tanjent@gmail.com | f3b7897 | 2012-03-01 03:38:55 +0000 | [diff] [blame] | 1 | //----------------------------------------------------------------------------- |
| 2 | // Flipping a single bit of a key should cause an "avalanche" of changes in |
| 3 | // the hash function's output. Ideally, each output bits should flip 50% of |
| 4 | // the time - if the probability of an output bit flipping is not 50%, that bit |
| 5 | // is "biased". Too much bias means that patterns applied to the input will |
| 6 | // cause "echoes" of the patterns in the output, which in turn can cause the |
| 7 | // hash function to fail to create an even, random distribution of hash values. |
| 8 | |
| 9 | |
| 10 | #pragma once |
| 11 | |
| 12 | #include "Types.h" |
| 13 | #include "Random.h" |
| 14 | |
| 15 | #include <vector> |
| 16 | #include <stdio.h> |
| 17 | #include <math.h> |
| 18 | |
| 19 | // Avalanche fails if a bit is biased by more than 1% |
| 20 | |
| 21 | #define AVALANCHE_FAIL 0.01 |
| 22 | |
| 23 | double maxBias ( std::vector<int> & counts, int reps ); |
| 24 | |
| 25 | //----------------------------------------------------------------------------- |
| 26 | |
| 27 | template < typename keytype, typename hashtype > |
| 28 | void calcBias ( pfHash hash, std::vector<int> & counts, int reps, Rand & r ) |
| 29 | { |
| 30 | const int keybytes = sizeof(keytype); |
| 31 | const int hashbytes = sizeof(hashtype); |
| 32 | |
| 33 | const int keybits = keybytes * 8; |
| 34 | const int hashbits = hashbytes * 8; |
| 35 | |
| 36 | keytype K; |
| 37 | hashtype A,B; |
| 38 | |
| 39 | for(int irep = 0; irep < reps; irep++) |
| 40 | { |
| 41 | if(irep % (reps/10) == 0) printf("."); |
| 42 | |
| 43 | r.rand_p(&K,keybytes); |
| 44 | |
| 45 | hash(&K,keybytes,0,&A); |
| 46 | |
| 47 | int * cursor = &counts[0]; |
| 48 | |
| 49 | for(int iBit = 0; iBit < keybits; iBit++) |
| 50 | { |
| 51 | flipbit(&K,keybytes,iBit); |
| 52 | hash(&K,keybytes,0,&B); |
| 53 | flipbit(&K,keybytes,iBit); |
| 54 | |
| 55 | for(int iOut = 0; iOut < hashbits; iOut++) |
| 56 | { |
| 57 | int bitA = getbit(&A,hashbytes,iOut); |
| 58 | int bitB = getbit(&B,hashbytes,iOut); |
| 59 | |
| 60 | (*cursor++) += (bitA ^ bitB); |
| 61 | } |
| 62 | } |
| 63 | } |
| 64 | } |
| 65 | |
| 66 | //----------------------------------------------------------------------------- |
| 67 | |
| 68 | template < typename keytype, typename hashtype > |
| 69 | bool AvalancheTest ( pfHash hash, const int reps ) |
| 70 | { |
| 71 | Rand r(48273); |
| 72 | |
| 73 | const int keybytes = sizeof(keytype); |
| 74 | const int hashbytes = sizeof(hashtype); |
| 75 | |
| 76 | const int keybits = keybytes * 8; |
| 77 | const int hashbits = hashbytes * 8; |
| 78 | |
| 79 | printf("Testing %3d-bit keys -> %3d-bit hashes, %8d reps",keybits,hashbits,reps); |
| 80 | |
| 81 | //---------- |
| 82 | |
| 83 | std::vector<int> bins(keybits*hashbits,0); |
| 84 | |
| 85 | calcBias<keytype,hashtype>(hash,bins,reps,r); |
| 86 | |
| 87 | //---------- |
| 88 | |
| 89 | bool result = true; |
| 90 | |
| 91 | double b = maxBias(bins,reps); |
| 92 | |
| 93 | printf(" worst bias is %f%%",b * 100.0); |
| 94 | |
| 95 | if(b > AVALANCHE_FAIL) |
| 96 | { |
| 97 | printf(" !!!!! "); |
| 98 | result = false; |
| 99 | } |
| 100 | |
| 101 | printf("\n"); |
| 102 | |
| 103 | return result; |
| 104 | } |
| 105 | |
| 106 | //---------------------------------------------------------------------------- |
| 107 | // Tests the Bit Independence Criteron. Stricter than Avalanche, but slow and |
| 108 | // not really all that useful. |
| 109 | |
| 110 | template< typename keytype, typename hashtype > |
| 111 | void BicTest ( pfHash hash, const int keybit, const int reps, double & maxBias, int & maxA, int & maxB, bool verbose ) |
| 112 | { |
| 113 | Rand r(11938); |
| 114 | |
| 115 | const int keybytes = sizeof(keytype); |
| 116 | const int hashbytes = sizeof(hashtype); |
| 117 | const int hashbits = hashbytes * 8; |
| 118 | |
| 119 | std::vector<int> bins(hashbits*hashbits*4,0); |
| 120 | |
| 121 | keytype key; |
| 122 | hashtype h1,h2; |
| 123 | |
| 124 | for(int irep = 0; irep < reps; irep++) |
| 125 | { |
| 126 | if(verbose) |
| 127 | { |
| 128 | if(irep % (reps/10) == 0) printf("."); |
| 129 | } |
| 130 | |
| 131 | r.rand_p(&key,keybytes); |
| 132 | hash(&key,keybytes,0,&h1); |
| 133 | |
| 134 | flipbit(key,keybit); |
| 135 | hash(&key,keybytes,0,&h2); |
| 136 | |
| 137 | hashtype d = h1 ^ h2; |
| 138 | |
| 139 | for(int out1 = 0; out1 < hashbits; out1++) |
| 140 | for(int out2 = 0; out2 < hashbits; out2++) |
| 141 | { |
| 142 | if(out1 == out2) continue; |
| 143 | |
| 144 | uint32_t b = getbit(d,out1) | (getbit(d,out2) << 1); |
| 145 | |
| 146 | bins[(out1 * hashbits + out2) * 4 + b]++; |
| 147 | } |
| 148 | } |
| 149 | |
| 150 | if(verbose) printf("\n"); |
| 151 | |
| 152 | maxBias = 0; |
| 153 | |
| 154 | for(int out1 = 0; out1 < hashbits; out1++) |
| 155 | { |
| 156 | for(int out2 = 0; out2 < hashbits; out2++) |
| 157 | { |
| 158 | if(out1 == out2) |
| 159 | { |
| 160 | if(verbose) printf("\\"); |
| 161 | continue; |
| 162 | } |
| 163 | |
| 164 | double bias = 0; |
| 165 | |
| 166 | for(int b = 0; b < 4; b++) |
| 167 | { |
| 168 | double b2 = double(bins[(out1 * hashbits + out2) * 4 + b]) / double(reps / 2); |
| 169 | b2 = fabs(b2 * 2 - 1); |
| 170 | |
| 171 | if(b2 > bias) bias = b2; |
| 172 | } |
| 173 | |
| 174 | if(bias > maxBias) |
| 175 | { |
| 176 | maxBias = bias; |
| 177 | maxA = out1; |
| 178 | maxB = out2; |
| 179 | } |
| 180 | |
| 181 | if(verbose) |
| 182 | { |
| 183 | if (bias < 0.01) printf("."); |
| 184 | else if(bias < 0.05) printf("o"); |
| 185 | else if(bias < 0.33) printf("O"); |
| 186 | else printf("X"); |
| 187 | } |
| 188 | } |
| 189 | |
| 190 | if(verbose) printf("\n"); |
| 191 | } |
| 192 | } |
| 193 | |
| 194 | //---------- |
| 195 | |
| 196 | template< typename keytype, typename hashtype > |
| 197 | bool BicTest ( pfHash hash, const int reps ) |
| 198 | { |
| 199 | const int keybytes = sizeof(keytype); |
| 200 | const int keybits = keybytes * 8; |
| 201 | |
| 202 | double maxBias = 0; |
| 203 | int maxK = 0; |
| 204 | int maxA = 0; |
| 205 | int maxB = 0; |
| 206 | |
| 207 | for(int i = 0; i < keybits; i++) |
| 208 | { |
| 209 | if(i % (keybits/10) == 0) printf("."); |
| 210 | |
| 211 | double bias; |
| 212 | int a,b; |
| 213 | |
| 214 | BicTest<keytype,hashtype>(hash,i,reps,bias,a,b,true); |
| 215 | |
| 216 | if(bias > maxBias) |
| 217 | { |
| 218 | maxBias = bias; |
| 219 | maxK = i; |
| 220 | maxA = a; |
| 221 | maxB = b; |
| 222 | } |
| 223 | } |
| 224 | |
| 225 | printf("Max bias %f - (%3d : %3d,%3d)\n",maxBias,maxK,maxA,maxB); |
| 226 | |
| 227 | // Bit independence is harder to pass than avalanche, so we're a bit more lax here. |
| 228 | |
| 229 | bool result = (maxBias < 0.05); |
| 230 | |
| 231 | return result; |
| 232 | } |
| 233 | |
| 234 | //----------------------------------------------------------------------------- |
| 235 | // BIC test variant - store all intermediate data in a table, draw diagram |
| 236 | // afterwards (much faster) |
| 237 | |
| 238 | template< typename keytype, typename hashtype > |
| 239 | void BicTest3 ( pfHash hash, const int reps, bool verbose = true ) |
| 240 | { |
| 241 | const int keybytes = sizeof(keytype); |
| 242 | const int keybits = keybytes * 8; |
| 243 | const int hashbytes = sizeof(hashtype); |
| 244 | const int hashbits = hashbytes * 8; |
| 245 | const int pagesize = hashbits*hashbits*4; |
| 246 | |
| 247 | Rand r(11938); |
| 248 | |
| 249 | double maxBias = 0; |
| 250 | int maxK = 0; |
| 251 | int maxA = 0; |
| 252 | int maxB = 0; |
| 253 | |
| 254 | keytype key; |
| 255 | hashtype h1,h2; |
| 256 | |
| 257 | std::vector<int> bins(keybits*pagesize,0); |
| 258 | |
| 259 | for(int keybit = 0; keybit < keybits; keybit++) |
| 260 | { |
| 261 | if(keybit % (keybits/10) == 0) printf("."); |
| 262 | |
| 263 | int * page = &bins[keybit*pagesize]; |
| 264 | |
| 265 | for(int irep = 0; irep < reps; irep++) |
| 266 | { |
| 267 | r.rand_p(&key,keybytes); |
| 268 | hash(&key,keybytes,0,&h1); |
| 269 | flipbit(key,keybit); |
| 270 | hash(&key,keybytes,0,&h2); |
| 271 | |
| 272 | hashtype d = h1 ^ h2; |
| 273 | |
| 274 | for(int out1 = 0; out1 < hashbits-1; out1++) |
| 275 | for(int out2 = out1+1; out2 < hashbits; out2++) |
| 276 | { |
| 277 | int * b = &page[(out1*hashbits+out2)*4]; |
| 278 | |
| 279 | uint32_t x = getbit(d,out1) | (getbit(d,out2) << 1); |
| 280 | |
| 281 | b[x]++; |
| 282 | } |
| 283 | } |
| 284 | } |
| 285 | |
| 286 | printf("\n"); |
| 287 | |
| 288 | for(int out1 = 0; out1 < hashbits-1; out1++) |
| 289 | { |
| 290 | for(int out2 = out1+1; out2 < hashbits; out2++) |
| 291 | { |
| 292 | if(verbose) printf("(%3d,%3d) - ",out1,out2); |
| 293 | |
| 294 | for(int keybit = 0; keybit < keybits; keybit++) |
| 295 | { |
| 296 | int * page = &bins[keybit*pagesize]; |
| 297 | int * bins = &page[(out1*hashbits+out2)*4]; |
| 298 | |
| 299 | double bias = 0; |
| 300 | |
| 301 | for(int b = 0; b < 4; b++) |
| 302 | { |
| 303 | double b2 = double(bins[b]) / double(reps / 2); |
| 304 | b2 = fabs(b2 * 2 - 1); |
| 305 | |
| 306 | if(b2 > bias) bias = b2; |
| 307 | } |
| 308 | |
| 309 | if(bias > maxBias) |
| 310 | { |
| 311 | maxBias = bias; |
| 312 | maxK = keybit; |
| 313 | maxA = out1; |
| 314 | maxB = out2; |
| 315 | } |
| 316 | |
| 317 | if(verbose) |
| 318 | { |
| 319 | if (bias < 0.01) printf("."); |
| 320 | else if(bias < 0.05) printf("o"); |
| 321 | else if(bias < 0.33) printf("O"); |
| 322 | else printf("X"); |
| 323 | } |
| 324 | } |
| 325 | |
| 326 | // Finished keybit |
| 327 | |
| 328 | if(verbose) printf("\n"); |
| 329 | } |
| 330 | |
| 331 | if(verbose) |
| 332 | { |
| 333 | for(int i = 0; i < keybits+12; i++) printf("-"); |
| 334 | printf("\n"); |
| 335 | } |
| 336 | } |
| 337 | |
| 338 | printf("Max bias %f - (%3d : %3d,%3d)\n",maxBias,maxK,maxA,maxB); |
| 339 | } |
| 340 | |
| 341 | |
| 342 | //----------------------------------------------------------------------------- |
| 343 | // BIC test variant - iterate over output bits, then key bits. No temp storage, |
| 344 | // but slooooow |
| 345 | |
| 346 | template< typename keytype, typename hashtype > |
| 347 | void BicTest2 ( pfHash hash, const int reps, bool verbose = true ) |
| 348 | { |
| 349 | const int keybytes = sizeof(keytype); |
| 350 | const int keybits = keybytes * 8; |
| 351 | const int hashbytes = sizeof(hashtype); |
| 352 | const int hashbits = hashbytes * 8; |
| 353 | |
| 354 | Rand r(11938); |
| 355 | |
| 356 | double maxBias = 0; |
| 357 | int maxK = 0; |
| 358 | int maxA = 0; |
| 359 | int maxB = 0; |
| 360 | |
| 361 | keytype key; |
| 362 | hashtype h1,h2; |
| 363 | |
| 364 | for(int out1 = 0; out1 < hashbits-1; out1++) |
| 365 | for(int out2 = out1+1; out2 < hashbits; out2++) |
| 366 | { |
| 367 | if(verbose) printf("(%3d,%3d) - ",out1,out2); |
| 368 | |
| 369 | for(int keybit = 0; keybit < keybits; keybit++) |
| 370 | { |
| 371 | int bins[4] = { 0, 0, 0, 0 }; |
| 372 | |
| 373 | for(int irep = 0; irep < reps; irep++) |
| 374 | { |
| 375 | r.rand_p(&key,keybytes); |
| 376 | hash(&key,keybytes,0,&h1); |
| 377 | flipbit(key,keybit); |
| 378 | hash(&key,keybytes,0,&h2); |
| 379 | |
| 380 | hashtype d = h1 ^ h2; |
| 381 | |
| 382 | uint32_t b = getbit(d,out1) | (getbit(d,out2) << 1); |
| 383 | |
| 384 | bins[b]++; |
| 385 | } |
| 386 | |
| 387 | double bias = 0; |
| 388 | |
| 389 | for(int b = 0; b < 4; b++) |
| 390 | { |
| 391 | double b2 = double(bins[b]) / double(reps / 2); |
| 392 | b2 = fabs(b2 * 2 - 1); |
| 393 | |
| 394 | if(b2 > bias) bias = b2; |
| 395 | } |
| 396 | |
| 397 | if(bias > maxBias) |
| 398 | { |
| 399 | maxBias = bias; |
| 400 | maxK = keybit; |
| 401 | maxA = out1; |
| 402 | maxB = out2; |
| 403 | } |
| 404 | |
| 405 | if(verbose) |
| 406 | { |
| 407 | if (bias < 0.05) printf("."); |
| 408 | else if(bias < 0.10) printf("o"); |
| 409 | else if(bias < 0.50) printf("O"); |
| 410 | else printf("X"); |
| 411 | } |
| 412 | } |
| 413 | |
| 414 | // Finished keybit |
| 415 | |
| 416 | if(verbose) printf("\n"); |
| 417 | } |
| 418 | |
| 419 | printf("Max bias %f - (%3d : %3d,%3d)\n",maxBias,maxK,maxA,maxB); |
| 420 | } |
| 421 | |
| 422 | //----------------------------------------------------------------------------- |