef WORDS_BIGENDIAN
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 8);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 24);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ka[1];
+ a += ka[0];
+ break;
+ case 7:
+ b += ((uint32) k[6] << 8);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 16);
+ /* fall through */
+ case 5:
+ b += ((uint32) k[4] << 24);
+ /* fall through */
+ case 4:
+ a += ka[0];
+ break;
+ case 3:
+ a += ((uint32) k[2] << 8);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 16);
+ /* fall through */
+ case 1:
+ a += ((uint32) k[0] << 24);
+ /* case 0: nothing left to add */
+ }
+#else /* !WORDS_BIGENDIAN */
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 24);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 8);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ka[1];
+ a += ka[0];
+ break;
+ case 7:
+ b += ((uint32) k[6] << 16);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 8);
+ /* fall through */
+ case 5:
+ b += k[4];
+ /* fall through */
+ case 4:
+ a += ka[0];
+ break;
+ case 3:
+ a += ((uint32) k[2] << 16);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 8);
+ /* fall through */
+ case 1:
+ a += k[0];
+ /* case 0: nothing left to add */
+ }
+#endif /* WORDS_BIGENDIAN */
+ }
+ else
+ {
+ /* Code path for non-aligned source data */
+
+ /* handle most of the key */
+ while (len >= 12)
+ {
+#ifdef WORDS_BIGENDIAN
+ a += (k[3] + ((uint32) k[2] << 8) + ((uint32) k[1] << 16) + ((uint32) k[0] << 24));
+ b += (k[7] + ((uint32) k[6] << 8) + ((uint32) k[5] << 16) + ((uint32) k[4] << 24));
+ c += (k[11] + ((uint32) k[10] << 8) + ((uint32) k[9] << 16) + ((uint32) k[8] << 24));
+#else /* !WORDS_BIGENDIAN */
+ a += (k[0] + ((uint32) k[1] << 8) + ((uint32) k[2] << 16) + ((uint32) k[3] << 24));
+ b += (k[4] + ((uint32) k[5] << 8) + ((uint32) k[6] << 16) + ((uint32) k[7] << 24));
+ c += (k[8] + ((uint32) k[9] << 8) + ((uint32) k[10] << 16) + ((uint32) k[11] << 24));
+#endif /* WORDS_BIGENDIAN */
+ mix(a, b, c);
+ k += 12;
+ len -= 12;
+ }
+
+ /* handle the last 11 bytes */
+#ifdef WORDS_BIGENDIAN
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 8);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 24);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += k[7];
+ /* fall through */
+ case 7:
+ b += ((uint32) k[6] << 8);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 16);
+ /* fall through */
+ case 5:
+ b += ((uint32) k[4] << 24);
+ /* fall through */
+ case 4:
+ a += k[3];
+ /* fall through */
+ case 3:
+ a += ((uint32) k[2] << 8);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 16);
+ /* fall through */
+ case 1:
+ a += ((uint32) k[0] << 24);
+ /* case 0: nothing left to add */
+ }
+#else /* !WORDS_BIGENDIAN */
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 24);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 8);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ((uint32) k[7] << 24);
+ /* fall through */
+ case 7:
+ b += ((uint32) k[6] << 16);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 8);
+ /* fall through */
+ case 5:
+ b += k[4];
+ /* fall through */
+ case 4:
+ a += ((uint32) k[3] << 24);
+ /* fall through */
+ case 3:
+ a += ((uint32) k[2] << 16);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 8);
+ /* fall through */
+ case 1:
+ a += k[0];
+ /* case 0: nothing left to add */
+ }
+#endif /* WORDS_BIGENDIAN */
+ }
+
+ final(a, b, c);
+
+ /* report the result */
+ return c;
+}
+
+/*
+ * hash_bytes_extended() -- hash into a 64-bit value, using an optional seed
+ * k : the key (the unaligned variable-length array of bytes)
+ * len : the length of the key, counting by bytes
+ * seed : a 64-bit seed (0 means no seed)
+ *
+ * Returns a uint64 value. Otherwise similar to hash_bytes.
+ */
+uint64
+hash_bytes_extended(const unsigned char *k, int keylen, uint64 seed)
+{
+ uint32 a,
+ b,
+ c,
+ len;
+
+ /* Set up the internal state */
+ len = keylen;
+ a = b = c = 0x9e3779b9 + len + 3923095;
+
+ /* If the seed is non-zero, use it to perturb the internal state. */
+ if (seed != 0)
+ {
+ /*
+ * In essence, the seed is treated as part of the data being hashed,
+ * but for simplicity, we pretend that it's padded with four bytes of
+ * zeroes so that the seed constitutes a 12-byte chunk.
+ */
+ a += (uint32) (seed >> 32);
+ b += (uint32) seed;
+ mix(a, b, c);
+ }
+
+ /* If the source pointer is word-aligned, we use word-wide fetches */
+ if (((uintptr_t) k & UINT32_ALIGN_MASK) == 0)
+ {
+ /* Code path for aligned source data */
+ const uint32 *ka = (const uint32 *) k;
+
+ /* handle most of the key */
+ while (len >= 12)
+ {
+ a += ka[0];
+ b += ka[1];
+ c += ka[2];
+ mix(a, b, c);
+ ka += 3;
+ len -= 12;
+ }
+
+ /* handle the last 11 bytes */
+ k = (const unsigned char *) ka;
+#ifdef WORDS_BIGENDIAN
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 8);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 24);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ka[1];
+ a += ka[0];
+ break;
+ case 7:
+ b += ((uint32) k[6] << 8);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 16);
+ /* fall through */
+ case 5:
+ b += ((uint32) k[4] << 24);
+ /* fall through */
+ case 4:
+ a += ka[0];
+ break;
+ case 3:
+ a += ((uint32) k[2] << 8);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 16);
+ /* fall through */
+ case 1:
+ a += ((uint32) k[0] << 24);
+ /* case 0: nothing left to add */
+ }
+#else /* !WORDS_BIGENDIAN */
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 24);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 8);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ka[1];
+ a += ka[0];
+ break;
+ case 7:
+ b += ((uint32) k[6] << 16);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 8);
+ /* fall through */
+ case 5:
+ b += k[4];
+ /* fall through */
+ case 4:
+ a += ka[0];
+ break;
+ case 3:
+ a += ((uint32) k[2] << 16);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 8);
+ /* fall through */
+ case 1:
+ a += k[0];
+ /* case 0: nothing left to add */
+ }
+#endif /* WORDS_BIGENDIAN */
+ }
+ else
+ {
+ /* Code path for non-aligned source data */
+
+ /* handle most of the key */
+ while (len >= 12)
+ {
+#ifdef WORDS_BIGENDIAN
+ a += (k[3] + ((uint32) k[2] << 8) + ((uint32) k[1] << 16) + ((uint32) k[0] << 24));
+ b += (k[7] + ((uint32) k[6] << 8) + ((uint32) k[5] << 16) + ((uint32) k[4] << 24));
+ c += (k[11] + ((uint32) k[10] << 8) + ((uint32) k[9] << 16) + ((uint32) k[8] << 24));
+#else /* !WORDS_BIGENDIAN */
+ a += (k[0] + ((uint32) k[1] << 8) + ((uint32) k[2] << 16) + ((uint32) k[3] << 24));
+ b += (k[4] + ((uint32) k[5] << 8) + ((uint32) k[6] << 16) + ((uint32) k[7] << 24));
+ c += (k[8] + ((uint32) k[9] << 8) + ((uint32) k[10] << 16) + ((uint32) k[11] << 24));
+#endif /* WORDS_BIGENDIAN */
+ mix(a, b, c);
+ k += 12;
+ len -= 12;
+ }
+
+ /* handle the last 11 bytes */
+#ifdef WORDS_BIGENDIAN
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 8);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 24);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += k[7];
+ /* fall through */
+ case 7:
+ b += ((uint32) k[6] << 8);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 16);
+ /* fall through */
+ case 5:
+ b += ((uint32) k[4] << 24);
+ /* fall through */
+ case 4:
+ a += k[3];
+ /* fall through */
+ case 3:
+ a += ((uint32) k[2] << 8);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 16);
+ /* fall through */
+ case 1:
+ a += ((uint32) k[0] << 24);
+ /* case 0: nothing left to add */
+ }
+#else /* !WORDS_BIGENDIAN */
+ switch (len)
+ {
+ case 11:
+ c += ((uint32) k[10] << 24);
+ /* fall through */
+ case 10:
+ c += ((uint32) k[9] << 16);
+ /* fall through */
+ case 9:
+ c += ((uint32) k[8] << 8);
+ /* fall through */
+ case 8:
+ /* the lowest byte of c is reserved for the length */
+ b += ((uint32) k[7] << 24);
+ /* fall through */
+ case 7:
+ b += ((uint32) k[6] << 16);
+ /* fall through */
+ case 6:
+ b += ((uint32) k[5] << 8);
+ /* fall through */
+ case 5:
+ b += k[4];
+ /* fall through */
+ case 4:
+ a += ((uint32) k[3] << 24);
+ /* fall through */
+ case 3:
+ a += ((uint32) k[2] << 16);
+ /* fall through */
+ case 2:
+ a += ((uint32) k[1] << 8);
+ /* fall through */
+ case 1:
+ a += k[0];
+ /* case 0: nothing left to add */
+ }
+#endif /* WORDS_BIGENDIAN */
+ }
+
+ final(a, b, c);
+
+ /* report the result */
+ return ((uint64) b << 32) | c;
+}
+
+/*
+ * hash_bytes_uint32() -- hash a 32-bit value to a 32-bit value
+ *
+ * This has the same result as
+ * hash_bytes(&k, sizeof(uint32))
+ * but is faster and doesn't force the caller to store k into memory.
+ */
+uint32
+hash_bytes_uint32(uint32 k)
+{
+ uint32 a,
+ b,
+ c;
+
+ a = b = c = 0x9e3779b9 + (uint32) sizeof(uint32) + 3923095;
+ a += k;
+
+ final(a, b, c);
+
+ /* report the result */
+ return c;
+}
+
+/*
+ * hash_bytes_uint32_extended() -- hash 32-bit value to 64-bit value, with seed
+ *
+ * Like hash_bytes_uint32, this is a convenience function.
+ */
+uint64
+hash_bytes_uint32_extended(uint32 k, uint64 seed)
+{
+ uint32 a,
+ b,
+ c;
+
+ a = b = c = 0x9e3779b9 + (uint32) sizeof(uint32) + 3923095;
+
+ if (seed != 0)
+ {
+ a += (uint32) (seed >> 32);
+ b += (uint32) seed;
+ mix(a, b, c);
+ }
+
+ a += k;
+
+ final(a, b, c);
+
+ /* report the result */
+ return ((uint64) b << 32) | c;
+}
+
+/*
+ * string_hash: hash function for keys that are NUL-terminated strings.
+ *
+ * NOTE: this is the default hash function if none is specified.
+ */
+uint32
+string_hash(const void *key, Size keysize)
+{
+ /*
+ * If the string exceeds keysize-1 bytes, we want to hash only that many,
+ * because when it is copied into the hash table it will be truncated at
+ * that length.
+ */
+ Size s_len = strlen((const char *) key);
+
+ s_len = Min(s_len, keysize - 1);
+ return hash_bytes((const unsigned char *) key, (int) s_len);
+}
+
+/*
+ * tag_hash: hash function for fixed-size tag values
+ */
+uint32
+tag_hash(const void *key, Size keysize)
+{
+ return hash_bytes((const unsigned char *) key, (int) keysize);
+}
+
+/*
+ * uint32_hash: hash function for keys that are uint32 or int32
+ *
+ * (tag_hash works for this case too, but is slower)
+ */
+uint32
+uint32_hash(const void *key, Size keysize)
+{
+ Assert(keysize == sizeof(uint32));
+ return hash_bytes_uint32(*((const uint32 *) key));
+}
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