/* ------------------------------------------------------------------------------- lookup3.c, by Bob Jenkins, May 2006, Public Domain. These are functions for producing 32-bit hashes for hash table lookup. hashword(), hashlittle(), hashbig(), mix(), and final() are externally useful functions. Routines to test the hash are included if SELF_TEST is defined. You can use this mir_free for any purpose. It has no warranty. You probably want to use hashlittle(). hashlittle() and hashbig() hash byte arrays. hashlittle() is is faster than hashbig() on little-endian machines. Intel and AMD are little-endian machines. 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(). ------------------------------------------------------------------------------- */ //#define SELF_TEST 1 #include "variables.h" typedef unsigned long int uint32; /* unsigned 4-byte quantities */ typedef unsigned short int uint16; /* unsigned 2-byte quantities */ typedef unsigned char uint8; /* unsigned 1-byte quantities */ /* * My best guess at if you are big-endian or little-endian. This may * need adjustment. */ #if defined(i386) || defined(__i486__) || defined(__i586__) || defined(__i686__) || defined(vax) || defined(MIPSEL) # define HASH_LITTLE_ENDIAN 1 # define HASH_BIG_ENDIAN 0 #elif defined(sparc) # define HASH_LITTLE_ENDIAN 0 # define HASH_BIG_ENDIAN 1 #else # define HASH_LITTLE_ENDIAN 0 # define HASH_BIG_ENDIAN 0 #endif #define hashsize(n) ((uint32)1<<(n)) #define hashmask(n) (hashsize(n)-1) #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's, and -- that all your machines have the same endianness, and -- that the length be the number of uint32'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 uint32s rather than in bytes. hashlittle() is more complicated than hashword() only because hashlittle() has to dance around fitting the key bytes into registers. -------------------------------------------------------------------- */ uint32 hashword( uint32 *k, size_t length, uint32 initval) { uint32 a,b,c; /* Set up the internal state */ a = b = c = 0xdeadbeef + (((uint32)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'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; } /* ------------------------------------------------------------------------------- hashlittle() -- hash a variable-length key into a 32-bit value k : the key (the unaligned variable-length array of bytes) length : 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. Two keys differing by one or two bits will have totally different hash values. 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 (uint8 **)k, do it like this: for (i=0, h=0; i 12) { a += k[0]; b += k[1]; c += k[2]; mix(a,b,c); length -= 12; k += 3; } /*----------------------------- handle the last (probably partial) block */ 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 if (HASH_LITTLE_ENDIAN && !((((uint8 *)key)-(uint8 *)0) & 0x1)) { uint16 *k = (uint16 *)key; /* read 16-bit chunks */ /*--------------- all but last block: aligned reads and different mixing */ while (length > 12) { a += k[0] + (((uint32)k[1])<<16); b += k[2] + (((uint32)k[3])<<16); c += k[4] + (((uint32)k[5])<<16); mix(a,b,c); length -= 12; k += 6; } /*----------------------------- handle the last (probably partial) block */ switch(length) { case 12: c+=k[4]+(((uint32)k[5])<<16); b+=k[2]+(((uint32)k[3])<<16); a+=k[0]+(((uint32)k[1])<<16); break; case 11: c+=((uint32)(k[5]&0xff))<<16;/* fall through */ case 10: c+=k[4]; b+=k[2]+(((uint32)k[3])<<16); a+=k[0]+(((uint32)k[1])<<16); break; case 9 : c+=k[4]&0xff; /* fall through */ case 8 : b+=k[2]+(((uint32)k[3])<<16); a+=k[0]+(((uint32)k[1])<<16); break; case 7 : b+=((uint32)(k[3]&0xff))<<16;/* fall through */ case 6 : b+=k[2]; a+=k[0]+(((uint32)k[1])<<16); break; case 5 : b+=k[2]&0xff; /* fall through */ case 4 : a+=k[0]+(((uint32)k[1])<<16); break; case 3 : a+=((uint32)(k[1]&0xff))<<16;/* fall through */ case 2 : a+=k[0]; break; case 1 : a+=k[0]&0xff; break; case 0 : return c; /* zero length requires no mixing */ } } else { /* need to read the key one byte at a time */ uint8 *k = (uint8 *)key; /*--------------- all but the last block: affect some 32 bits of (a,b,c) */ while (length > 12) { a += k[0]; a += ((uint32)k[1])<<8; a += ((uint32)k[2])<<16; a += ((uint32)k[3])<<24; b += k[4]; b += ((uint32)k[5])<<8; b += ((uint32)k[6])<<16; b += ((uint32)k[7])<<24; c += k[8]; c += ((uint32)k[9])<<8; c += ((uint32)k[10])<<16; c += ((uint32)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)k[11])<<24; case 11: c+=((uint32)k[10])<<16; case 10: c+=((uint32)k[9])<<8; case 9 : c+=k[8]; case 8 : b+=((uint32)k[7])<<24; case 7 : b+=((uint32)k[6])<<16; case 6 : b+=((uint32)k[5])<<8; case 5 : b+=k[4]; case 4 : a+=((uint32)k[3])<<24; case 3 : a+=((uint32)k[2])<<16; case 2 : a+=((uint32)k[1])<<8; case 1 : a+=k[0]; break; case 0 : return c; } } final(a,b,c); return c; } /* * 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 hashbig( void *key, size_t length, uint32 initval) { uint32 a,b,c; /* Set up the internal state */ a = b = c = 0xdeadbeef + ((uint32)length) + initval; if (HASH_BIG_ENDIAN && !((((uint8 *)key)-(uint8 *)0) & 0x3)) { uint32 *k = (uint32 *)key; /* read 32-bit chunks */ /*------ 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 */ switch(length) { case 12: c+=k[2]; b+=k[1]; a+=k[0]; break; case 11: c+=k[2]<<8; b+=k[1]; a+=k[0]; break; case 10: c+=k[2]<<16; b+=k[1]; a+=k[0]; break; case 9 : c+=k[2]<<24; b+=k[1]; a+=k[0]; break; case 8 : b+=k[1]; a+=k[0]; break; case 7 : b+=k[1]<<8; a+=k[0]; break; case 6 : b+=k[1]<<16; a+=k[0]; break; case 5 : b+=k[1]<<24; a+=k[0]; break; case 4 : a+=k[0]; break; case 3 : a+=k[0]<<8; break; case 2 : a+=k[0]<<16; break; case 1 : a+=k[0]<<24; break; case 0 : return c; /* zero length strings require no mixing */ } } else { /* need to read the key one byte at a time */ uint8 *k = (uint8 *)key; /*--------------- all but the last block: affect some 32 bits of (a,b,c) */ while (length > 12) { a += ((uint32)k[0])<<24; a += ((uint32)k[1])<<16; a += ((uint32)k[2])<<8; a += ((uint32)k[3]); b += ((uint32)k[4])<<24; b += ((uint32)k[5])<<16; b += ((uint32)k[6])<<8; b += ((uint32)k[7]); c += ((uint32)k[8])<<24; c += ((uint32)k[9])<<16; c += ((uint32)k[10])<<8; c += ((uint32)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+=((uint32)k[11])<<24; case 11: c+=((uint32)k[10])<<16; case 10: c+=((uint32)k[9])<<8; case 9 : c+=k[8]; case 8 : b+=((uint32)k[7])<<24; case 7 : b+=((uint32)k[6])<<16; case 6 : b+=((uint32)k[5])<<8; case 5 : b+=k[4]; case 4 : a+=((uint32)k[3])<<24; case 3 : a+=((uint32)k[2])<<16; case 2 : a+=((uint32)k[1])<<8; case 1 : a+=k[0]; break; case 0 : return c; } } final(a,b,c); return c; } #ifdef SELF_TEST /* used for timings */ void driver1() { uint8 buf[256]; uint32 i; uint32 h=0; time_t a,z; time(&a); for (i=0; i<256; ++i) buf[i] = 'x'; for (i=0; i<1; ++i) { h = hashlittle(&buf[0],1,h); } time(&z); if (z-a > 0) printf("time %ld %.8lx\n", z-a, h); } /* check that every input bit changes every output bit half the time */ #define HASHSTATE 1 #define HASHLEN 1 #define MAXPAIR 60 #define MAXLEN 70 void driver2() { uint8 qa[MAXLEN+1], qb[MAXLEN+2], *a = &qa[0], *b = &qb[1]; uint32 c[HASHSTATE], d[HASHSTATE], i, j=0, k, l, m, z; uint32 e[HASHSTATE],f[HASHSTATE],g[HASHSTATE],h[HASHSTATE]; uint32 x[HASHSTATE],y[HASHSTATE]; uint32 hlen; printf("No more than %d trials should ever be needed \n",MAXPAIR/2); for (hlen=0; hlen < MAXLEN; ++hlen) { z=0; for (i=0; i>(8-j)); c[0] = hashlittle(a, hlen, m); b[i] ^= ((k+1)<>(8-j)); d[0] = hashlittle(b, hlen, m); /* check every bit is 1, 0, set, and not set at least once */ for (l=0; lz) z=k; if (k==MAXPAIR) { printf("Some bit didn't change: "); printf("%.8lx %.8lx %.8lx %.8lx %.8lx %.8lx ", e[0],f[0],g[0],h[0],x[0],y[0]); printf("i %ld j %ld m %ld len %ld\n",i,j,m,hlen); } if (z==MAXPAIR) goto done; } } } done: if (z < MAXPAIR) { printf("Mix success %2ld bytes %2ld initvals ",i,m); printf("required %ld trials\n",z/2); } } printf("\n"); } /* Check for reading beyond the end of the buffer and alignment problems */ void driver3() { uint8 buf[MAXLEN+20], *b; uint32 len; uint8 q[] = "This is the time for all good men to come to the aid of their country..."; //uint32 dummy1; uint8 qq[] = "xThis is the time for all good men to come to the aid of their country..."; //uint32 dummy2; uint8 qqq[] = "xxThis is the time for all good men to come to the aid of their country..."; //uint32 dummy3; uint8 qqqq[] = "xxxThis is the time for all good men to come to the aid of their country..."; uint32 h,i,j,ref,x,y; uint8 *p; printf("Endianness. These lines should all be the same (for values filled in):\n"); printf("%.8lx %.8lx %.8lx\n", hashword((uint32 *)q, (sizeof(q)-1)/4, 13), hashword((uint32 *)q, (sizeof(q)-5)/4, 13), hashword((uint32 *)q, (sizeof(q)-9)/4, 13)); p = q; printf("%.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx\n", hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13), hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13), hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13), hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13), hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13), hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13)); p = &qq[1]; printf("%.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx\n", hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13), hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13), hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13), hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13), hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13), hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13)); p = &qqq[2]; printf("%.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx\n", hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13), hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13), hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13), hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13), hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13), hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13)); p = &qqqq[3]; printf("%.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx %.8lx\n", hashlittle(p, sizeof(q)-1, 13), hashlittle(p, sizeof(q)-2, 13), hashlittle(p, sizeof(q)-3, 13), hashlittle(p, sizeof(q)-4, 13), hashlittle(p, sizeof(q)-5, 13), hashlittle(p, sizeof(q)-6, 13), hashlittle(p, sizeof(q)-7, 13), hashlittle(p, sizeof(q)-8, 13), hashlittle(p, sizeof(q)-9, 13), hashlittle(p, sizeof(q)-10, 13), hashlittle(p, sizeof(q)-11, 13), hashlittle(p, sizeof(q)-12, 13)); printf("\n"); for (h=0, b=buf+1; h<8; ++h, ++b) { for (i=0; i