path: root/src/common/hashfn.c

/*-------------------------------------------------------------------------
 *
 * hashfn.c
 *		Generic hashing functions, and hash functions for use in dynahash.c
 *		hashtables
 *
 *
 * Portions Copyright (c) 1996-2020, 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"


/*
 * 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)

/* Rotate a uint32 value left by k bits - note multiple evaluation! */
#define rot(x,k) (((x)<<(k)) | ((x)>>(32-(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));
}