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819dc7d4 DG |
1 | /* |
2 | * Copyright (C) - Bob Jenkins, May 2006, Public Domain. | |
3 | * Copyright (C) 2011 - David Goulet <david.goulet@polymtl.ca> | |
4 | * | |
5 | * These are functions for producing 32-bit hashes for hash table lookup. | |
6 | * hashword(), hashlittle(), hashlittle2(), hashbig(), mix(), and final() are | |
7 | * externally useful functions. Routines to test the hash are included if | |
8 | * SELF_TEST is defined. You can use this free for any purpose. It's in the | |
9 | * public domain. It has no warranty. | |
10 | * | |
11 | * You probably want to use hashlittle(). hashlittle() and hashbig() hash byte | |
12 | * arrays. hashlittle() is is faster than hashbig() on little-endian machines. | |
13 | * Intel and AMD are little-endian machines. On second thought, you probably | |
14 | * want hashlittle2(), which is identical to hashlittle() except it returns two | |
15 | * 32-bit hashes for the price of one. You could implement hashbig2() if you | |
16 | * 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, then | |
31 | * mix those integers. This is fast (you can do a lot more thorough mixing | |
32 | * with 12*3 instructions on 3 integers than you can with 3 instructions on 1 | |
33 | * byte), but shoehorning those bytes into integers efficiently is messy. | |
34 | */ | |
35 | ||
36 | #include <stdio.h> /* defines printf for tests */ | |
37 | #include <time.h> /* defines time_t for timings in the test */ | |
38 | #include <stdint.h> /* defines uint32_t etc */ | |
39 | #include <sys/param.h> /* attempt to define endianness */ | |
40 | #include <endian.h> /* attempt to define endianness */ | |
41 | #include <string.h> | |
42 | #include <assert.h> | |
43 | ||
44 | /* | |
45 | * My best guess at if you are big-endian or little-endian. This may | |
46 | * need adjustment. | |
47 | */ | |
48 | #if (defined(__BYTE_ORDER) && defined(__LITTLE_ENDIAN) && \ | |
49 | __BYTE_ORDER == __LITTLE_ENDIAN) || \ | |
50 | (defined(i386) || defined(__i386__) || defined(__i486__) || \ | |
51 | defined(__i586__) || defined(__i686__) || defined(vax) || defined(MIPSEL)) | |
52 | # define HASH_LITTLE_ENDIAN 1 | |
53 | # define HASH_BIG_ENDIAN 0 | |
54 | #elif (defined(__BYTE_ORDER) && defined(__BIG_ENDIAN) && \ | |
55 | __BYTE_ORDER == __BIG_ENDIAN) || \ | |
56 | (defined(sparc) || defined(POWERPC) || defined(mc68000) || defined(sel)) | |
57 | # define HASH_LITTLE_ENDIAN 0 | |
58 | # define HASH_BIG_ENDIAN 1 | |
59 | #else | |
60 | # define HASH_LITTLE_ENDIAN 0 | |
61 | # define HASH_BIG_ENDIAN 0 | |
62 | #endif | |
63 | ||
64 | #define hashsize(n) ((uint32_t)1<<(n)) | |
65 | #define hashmask(n) (hashsize(n)-1) | |
66 | #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) | |
67 | ||
68 | /* | |
69 | * mix -- mix 3 32-bit values reversibly. | |
70 | * | |
71 | * This is reversible, so any information in (a,b,c) before mix() is | |
72 | * still in (a,b,c) after mix(). | |
73 | * | |
74 | * If four pairs of (a,b,c) inputs are run through mix(), or through | |
75 | * mix() in reverse, there are at least 32 bits of the output that | |
76 | * are sometimes the same for one pair and different for another pair. | |
77 | * This was tested for: | |
78 | * * pairs that differed by one bit, by two bits, in any combination | |
79 | * of top bits of (a,b,c), or in any combination of bottom bits of | |
80 | * (a,b,c). | |
81 | * * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed | |
82 | * the output delta to a Gray code (a^(a>>1)) so a string of 1's (as | |
83 | * is commonly produced by subtraction) look like a single 1-bit | |
84 | * difference. | |
85 | * * the base values were pseudorandom, all zero but one bit set, or | |
86 | * all zero plus a counter that starts at zero. | |
87 | * | |
88 | * Some k values for my "a-=c; a^=rot(c,k); c+=b;" arrangement that | |
89 | * satisfy this are | |
90 | * 4 6 8 16 19 4 | |
91 | * 9 15 3 18 27 15 | |
92 | * 14 9 3 7 17 3 | |
93 | * Well, "9 15 3 18 27 15" didn't quite get 32 bits diffing | |
94 | * for "differ" defined as + with a one-bit base and a two-bit delta. I | |
95 | * used http://burtleburtle.net/bob/hash/avalanche.html to choose | |
96 | * the operations, constants, and arrangements of the variables. | |
97 | * | |
98 | * This does not achieve avalanche. There are input bits of (a,b,c) | |
99 | * that fail to affect some output bits of (a,b,c), especially of a. The | |
100 | * most thoroughly mixed value is c, but it doesn't really even achieve | |
101 | * avalanche in c. | |
102 | * | |
103 | * This allows some parallelism. Read-after-writes are good at doubling | |
104 | * the number of bits affected, so the goal of mixing pulls in the opposite | |
105 | * direction as the goal of parallelism. I did what I could. Rotates | |
106 | * seem to cost as much as shifts on every machine I could lay my hands | |
107 | * on, and rotates are much kinder to the top and bottom bits, so I used | |
108 | * rotates. | |
109 | */ | |
110 | #define mix(a,b,c) \ | |
111 | { \ | |
112 | a -= c; a ^= rot(c, 4); c += b; \ | |
113 | b -= a; b ^= rot(a, 6); a += c; \ | |
114 | c -= b; c ^= rot(b, 8); b += a; \ | |
115 | a -= c; a ^= rot(c,16); c += b; \ | |
116 | b -= a; b ^= rot(a,19); a += c; \ | |
117 | c -= b; c ^= rot(b, 4); b += a; \ | |
118 | } | |
119 | ||
120 | /* | |
121 | * final -- final mixing of 3 32-bit values (a,b,c) into c | |
122 | * | |
123 | * Pairs of (a,b,c) values differing in only a few bits will usually | |
124 | * produce values of c that look totally different. This was tested for | |
125 | * * pairs that differed by one bit, by two bits, in any combination | |
126 | * of top bits of (a,b,c), or in any combination of bottom bits of | |
127 | * (a,b,c). | |
128 | * * "differ" is defined as +, -, ^, or ~^. For + and -, I transformed | |
129 | * the output delta to a Gray code (a^(a>>1)) so a string of 1's (as | |
130 | * is commonly produced by subtraction) look like a single 1-bit | |
131 | * difference. | |
132 | * * the base values were pseudorandom, all zero but one bit set, or | |
133 | * all zero plus a counter that starts at zero. | |
134 | * | |
135 | * These constants passed: | |
136 | * 14 11 25 16 4 14 24 | |
137 | * 12 14 25 16 4 14 24 | |
138 | * and these came close: | |
139 | * 4 8 15 26 3 22 24 | |
140 | * 10 8 15 26 3 22 24 | |
141 | * 11 8 15 26 3 22 24 | |
142 | */ | |
143 | #define final(a,b,c) \ | |
144 | { \ | |
145 | c ^= b; c -= rot(b,14); \ | |
146 | a ^= c; a -= rot(c,11); \ | |
147 | b ^= a; b -= rot(a,25); \ | |
148 | c ^= b; c -= rot(b,16); \ | |
149 | a ^= c; a -= rot(c,4); \ | |
150 | b ^= a; b -= rot(a,14); \ | |
151 | c ^= b; c -= rot(b,24); \ | |
152 | } | |
153 | ||
154 | /* | |
155 | * hashword2() -- same as hashword(), but take two seeds and return two 32-bit | |
156 | * values. pc and pb must both be nonnull, and *pc and *pb must both be | |
157 | * initialized with seeds. If you pass in (*pb)==0, the output (*pc) will be | |
158 | * the same as the return value from hashword(). | |
159 | */ | |
160 | static void hashword2(const uint32_t *k, size_t length, | |
161 | uint32_t *pc, uint32_t *pb) | |
162 | { | |
163 | uint32_t a, b, c; | |
164 | ||
165 | /* Set up the internal state */ | |
166 | a = b = c = 0xdeadbeef + ((uint32_t) (length << 2)) + *pc; | |
167 | c += *pb; | |
168 | ||
169 | while (length > 3) { | |
170 | a += k[0]; | |
171 | b += k[1]; | |
172 | c += k[2]; | |
173 | mix(a, b, c); | |
174 | length -= 3; | |
175 | k += 3; | |
176 | } | |
177 | ||
178 | switch (length) { | |
179 | case 3 : | |
180 | c += k[2]; | |
181 | case 2 : | |
182 | b += k[1]; | |
183 | case 1 : | |
184 | a += k[0]; | |
185 | final(a, b, c); | |
186 | case 0: /* case 0: nothing left to add */ | |
187 | break; | |
188 | } | |
189 | ||
190 | *pc = c; | |
191 | *pb = b; | |
192 | } | |
193 | ||
194 | /* | |
195 | * hashlittle() -- hash a variable-length key into a 32-bit value | |
196 | * k : the key (the unaligned variable-length array of bytes) | |
197 | * length : the length of the key, counting by bytes | |
198 | * initval : can be any 4-byte value | |
199 | * Returns a 32-bit value. Every bit of the key affects every bit of | |
200 | * the return value. Two keys differing by one or two bits will have | |
201 | * totally different hash values. | |
202 | * | |
203 | * The best hash table sizes are powers of 2. There is no need to do | |
204 | * mod a prime (mod is sooo slow!). If you need less than 32 bits, | |
205 | * use a bitmask. For example, if you need only 10 bits, do | |
206 | * h = (h & hashmask(10)); | |
207 | * In which case, the hash table should have hashsize(10) elements. | |
208 | * | |
209 | * If you are hashing n strings (uint8_t **)k, do it like this: | |
210 | * for (i=0, h=0; i<n; ++i) h = hashlittle( k[i], len[i], h); | |
211 | * | |
212 | * By Bob Jenkins, 2006. bob_jenkins@burtleburtle.net. You may use this | |
213 | * code any way you wish, private, educational, or commercial. It's free. | |
214 | * | |
215 | * Use for hash table lookup, or anything where one collision in 2^^32 is | |
216 | * acceptable. Do NOT use for cryptographic purposes. | |
217 | */ | |
218 | ||
219 | static uint32_t hashlittle(const void *key, size_t length, uint32_t initval) | |
220 | { | |
221 | uint32_t a,b,c; | |
222 | union { | |
223 | const void *ptr; | |
224 | size_t i; | |
225 | } u; /* needed for Mac Powerbook G4 */ | |
226 | ||
227 | /* Set up the internal state */ | |
228 | a = b = c = 0xdeadbeef + ((uint32_t)length) + initval; | |
229 | ||
230 | u.ptr = key; | |
231 | if (HASH_LITTLE_ENDIAN && ((u.i & 0x3) == 0)) { | |
232 | const uint32_t *k = (const uint32_t *)key; /* read 32-bit chunks */ | |
233 | ||
234 | /*------ all but last block: aligned reads and affect 32 bits of (a,b,c) */ | |
235 | while (length > 12) { | |
236 | a += k[0]; | |
237 | b += k[1]; | |
238 | c += k[2]; | |
239 | mix(a,b,c); | |
240 | length -= 12; | |
241 | k += 3; | |
242 | } | |
243 | ||
244 | /* | |
245 | * "k[2]&0xffffff" actually reads beyond the end of the string, but | |
246 | * then masks off the part it's not allowed to read. Because the | |
247 | * string is aligned, the masked-off tail is in the same word as the | |
248 | * rest of the string. Every machine with memory protection I've seen | |
249 | * does it on word boundaries, so is OK with this. But VALGRIND will | |
250 | * still catch it and complain. The masking trick does make the hash | |
251 | * noticably faster for short strings (like English words). | |
252 | */ | |
253 | #ifndef VALGRIND | |
254 | ||
255 | switch (length) { | |
256 | case 12: c+=k[2]; b+=k[1]; a+=k[0]; break; | |
257 | case 11: c+=k[2]&0xffffff; b+=k[1]; a+=k[0]; break; | |
258 | case 10: c+=k[2]&0xffff; b+=k[1]; a+=k[0]; break; | |
259 | case 9 : c+=k[2]&0xff; b+=k[1]; a+=k[0]; break; | |
260 | case 8 : b+=k[1]; a+=k[0]; break; | |
261 | case 7 : b+=k[1]&0xffffff; a+=k[0]; break; | |
262 | case 6 : b+=k[1]&0xffff; a+=k[0]; break; | |
263 | case 5 : b+=k[1]&0xff; a+=k[0]; break; | |
264 | case 4 : a+=k[0]; break; | |
265 | case 3 : a+=k[0]&0xffffff; break; | |
266 | case 2 : a+=k[0]&0xffff; break; | |
267 | case 1 : a+=k[0]&0xff; break; | |
268 | case 0 : return c; /* zero length strings require no mixing */ | |
269 | } | |
270 | #else /* make valgrind happy */ | |
271 | const uint8_t *k8; | |
272 | ||
273 | k8 = (const uint8_t *)k; | |
274 | switch (length) { | |
275 | case 12: c+=k[2]; b+=k[1]; a+=k[0]; break; | |
276 | case 11: c+=((uint32_t)k8[10])<<16; /* fall through */ | |
277 | case 10: c+=((uint32_t)k8[9])<<8; /* fall through */ | |
278 | case 9 : c+=k8[8]; /* fall through */ | |
279 | case 8 : b+=k[1]; a+=k[0]; break; | |
280 | case 7 : b+=((uint32_t)k8[6])<<16; /* fall through */ | |
281 | case 6 : b+=((uint32_t)k8[5])<<8; /* fall through */ | |
282 | case 5 : b+=k8[4]; /* fall through */ | |
283 | case 4 : a+=k[0]; break; | |
284 | case 3 : a+=((uint32_t)k8[2])<<16; /* fall through */ | |
285 | case 2 : a+=((uint32_t)k8[1])<<8; /* fall through */ | |
286 | case 1 : a+=k8[0]; break; | |
287 | case 0 : return c; | |
288 | } | |
289 | #endif /* !valgrind */ | |
290 | } else if (HASH_LITTLE_ENDIAN && ((u.i & 0x1) == 0)) { | |
291 | const uint16_t *k = (const uint16_t *)key; /* read 16-bit chunks */ | |
292 | const uint8_t *k8; | |
293 | ||
294 | /*--------------- all but last block: aligned reads and different mixing */ | |
295 | while (length > 12) { | |
296 | a += k[0] + (((uint32_t)k[1])<<16); | |
297 | b += k[2] + (((uint32_t)k[3])<<16); | |
298 | c += k[4] + (((uint32_t)k[5])<<16); | |
299 | mix(a,b,c); | |
300 | length -= 12; | |
301 | k += 6; | |
302 | } | |
303 | ||
304 | k8 = (const uint8_t *)k; | |
305 | switch (length) { | |
306 | case 12: | |
307 | c+=k[4]+(((uint32_t)k[5])<<16); | |
308 | b+=k[2]+(((uint32_t)k[3])<<16); | |
309 | a+=k[0]+(((uint32_t)k[1])<<16); | |
310 | break; | |
311 | case 11: | |
312 | c+=((uint32_t)k8[10])<<16; /* fall through */ | |
313 | case 10: | |
314 | c+=k[4]; | |
315 | b+=k[2]+(((uint32_t)k[3])<<16); | |
316 | a+=k[0]+(((uint32_t)k[1])<<16); | |
317 | break; | |
318 | case 9: | |
319 | c+=k8[8]; /* fall through */ | |
320 | case 8: | |
321 | b+=k[2]+(((uint32_t)k[3])<<16); | |
322 | a+=k[0]+(((uint32_t)k[1])<<16); | |
323 | break; | |
324 | case 7: | |
325 | b+=((uint32_t)k8[6])<<16; /* fall through */ | |
326 | case 6: | |
327 | b+=k[2]; | |
328 | a+=k[0]+(((uint32_t)k[1])<<16); | |
329 | break; | |
330 | case 5: | |
331 | b+=k8[4]; /* fall through */ | |
332 | case 4: | |
333 | a+=k[0]+(((uint32_t)k[1])<<16); | |
334 | break; | |
335 | case 3: | |
336 | a+=((uint32_t)k8[2])<<16; /* fall through */ | |
337 | case 2: | |
338 | a+=k[0]; | |
339 | break; | |
340 | case 1: | |
341 | a+=k8[0]; | |
342 | break; | |
343 | case 0: | |
344 | return c; /* zero length requires no mixing */ | |
345 | } | |
346 | ||
347 | } else { /* need to read the key one byte at a time */ | |
348 | const uint8_t *k = (const uint8_t *)key; | |
349 | ||
350 | while (length > 12) { | |
351 | a += k[0]; | |
352 | a += ((uint32_t)k[1])<<8; | |
353 | a += ((uint32_t)k[2])<<16; | |
354 | a += ((uint32_t)k[3])<<24; | |
355 | b += k[4]; | |
356 | b += ((uint32_t)k[5])<<8; | |
357 | b += ((uint32_t)k[6])<<16; | |
358 | b += ((uint32_t)k[7])<<24; | |
359 | c += k[8]; | |
360 | c += ((uint32_t)k[9])<<8; | |
361 | c += ((uint32_t)k[10])<<16; | |
362 | c += ((uint32_t)k[11])<<24; | |
363 | mix(a,b,c); | |
364 | length -= 12; | |
365 | k += 12; | |
366 | } | |
367 | ||
368 | switch(length) { /* all the case statements fall through */ | |
369 | case 12: c+=((uint32_t)k[11])<<24; | |
370 | case 11: c+=((uint32_t)k[10])<<16; | |
371 | case 10: c+=((uint32_t)k[9])<<8; | |
372 | case 9: c+=k[8]; | |
373 | case 8: b+=((uint32_t)k[7])<<24; | |
374 | case 7: b+=((uint32_t)k[6])<<16; | |
375 | case 6: b+=((uint32_t)k[5])<<8; | |
376 | case 5: b+=k[4]; | |
377 | case 4: a+=((uint32_t)k[3])<<24; | |
378 | case 3: a+=((uint32_t)k[2])<<16; | |
379 | case 2: a+=((uint32_t)k[1])<<8; | |
380 | case 1: | |
381 | a+=k[0]; | |
382 | break; | |
383 | case 0: | |
384 | return c; | |
385 | } | |
386 | } | |
387 | ||
388 | final(a,b,c); | |
389 | return c; | |
390 | } | |
391 | ||
392 | /* | |
393 | * Hash function for number value. | |
394 | */ | |
395 | unsigned long hash_key(void *_key, size_t length, unsigned long seed) | |
396 | { | |
397 | union { | |
398 | uint64_t v64; | |
399 | uint32_t v32[2]; | |
400 | } v; | |
401 | union { | |
402 | uint64_t v64; | |
403 | uint32_t v32[2]; | |
404 | } key; | |
405 | ||
406 | assert(length == sizeof(unsigned long)); | |
407 | v.v64 = (uint64_t) seed; | |
408 | key.v64 = (uint64_t) _key; | |
409 | hashword2(key.v32, 2, &v.v32[0], &v.v32[1]); | |
410 | return v.v64; | |
411 | } | |
412 | ||
413 | /* | |
414 | * Hash function for string. | |
415 | */ | |
416 | unsigned long hash_key_str(void *key, size_t length, unsigned long seed) | |
417 | { | |
418 | return hashlittle(key, length, seed); | |
419 | } | |
420 | ||
421 | /* | |
422 | * Hash function compare for number value. | |
423 | */ | |
424 | unsigned long hash_compare_key(void *key1, size_t key1_len, | |
425 | void *key2, size_t key2_len) | |
426 | { | |
427 | if (key1_len != key2_len) { | |
428 | return -1; | |
429 | } | |
430 | ||
431 | if (key1 == key2) { | |
432 | return 0; | |
433 | } | |
434 | ||
435 | return 1; | |
436 | } | |
437 | ||
438 | /* | |
439 | * Hash compare function for string. | |
440 | */ | |
441 | unsigned long hash_compare_key_str(void *key1, size_t key1_len, | |
442 | void *key2, size_t key2_len) | |
443 | { | |
444 | if (key1_len != key2_len) { | |
445 | return -1; | |
446 | } | |
447 | ||
448 | if (strncmp(key1, key2, key1_len) == 0) { | |
449 | return 0; | |
450 | } | |
451 | ||
452 | return 1; | |
453 | } |