| 1 | /* |
| 2 | ------------------------------------------------------------------------------- |
| 3 | lookup3.c, by Bob Jenkins, May 2006, Public Domain. |
| 4 | |
| 5 | These are functions for producing 32-bit hashes for hash table lookup. |
| 6 | hashword(), hashlittle(), hashlittle2(), hashbig(), mix(), and final() |
| 7 | are externally useful functions. Routines to test the hash are included |
| 8 | if SELF_TEST is defined. You can use this free for any purpose. It's in |
| 9 | the public domain. It has no warranty. |
| 10 | |
| 11 | You probably want to use hashlittle(). hashlittle() and hashbig() |
| 12 | hash byte arrays. hashlittle() is is faster than hashbig() on |
| 13 | little-endian machines. Intel and AMD are little-endian machines. |
| 14 | On second thought, you probably want hashlittle2(), which is identical to |
| 15 | hashlittle() except it returns two 32-bit hashes for the price of one. |
| 16 | You could implement hashbig2() if you wanted but I haven't bothered here. |
| 17 | |
| 18 | If you want to find a hash of, say, exactly 7 integers, do |
| 19 | a = i1; b = i2; c = i3; |
| 20 | mix(a,b,c); |
| 21 | a += i4; b += i5; c += i6; |
| 22 | mix(a,b,c); |
| 23 | a += i7; |
| 24 | final(a,b,c); |
| 25 | then use c as the hash value. If you have a variable length array of |
| 26 | 4-byte integers to hash, use hashword(). If you have a byte array (like |
| 27 | a character string), use hashlittle(). If you have several byte arrays, or |
| 28 | a mix of things, see the comments above hashlittle(). |
| 29 | |
| 30 | Why is this so big? I read 12 bytes at a time into 3 4-byte integers, |
| 31 | then mix those integers. This is fast (you can do a lot more thorough |
| 32 | mixing with 12*3 instructions on 3 integers than you can with 3 instructions |
| 33 | on 1 byte), but shoehorning those bytes into integers efficiently is messy. |
| 34 | ------------------------------------------------------------------------------- |
| 35 | */ |
| 36 | |
| 37 | /* |
| 38 | * Only minimal parts kept, see http://burtleburtle.net/bob/hash/doobs.html for |
| 39 | * full file and great info. |
| 40 | */ |
| 41 | |
| 42 | #ifndef LOOKUP_H |
| 43 | #define LOOKUP_H |
| 44 | |
| 45 | #include <stdint.h> /* defines uint32_t etc */ |
| 46 | |
| 47 | |
| 48 | #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) |
| 49 | |
| 50 | |
| 51 | /* |
| 52 | ------------------------------------------------------------------------------- |
| 53 | mix -- mix 3 32-bit values reversibly. |
| 54 | |
| 55 | This is reversible, so any information in (a,b,c) before mix() is |
| 56 | still in (a,b,c) after mix(). |
| 57 | |
| 58 | If four pairs of (a,b,c) inputs are run through mix(), or through |
| 59 | mix() in reverse, there are at least 32 bits of the output that |
| 60 | are sometimes the same for one pair and different for another pair. |
| 61 | This was tested for: |
| 62 | * pairs that differed by one bit, by two bits, in any combination |
| 63 | of top bits of (a,b,c), or in any combination of bottom bits of |
| 64 | (a,b,c). |
| 65 | * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed |
| 66 | the output delta to a Gray code (a^(a>>1)) so a string of 1's (as |
| 67 | is commonly produced by subtraction) look like a single 1-bit |
| 68 | difference. |
| 69 | * the base values were pseudorandom, all zero but one bit set, or |
| 70 | all zero plus a counter that starts at zero. |
| 71 | |
| 72 | Some k values for my "a-=c; a^=rot(c,k); c+=b;" arrangement that |
| 73 | satisfy this are |
| 74 | 4 6 8 16 19 4 |
| 75 | 9 15 3 18 27 15 |
| 76 | 14 9 3 7 17 3 |
| 77 | Well, "9 15 3 18 27 15" didn't quite get 32 bits diffing |
| 78 | for "differ" defined as + with a one-bit base and a two-bit delta. I |
| 79 | used http://burtleburtle.net/bob/hash/avalanche.html to choose |
| 80 | the operations, constants, and arrangements of the variables. |
| 81 | |
| 82 | This does not achieve avalanche. There are input bits of (a,b,c) |
| 83 | that fail to affect some output bits of (a,b,c), especially of a. The |
| 84 | most thoroughly mixed value is c, but it doesn't really even achieve |
| 85 | avalanche in c. |
| 86 | |
| 87 | This allows some parallelism. Read-after-writes are good at doubling |
| 88 | the number of bits affected, so the goal of mixing pulls in the opposite |
| 89 | direction as the goal of parallelism. I did what I could. Rotates |
| 90 | seem to cost as much as shifts on every machine I could lay my hands |
| 91 | on, and rotates are much kinder to the top and bottom bits, so I used |
| 92 | rotates. |
| 93 | ------------------------------------------------------------------------------- |
| 94 | */ |
| 95 | #define mix(a,b,c) \ |
| 96 | { \ |
| 97 | a -= c; a ^= rot(c, 4); c += b; \ |
| 98 | b -= a; b ^= rot(a, 6); a += c; \ |
| 99 | c -= b; c ^= rot(b, 8); b += a; \ |
| 100 | a -= c; a ^= rot(c,16); c += b; \ |
| 101 | b -= a; b ^= rot(a,19); a += c; \ |
| 102 | c -= b; c ^= rot(b, 4); b += a; \ |
| 103 | } |
| 104 | |
| 105 | |
| 106 | /* |
| 107 | ------------------------------------------------------------------------------- |
| 108 | final -- final mixing of 3 32-bit values (a,b,c) into c |
| 109 | |
| 110 | Pairs of (a,b,c) values differing in only a few bits will usually |
| 111 | produce values of c that look totally different. This was tested for |
| 112 | * pairs that differed by one bit, by two bits, in any combination |
| 113 | of top bits of (a,b,c), or in any combination of bottom bits of |
| 114 | (a,b,c). |
| 115 | * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed |
| 116 | the output delta to a Gray code (a^(a>>1)) so a string of 1's (as |
| 117 | is commonly produced by subtraction) look like a single 1-bit |
| 118 | difference. |
| 119 | * the base values were pseudorandom, all zero but one bit set, or |
| 120 | all zero plus a counter that starts at zero. |
| 121 | |
| 122 | These constants passed: |
| 123 | 14 11 25 16 4 14 24 |
| 124 | 12 14 25 16 4 14 24 |
| 125 | and these came close: |
| 126 | 4 8 15 26 3 22 24 |
| 127 | 10 8 15 26 3 22 24 |
| 128 | 11 8 15 26 3 22 24 |
| 129 | ------------------------------------------------------------------------------- |
| 130 | */ |
| 131 | #define final(a,b,c) \ |
| 132 | { \ |
| 133 | c ^= b; c -= rot(b,14); \ |
| 134 | a ^= c; a -= rot(c,11); \ |
| 135 | b ^= a; b -= rot(a,25); \ |
| 136 | c ^= b; c -= rot(b,16); \ |
| 137 | a ^= c; a -= rot(c,4); \ |
| 138 | b ^= a; b -= rot(a,14); \ |
| 139 | c ^= b; c -= rot(b,24); \ |
| 140 | } |
| 141 | |
| 142 | |
| 143 | #endif |