Patch: Better hash function
Steven Grimm
sgrimm at facebook.com
Thu Oct 12 00:22:16 UTC 2006
This patch replaces the old hash function with a newer one from the same
author (see http://www.burtleburtle.net/bob/hash/doobs.html -- this is
the code from lookup3.c referenced on that page). The new function is
significantly faster and produces better output.
The only controversial thing here is that there's now a test in
configure.ac to detect whether the system is little- or big-endian,
because the new algorithm needs to do different things depending on byte
order. I've tested it on MacOS X and Linux, but before I commit this I'd
appreciate some confirmation that the byte order test works on other
platforms.
-Steve
-------------- next part --------------
Index: assoc.c
===================================================================
--- assoc.c (revision 411)
+++ assoc.c (working copy)
@@ -12,6 +12,7 @@
*
* $Id$
*/
+#include "config.h"
#include <sys/types.h>
#include <sys/stat.h>
#include <sys/time.h>
@@ -39,91 +40,424 @@
#define hashsize(n) ((ub4)1<<(n))
#define hashmask(n) (hashsize(n)-1)
+/*
+ * Since the hash function does bit manipulation, it needs to know
+ * whether it's big or little-endian. ENDIAN_LITTLE and ENDIAN_BIG
+ * are set in the configure script.
+ */
+#if ENDIAN_BIG == 1
+# define HASH_LITTLE_ENDIAN 0
+# define HASH_BIG_ENDIAN 1
+#else
+# if ENDIAN_LITTLE == 1
+# define HASH_LITTLE_ENDIAN 1
+# define HASH_BIG_ENDIAN 0
+# else
+# define HASH_LITTLE_ENDIAN 0
+# define HASH_BIG_ENDIAN 0
+# endif
+#endif
+
+#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.
+
+Some k values for my "a-=c; a^=rot(c,k); c+=b;" arrangement that
+satisfy this are
+ 4 6 8 16 19 4
+ 9 15 3 18 27 15
+ 14 9 3 7 17 3
+Well, "9 15 3 18 27 15" didn't quite get 32 bits diffing
+for "differ" defined as + with a one-bit base and a two-bit delta. I
+used http://burtleburtle.net/bob/hash/avalanche.html to choose
+the operations, constants, and arrangements of the variables.
+
+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; \
}
/*
---------------------------------------------------------------------
-hash() -- 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
- initval : can be any 4-byte value
-Returns a 32-bit 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.
+-------------------------------------------------------------------------------
+final -- final mixing of 3 32-bit values (a,b,c) into c
-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. For example, if you need only 10 bits, do
- h = (h & hashmask(10));
-In which case, the hash table should have hashsize(10) elements.
+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.
-If you are hashing n strings (ub1 **)k, do it like this:
- for (i=0, h=0; i<n; ++i) h = hash( k[i], len[i], h);
+These constants passed:
+ 14 11 25 16 4 14 24
+ 12 14 25 16 4 14 24
+and these came close:
+ 4 8 15 26 3 22 24
+ 10 8 15 26 3 22 24
+ 11 8 15 26 3 22 24
+-------------------------------------------------------------------------------
+*/
+#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); \
+}
-By Bob Jenkins, 1996. bob_jenkins at burtleburtle.net. You may use this
-code any way you wish, private, educational, or commercial. It's free.
+#if HASH_LITTLE_ENDIAN == 1
+uint32_t hash(
+ const void *key, /* the key to hash */
+ size_t length, /* length of the key */
+ uint32_t initval) /* initval */
+{
+ uint32_t a,b,c; /* internal state */
+ union { const void *ptr; size_t i; } u; /* needed for Mac Powerbook G4 */
-See http://burtleburtle.net/bob/hash/evahash.html
-Use for hash table lookup, or anything where one collision in 2^^32 is
-acceptable. Do NOT use for cryptographic purposes.
---------------------------------------------------------------------
-*/
+ /* Set up the internal state */
+ a = b = c = 0xdeadbeef + ((uint32_t)length) + initval;
-ub4 hash( k, length, initval)
- register ub1 *k; /* the key */
- register ub4 length; /* the length of the key */
- register ub4 initval; /* the previous hash, or an arbitrary value */
+ u.ptr = key;
+ if (HASH_LITTLE_ENDIAN && ((u.i & 0x3) == 0)) {
+ const uint32_t *k = key; /* read 32-bit chunks */
+#ifdef VALGRIND
+ const uint8_t *k8;
+#endif // ifdef VALGRIND
+
+ /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
+ while (length > 12)
+ {
+ a += k[0];
+ b += k[1];
+ c += k[2];
+ mix(a,b,c);
+ length -= 12;
+ k += 3;
+ }
+
+ /*----------------------------- handle the last (probably partial) block */
+ /*
+ * "k[2]&0xffffff" actually reads beyond the end of the string, but
+ * then masks off the part it's not allowed to read. Because the
+ * string is aligned, the masked-off tail is in the same word as the
+ * rest of the string. Every machine with memory protection I've seen
+ * does it on word boundaries, so is OK with this. But VALGRIND will
+ * still catch it and complain. The masking trick does make the hash
+ * noticably faster for short strings (like English words).
+ */
+#ifndef VALGRIND
+
+ switch(length)
+ {
+ case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
+ case 11: c+=k[2]&0xffffff; b+=k[1]; a+=k[0]; break;
+ case 10: c+=k[2]&0xffff; b+=k[1]; a+=k[0]; break;
+ case 9 : c+=k[2]&0xff; b+=k[1]; a+=k[0]; break;
+ case 8 : b+=k[1]; a+=k[0]; break;
+ case 7 : b+=k[1]&0xffffff; a+=k[0]; break;
+ case 6 : b+=k[1]&0xffff; a+=k[0]; break;
+ case 5 : b+=k[1]&0xff; a+=k[0]; break;
+ case 4 : a+=k[0]; break;
+ case 3 : a+=k[0]&0xffffff; break;
+ case 2 : a+=k[0]&0xffff; break;
+ case 1 : a+=k[0]&0xff; break;
+ case 0 : return c; /* zero length strings require no mixing */
+ }
+
+#else /* make valgrind happy */
+
+ k8 = (const uint8_t *)k;
+ switch(length)
+ {
+ case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
+ case 11: c+=((uint32_t)k8[10])<<16; /* fall through */
+ case 10: c+=((uint32_t)k8[9])<<8; /* fall through */
+ case 9 : c+=k8[8]; /* fall through */
+ case 8 : b+=k[1]; a+=k[0]; break;
+ case 7 : b+=((uint32_t)k8[6])<<16; /* fall through */
+ case 6 : b+=((uint32_t)k8[5])<<8; /* fall through */
+ case 5 : b+=k8[4]; /* fall through */
+ case 4 : a+=k[0]; break;
+ case 3 : a+=((uint32_t)k8[2])<<16; /* fall through */
+ case 2 : a+=((uint32_t)k8[1])<<8; /* fall through */
+ case 1 : a+=k8[0]; break;
+ case 0 : return c; /* zero length strings require no mixing */
+ }
+
+#endif /* !valgrind */
+
+ } else if (HASH_LITTLE_ENDIAN && ((u.i & 0x1) == 0)) {
+ const uint16_t *k = key; /* read 16-bit chunks */
+ const uint8_t *k8;
+
+ /*--------------- all but last block: aligned reads and different mixing */
+ while (length > 12)
+ {
+ a += k[0] + (((uint32_t)k[1])<<16);
+ b += k[2] + (((uint32_t)k[3])<<16);
+ c += k[4] + (((uint32_t)k[5])<<16);
+ mix(a,b,c);
+ length -= 12;
+ k += 6;
+ }
+
+ /*----------------------------- handle the last (probably partial) block */
+ k8 = (const uint8_t *)k;
+ switch(length)
+ {
+ case 12: c+=k[4]+(((uint32_t)k[5])<<16);
+ b+=k[2]+(((uint32_t)k[3])<<16);
+ a+=k[0]+(((uint32_t)k[1])<<16);
+ break;
+ case 11: c+=((uint32_t)k8[10])<<16; /* fall through */
+ case 10: c+=k[4];
+ b+=k[2]+(((uint32_t)k[3])<<16);
+ a+=k[0]+(((uint32_t)k[1])<<16);
+ break;
+ case 9 : c+=k8[8]; /* fall through */
+ case 8 : b+=k[2]+(((uint32_t)k[3])<<16);
+ a+=k[0]+(((uint32_t)k[1])<<16);
+ break;
+ case 7 : b+=((uint32_t)k8[6])<<16; /* fall through */
+ case 6 : b+=k[2];
+ a+=k[0]+(((uint32_t)k[1])<<16);
+ break;
+ case 5 : b+=k8[4]; /* fall through */
+ case 4 : a+=k[0]+(((uint32_t)k[1])<<16);
+ break;
+ case 3 : a+=((uint32_t)k8[2])<<16; /* fall through */
+ case 2 : a+=k[0];
+ break;
+ case 1 : a+=k8[0];
+ break;
+ case 0 : return c; /* zero length strings require no mixing */
+ }
+
+ } else { /* need to read the key one byte at a time */
+ const uint8_t *k = key;
+
+ /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
+ while (length > 12)
+ {
+ a += k[0];
+ a += ((uint32_t)k[1])<<8;
+ a += ((uint32_t)k[2])<<16;
+ a += ((uint32_t)k[3])<<24;
+ b += k[4];
+ b += ((uint32_t)k[5])<<8;
+ b += ((uint32_t)k[6])<<16;
+ b += ((uint32_t)k[7])<<24;
+ c += k[8];
+ c += ((uint32_t)k[9])<<8;
+ c += ((uint32_t)k[10])<<16;
+ c += ((uint32_t)k[11])<<24;
+ mix(a,b,c);
+ length -= 12;
+ k += 12;
+ }
+
+ /*-------------------------------- last block: affect all 32 bits of (c) */
+ switch(length) /* all the case statements fall through */
+ {
+ case 12: c+=((uint32_t)k[11])<<24;
+ case 11: c+=((uint32_t)k[10])<<16;
+ case 10: c+=((uint32_t)k[9])<<8;
+ case 9 : c+=k[8];
+ case 8 : b+=((uint32_t)k[7])<<24;
+ case 7 : b+=((uint32_t)k[6])<<16;
+ case 6 : b+=((uint32_t)k[5])<<8;
+ case 5 : b+=k[4];
+ case 4 : a+=((uint32_t)k[3])<<24;
+ case 3 : a+=((uint32_t)k[2])<<16;
+ case 2 : a+=((uint32_t)k[1])<<8;
+ case 1 : a+=k[0];
+ break;
+ case 0 : return c; /* zero length strings require no mixing */
+ }
+ }
+
+ final(a,b,c);
+ return c; /* zero length strings require no mixing */
+}
+
+#elif HASH_BIG_ENDIAN == 1
+/*
+ * hashbig():
+ * This is the same as hashword() on big-endian machines. It is different
+ * from hashlittle() on all machines. hashbig() takes advantage of
+ * big-endian byte ordering.
+ */
+uint32_t hash( const void *key, size_t length, uint32_t initval)
{
- register ub4 a,b,c,len;
+ uint32_t a,b,c;
+ union { const void *ptr; size_t i; } u; /* to cast key to (size_t) happily */
- /* Set up the internal state */
- len = length;
- a = b = 0x9e3779b9; /* the golden ratio; an arbitrary value */
- c = initval; /* the previous hash value */
+ /* Set up the internal state */
+ a = b = c = 0xdeadbeef + ((uint32_t)length) + initval;
- /*---------------------------------------- handle most of the key */
- while (len >= 12)
- {
- a += (k[0] +((ub4)k[1]<<8) +((ub4)k[2]<<16) +((ub4)k[3]<<24));
- b += (k[4] +((ub4)k[5]<<8) +((ub4)k[6]<<16) +((ub4)k[7]<<24));
- c += (k[8] +((ub4)k[9]<<8) +((ub4)k[10]<<16)+((ub4)k[11]<<24));
- mix(a,b,c);
- k += 12; len -= 12;
- }
+ u.ptr = key;
+ if (HASH_BIG_ENDIAN && ((u.i & 0x3) == 0)) {
+ const uint32_t *k = key; /* read 32-bit chunks */
+#ifdef VALGRIND
+ const uint8_t *k8;
+#endif // ifdef VALGRIND
- /*------------------------------------- handle the last 11 bytes */
- c += length;
- switch(len) /* all the case statements fall through */
- {
- case 11: c+=((ub4)k[10]<<24);
- case 10: c+=((ub4)k[9]<<16);
- case 9 : c+=((ub4)k[8]<<8);
- /* the first byte of c is reserved for the length */
- case 8 : b+=((ub4)k[7]<<24);
- case 7 : b+=((ub4)k[6]<<16);
- case 6 : b+=((ub4)k[5]<<8);
- case 5 : b+=k[4];
- case 4 : a+=((ub4)k[3]<<24);
- case 3 : a+=((ub4)k[2]<<16);
- case 2 : a+=((ub4)k[1]<<8);
- case 1 : a+=k[0];
- /* case 0: nothing left to add */
- }
- mix(a,b,c);
- /*-------------------------------------------- report the result */
- return c;
+ /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */
+ while (length > 12)
+ {
+ a += k[0];
+ b += k[1];
+ c += k[2];
+ mix(a,b,c);
+ length -= 12;
+ k += 3;
+ }
+
+ /*----------------------------- handle the last (probably partial) block */
+ /*
+ * "k[2]<<8" actually reads beyond the end of the string, but
+ * then shifts out the part it's not allowed to read. Because the
+ * string is aligned, the illegal read is in the same word as the
+ * rest of the string. Every machine with memory protection I've seen
+ * does it on word boundaries, so is OK with this. But VALGRIND will
+ * still catch it and complain. The masking trick does make the hash
+ * noticably faster for short strings (like English words).
+ */
+#ifndef VALGRIND
+
+ switch(length)
+ {
+ case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
+ case 11: c+=k[2]&0xffffff00; b+=k[1]; a+=k[0]; break;
+ case 10: c+=k[2]&0xffff0000; b+=k[1]; a+=k[0]; break;
+ case 9 : c+=k[2]&0xff000000; b+=k[1]; a+=k[0]; break;
+ case 8 : b+=k[1]; a+=k[0]; break;
+ case 7 : b+=k[1]&0xffffff00; a+=k[0]; break;
+ case 6 : b+=k[1]&0xffff0000; a+=k[0]; break;
+ case 5 : b+=k[1]&0xff000000; a+=k[0]; break;
+ case 4 : a+=k[0]; break;
+ case 3 : a+=k[0]&0xffffff00; break;
+ case 2 : a+=k[0]&0xffff0000; break;
+ case 1 : a+=k[0]&0xff000000; break;
+ case 0 : return c; /* zero length strings require no mixing */
+ }
+
+#else /* make valgrind happy */
+
+ k8 = (const uint8_t *)k;
+ switch(length) /* all the case statements fall through */
+ {
+ case 12: c+=k[2]; b+=k[1]; a+=k[0]; break;
+ case 11: c+=((uint32_t)k8[10])<<8; /* fall through */
+ case 10: c+=((uint32_t)k8[9])<<16; /* fall through */
+ case 9 : c+=((uint32_t)k8[8])<<24; /* fall through */
+ case 8 : b+=k[1]; a+=k[0]; break;
+ case 7 : b+=((uint32_t)k8[6])<<8; /* fall through */
+ case 6 : b+=((uint32_t)k8[5])<<16; /* fall through */
+ case 5 : b+=((uint32_t)k8[4])<<24; /* fall through */
+ case 4 : a+=k[0]; break;
+ case 3 : a+=((uint32_t)k8[2])<<8; /* fall through */
+ case 2 : a+=((uint32_t)k8[1])<<16; /* fall through */
+ case 1 : a+=((uint32_t)k8[0])<<24; break;
+ case 0 : return c;
+ }
+
+#endif /* !VALGRIND */
+
+ } else { /* need to read the key one byte at a time */
+ const uint8_t *k = key;
+
+ /*--------------- all but the last block: affect some 32 bits of (a,b,c) */
+ while (length > 12)
+ {
+ a += ((uint32_t)k[0])<<24;
+ a += ((uint32_t)k[1])<<16;
+ a += ((uint32_t)k[2])<<8;
+ a += ((uint32_t)k[3]);
+ b += ((uint32_t)k[4])<<24;
+ b += ((uint32_t)k[5])<<16;
+ b += ((uint32_t)k[6])<<8;
+ b += ((uint32_t)k[7]);
+ c += ((uint32_t)k[8])<<24;
+ c += ((uint32_t)k[9])<<16;
+ c += ((uint32_t)k[10])<<8;
+ c += ((uint32_t)k[11]);
+ mix(a,b,c);
+ length -= 12;
+ k += 12;
+ }
+
+ /*-------------------------------- last block: affect all 32 bits of (c) */
+ switch(length) /* all the case statements fall through */
+ {
+ case 12: c+=k[11];
+ case 11: c+=((uint32_t)k[10])<<8;
+ case 10: c+=((uint32_t)k[9])<<16;
+ case 9 : c+=((uint32_t)k[8])<<24;
+ case 8 : b+=k[7];
+ case 7 : b+=((uint32_t)k[6])<<8;
+ case 6 : b+=((uint32_t)k[5])<<16;
+ case 5 : b+=((uint32_t)k[4])<<24;
+ case 4 : a+=k[3];
+ case 3 : a+=((uint32_t)k[2])<<8;
+ case 2 : a+=((uint32_t)k[1])<<16;
+ case 1 : a+=((uint32_t)k[0])<<24;
+ break;
+ case 0 : return c;
+ }
+ }
+
+ final(a,b,c);
+ return c;
}
+#else // HASH_XXX_ENDIAN == 1
+#error Must define HASH_BIG_ENDIAN or HASH_LITTLE_ENDIAN
+#endif // hash_XXX_ENDIAN == 1
static item** hashtable = 0;
Index: configure.ac
===================================================================
--- configure.ac (revision 411)
+++ configure.ac (working copy)
@@ -129,6 +129,32 @@
AC_C_SOCKLEN_T
+dnl Check if we're a little-endian or a big-endian system, needed by hash code
+AC_DEFUN(AC_C_ENDIAN,
+[AC_CACHE_CHECK(for endianness, ac_cv_c_endian,
+[
+ AC_RUN_IFELSE(
+ [AC_LANG_PROGRAM([], [dnl
+ long val = 1;
+ char *c = (char *) &val;
+ exit(*c == 1);
+ ])
+ ],[
+ ac_cv_c_endian=big
+ ],[
+ ac_cv_c_endian=little
+ ])
+])
+if test $ac_cv_c_endian = big; then
+ AC_DEFINE(ENDIAN_BIG, 1, [machine is bigendian])
+fi
+if test $ac_cv_c_endian = little; then
+ AC_DEFINE(ENDIAN_LITTLE, 1, [machine is littleendian])
+fi
+])
+
+AC_C_ENDIAN
+
AC_CHECK_FUNCS(mlockall)
AC_CONFIG_FILES(Makefile doc/Makefile)
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