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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