sys/libkern/jenkins_hash.c

#ifndef __LIBKERN_JENKINS_H__
#define __LIBKERN_JENKINS_H__
/*
 * Taken from http://burtleburtle.net/bob/c/lookup3.c
 * $FreeBSD: head/sys/libkern/jenkins.h 218965 2011-02-23 09:22:33Z brucec $
 */

/*
-------------------------------------------------------------------------------
  lookup3.c, by Bob Jenkins, May 2006, Public Domain.

  These are functions for producing 32-bit hashes for hash table lookup.
  hashword(), hashlittle(), hashlittle2(), hashbig(), mix(), and final()
  are externally useful functions.  Routines to test the hash are included
  if SELF_TEST is defined.  You can use this free for any purpose.  It's in
  the public domain.  It has no warranty.

  You probably want to use hashlittle().  hashlittle() and hashbig()
  hash byte arrays.  hashlittle() is faster than hashbig() on
  little-endian machines.  Intel and AMD are little-endian machines.
  On second thought, you probably want hashlittle2(), which is identical to
  hashlittle() except it returns two 32-bit hashes for the price of one.
  You could implement hashbig2() if you wanted but I haven't bothered here.

  If you want to find a hash of, say, exactly 7 integers, do
    a = i1;  b = i2;  c = i3;
    mix(a,b,c);
    a += i4; b += i5; c += i6;
    mix(a,b,c);
    a += i7;
    final(a,b,c);
  then use c as the hash value.  If you have a variable length array of
  4-byte integers to hash, use hashword().  If you have a byte array (like
  a character string), use hashlittle().  If you have several byte arrays, or
  a mix of things, see the comments above hashlittle().

  Why is this so big?  I read 12 bytes at a time into 3 4-byte integers,
  then mix those integers.  This is fast (you can do a lot more thorough
  mixing with 12*3 instructions on 3 integers than you can with 3 instructions
  on 1 byte), but shoehorning those bytes into integers efficiently is messy.
-------------------------------------------------------------------------------
*/

#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 -= 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.

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); \
}

/*
--------------------------------------------------------------------
 This works on all machines.  To be useful, it requires
 -- that the key be an array of uint32_t's, and
 -- that the length be the number of uint32_t's in the key

 The function hashword() is identical to hashlittle() on little-endian
 machines, and identical to hashbig() on big-endian machines,
 except that the length has to be measured in uint32_ts rather than in
 bytes.  hashlittle() is more complicated than hashword() only because
 hashlittle() has to dance around fitting the key bytes into registers.
--------------------------------------------------------------------
*/
static uint32_t
jenkins_hashword(
                const uint32_t *k,  /* the key, an array of uint32_t values */
                size_t length,      /* the length of the key, in uint32_ts */
                uint32_t initval    /* the previous hash, or an arbitrary value */
)
{
  uint32_t a,b,c;

  /* Set up the internal state */
  a = b = c = 0xdeadbeef + (((uint32_t)length)<<2) + initval;

  /*------------------------------------------------- handle most of the key */
  while (length > 3)
  {
    a += k[0];
    b += k[1];
    c += k[2];
    mix(a,b,c);
    length -= 3;
    k += 3;
  }

  /*------------------------------------------- handle the last 3 uint32_t's */
  switch(length)                     /* all the case statements fall through */
  {
  case 3 : c+=k[2];
  case 2 : b+=k[1];
  case 1 : a+=k[0];
    final(a,b,c);
  case 0:     /* case 0: nothing left to add */
    break;
  }
  /*------------------------------------------------------ report the result */
  return c;
}
#endif