_A Hash Function for Hash Table Lookup_
by Bob Jenkins

Example 1:

initialize(state)
for (each block)
{
  combine(state, block);
  mix(state);
}
return postprocess(state);


Example 2: Typical hash function

for (hash=0, i=0; i<hash; ++i)
  hash ^= ((hash<<5)^(hash>>27))^key[i];
return (hash % prime);

Listing One
typedef  unsigned long  int  ub4;   /* unsigned 4-byte quantities */
typedef  unsigned       char ub1;   /* unsigned 1-byte quantities */

#define hashsize(n) ((ub4)1<<(n))
#define hashmask(n) (hashsize(n)-1)

/* mix -- mix 3 32-bit values reversibly.
For every delta with one or two bits set, and the deltas of all three
  high bits or all three low bits, whether the original value of a,b,c
  is almost all zero or is uniformly distributed,
* If mix() is run forward or backward, at least 32 bits in a,b,c
  have at least 1/4 probability of changing.
* If mix() is run forward, every bit of c will change between 1/3 and
  2/3 of the time.  (Well, 22/100 and 78/100 for some 2-bit deltas.)
mix() takes 36 machine instructions, but only 18 cycles on a superscalar
  machine (like a Pentium or a Sparc).  No faster mixer seems to work,
  that's the result of my brute-force search.  There were about 2^68
  hashes to choose from.  I only tested about a billion of those.
*/
#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); \
}

/* 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.
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.
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);
By Bob Jenkins, 1996.  bob_jenkins@compuserve.com.  You may use this
code any way you wish, private, educational, or commercial.  It's free.
See http://ourworld.compuserve.com/homepages/bob_jenkins/evahash.htm
Use for hash table lookup, or anything where one collision in 2^^32 is
acceptable.  Do NOT use for cryptographic purposes.
*/

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 */
{
   register ub4 a,b,c,len;

   /* Set up the internal state */
   len = length;
   a = b = 0x9e3779b9;  /* the golden ratio; an arbitrary value */
   c = initval;         /* the previous hash value */

   /*---------------------------------------- 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;
   }
   /*------------------------------------- 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;
}

Listing Two
/* Additive Hash */
int additive(char *key, int len, int prime)
{
  int hash, i;
  for (hash=len, i=0; i<len; ++i) 
    hash += key[i];
  return (hash % prime);
}

/* Rotating Hash */
int rotating(char *key, int len, int prime)
{
  int hash, i;
  for (hash=len, i=0; i<len; ++i)
    hash = (hash<<5)^(hash>>27)^key[i];
  return (hash % prime);
}

/* Pearson's Hash */
char pearson(char *key, int len, char tab[256])
{
  char hash;
  int  i;
  for (hash=len, i=0; i<len; ++i) 
    hash=tab[hash^key[i]];
  return (hash);
}

/* CRC Hash and Generalized CRC Hash */
int crc(char *key, int len, int mask, int tab[256])
{
  int hash, i;
  for (hash=len, i=0; i<len; ++i)
    hash = (hash<<8)^tab[(hash>>24)^key[i]];
  return (hash & mask);
}

/* Universal Hash */
int universal(char *key, int len, int mask, int tab[MAXBITS])
{
  int hash, i;
  for (hash=len, i=0; i<(length<<3); i+=8)
  {
    register char k = key[i>>3];
    if (k&0x01) hash ^= tab[i+0];
    if (k&0x02) hash ^= tab[i+1];
    if (k&0x04) hash ^= tab[i+2];
    if (k&0x08) hash ^= tab[i+3];
    if (k&0x10) hash ^= tab[i+4];
    if (k&0x20) hash ^= tab[i+5];
    if (k&0x40) hash ^= tab[i+6];
    if (k&0x80) hash ^= tab[i+7];
  }
  return (hash & mask);
}

/* Zobrist Hash */
int zobrist( char *key, int len, int mask, int tab[MAXBYTES][256])
{
  int hash, i;
  for (hash=len, i=0; i<len; ++i)
    hash ^= tab[i][key[i]];
  return (hash & mask);
}

Listing Three 
/* Compute the Funnel-15 result for CRC */
void hum()
{
  ub4 i,j,k,whum,x;
  x=0x80000000;
  whum=31;
  for (i=0; i<(15*8); ++i)
  {
    x = (x & 0x80000000) ? ((x << 1) ^ 0x04c11db7) : (x << 1);
    printf("%.8lx\n",x);
    for (k=0, j=1; j; j=(j<<1)) if (j&x&0xff) ++k;
    if (k<whum)
    {
      printf("k is %ld\n",k);
      whum=k;
    }
  }
  printf("whum is %ld %ld %ld %ld\n",whum,x,k,j);
}