Howard Hinnant | c51e102 | 2010-05-11 19:42:16 +0000 | [diff] [blame^] | 1 | //===-------------------------- hash.cpp ----------------------------------===// |
| 2 | // |
| 3 | // ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊThe LLVM Compiler Infrastructure |
| 4 | // |
| 5 | // This file is distributed under the University of Illinois Open Source |
| 6 | // License. See LICENSE.TXT for details. |
| 7 | // |
| 8 | //===----------------------------------------------------------------------===// |
| 9 | |
| 10 | #include "__hash_table" |
| 11 | #include "algorithm" |
| 12 | |
| 13 | _LIBCPP_BEGIN_NAMESPACE_STD |
| 14 | |
| 15 | namespace { |
| 16 | |
| 17 | // handle all next_prime(i) for i in [1, 210), special case 0 |
| 18 | const unsigned small_primes[] = |
| 19 | { |
| 20 | 0, |
| 21 | 2, |
| 22 | 3, |
| 23 | 5, |
| 24 | 7, |
| 25 | 11, |
| 26 | 13, |
| 27 | 17, |
| 28 | 19, |
| 29 | 23, |
| 30 | 29, |
| 31 | 31, |
| 32 | 37, |
| 33 | 41, |
| 34 | 43, |
| 35 | 47, |
| 36 | 53, |
| 37 | 59, |
| 38 | 61, |
| 39 | 67, |
| 40 | 71, |
| 41 | 73, |
| 42 | 79, |
| 43 | 83, |
| 44 | 89, |
| 45 | 97, |
| 46 | 101, |
| 47 | 103, |
| 48 | 107, |
| 49 | 109, |
| 50 | 113, |
| 51 | 127, |
| 52 | 131, |
| 53 | 137, |
| 54 | 139, |
| 55 | 149, |
| 56 | 151, |
| 57 | 157, |
| 58 | 163, |
| 59 | 167, |
| 60 | 173, |
| 61 | 179, |
| 62 | 181, |
| 63 | 191, |
| 64 | 193, |
| 65 | 197, |
| 66 | 199, |
| 67 | 211 |
| 68 | }; |
| 69 | |
| 70 | // potential primes = 210*k + indices[i], k >= 1 |
| 71 | // these numbers are not divisible by 2, 3, 5 or 7 |
| 72 | // (or any integer 2 <= j <= 10 for that matter). |
| 73 | const unsigned indices[] = |
| 74 | { |
| 75 | 1, |
| 76 | 11, |
| 77 | 13, |
| 78 | 17, |
| 79 | 19, |
| 80 | 23, |
| 81 | 29, |
| 82 | 31, |
| 83 | 37, |
| 84 | 41, |
| 85 | 43, |
| 86 | 47, |
| 87 | 53, |
| 88 | 59, |
| 89 | 61, |
| 90 | 67, |
| 91 | 71, |
| 92 | 73, |
| 93 | 79, |
| 94 | 83, |
| 95 | 89, |
| 96 | 97, |
| 97 | 101, |
| 98 | 103, |
| 99 | 107, |
| 100 | 109, |
| 101 | 113, |
| 102 | 121, |
| 103 | 127, |
| 104 | 131, |
| 105 | 137, |
| 106 | 139, |
| 107 | 143, |
| 108 | 149, |
| 109 | 151, |
| 110 | 157, |
| 111 | 163, |
| 112 | 167, |
| 113 | 169, |
| 114 | 173, |
| 115 | 179, |
| 116 | 181, |
| 117 | 187, |
| 118 | 191, |
| 119 | 193, |
| 120 | 197, |
| 121 | 199, |
| 122 | 209 |
| 123 | }; |
| 124 | |
| 125 | } |
| 126 | |
| 127 | // Returns: If n == 0, returns 0. Else returns the lowest prime number that |
| 128 | // is greater than or equal to n. |
| 129 | // |
| 130 | // The algorithm creates a list of small primes, plus an open-ended list of |
| 131 | // potential primes. All prime numbers are potential prime numbers. However |
| 132 | // some potential prime numbers are not prime. In an ideal world, all potential |
| 133 | // prime numbers would be prime. Candiate prime numbers are chosen as the next |
| 134 | // highest potential prime. Then this number is tested for prime by dividing it |
| 135 | // by all potential prime numbers less than the sqrt of the candidate. |
| 136 | // |
| 137 | // This implementation defines potential primes as those numbers not divisible |
| 138 | // by 2, 3, 5, and 7. Other (common) implementations define potential primes |
| 139 | // as those not divisible by 2. A few other implementations define potential |
| 140 | // primes as those not divisible by 2 or 3. By raising the number of small |
| 141 | // primes which the potential prime is not divisible by, the set of potential |
| 142 | // primes more closely approximates the set of prime numbers. And thus there |
| 143 | // are fewer potential primes to search, and fewer potential primes to divide |
| 144 | // against. |
| 145 | |
| 146 | size_t |
| 147 | __next_prime(size_t n) |
| 148 | { |
| 149 | const size_t L = 210; |
| 150 | const size_t N = sizeof(small_primes) / sizeof(small_primes[0]); |
| 151 | // If n is small enough, search in small_primes |
| 152 | if (n <= small_primes[N-1]) |
| 153 | return *std::lower_bound(small_primes, small_primes + N, n); |
| 154 | // Else n > largest small_primes |
| 155 | // Start searching list of potential primes: L * k0 + indices[in] |
| 156 | const size_t M = sizeof(indices) / sizeof(indices[0]); |
| 157 | // Select first potential prime >= n |
| 158 | // Known a-priori n >= L |
| 159 | size_t k0 = n / L; |
| 160 | size_t in = std::lower_bound(indices, indices + M, n % L) - indices; |
| 161 | n = L * k0 + indices[in]; |
| 162 | while (true) |
| 163 | { |
| 164 | // Divide n by all primes or potential primes (i) until: |
| 165 | // 1. The division is even, so try next potential prime. |
| 166 | // 2. The i > sqrt(n), in which case n is prime. |
| 167 | // It is known a-priori that n is not divisible by 2, 3, 5 or 7, |
| 168 | // so don't test those (j == 5 -> divide by 11 first). And the |
| 169 | // potential primes start with 211, so don't test against the last |
| 170 | // small prime. |
| 171 | for (size_t j = 5; j < N - 1; ++j) |
| 172 | { |
| 173 | if (n % small_primes[j] == 0) |
| 174 | goto next; |
| 175 | if (n / small_primes[j] < small_primes[j]) |
| 176 | return n; |
| 177 | } |
| 178 | // n wasn't divisible by small primes, try potential primes |
| 179 | { |
| 180 | size_t i = 211; |
| 181 | while (true) |
| 182 | { |
| 183 | if (n % i == 0) |
| 184 | break; |
| 185 | if (n / i < i) |
| 186 | return n; |
| 187 | |
| 188 | i += 10; |
| 189 | if (n % i == 0) |
| 190 | break; |
| 191 | if (n / i < i) |
| 192 | return n; |
| 193 | |
| 194 | i += 2; |
| 195 | if (n % i == 0) |
| 196 | break; |
| 197 | if (n / i < i) |
| 198 | return n; |
| 199 | |
| 200 | i += 4; |
| 201 | if (n % i == 0) |
| 202 | break; |
| 203 | if (n / i < i) |
| 204 | return n; |
| 205 | |
| 206 | i += 2; |
| 207 | if (n % i == 0) |
| 208 | break; |
| 209 | if (n / i < i) |
| 210 | return n; |
| 211 | |
| 212 | i += 4; |
| 213 | if (n % i == 0) |
| 214 | break; |
| 215 | if (n / i < i) |
| 216 | return n; |
| 217 | |
| 218 | i += 6; |
| 219 | if (n % i == 0) |
| 220 | break; |
| 221 | if (n / i < i) |
| 222 | return n; |
| 223 | |
| 224 | i += 2; |
| 225 | if (n % i == 0) |
| 226 | break; |
| 227 | if (n / i < i) |
| 228 | return n; |
| 229 | |
| 230 | i += 6; |
| 231 | if (n % i == 0) |
| 232 | break; |
| 233 | if (n / i < i) |
| 234 | return n; |
| 235 | |
| 236 | i += 4; |
| 237 | if (n % i == 0) |
| 238 | break; |
| 239 | if (n / i < i) |
| 240 | return n; |
| 241 | |
| 242 | i += 2; |
| 243 | if (n % i == 0) |
| 244 | break; |
| 245 | if (n / i < i) |
| 246 | return n; |
| 247 | |
| 248 | i += 4; |
| 249 | if (n % i == 0) |
| 250 | break; |
| 251 | if (n / i < i) |
| 252 | return n; |
| 253 | |
| 254 | i += 6; |
| 255 | if (n % i == 0) |
| 256 | break; |
| 257 | if (n / i < i) |
| 258 | return n; |
| 259 | |
| 260 | i += 6; |
| 261 | if (n % i == 0) |
| 262 | break; |
| 263 | if (n / i < i) |
| 264 | return n; |
| 265 | |
| 266 | i += 2; |
| 267 | if (n % i == 0) |
| 268 | break; |
| 269 | if (n / i < i) |
| 270 | return n; |
| 271 | |
| 272 | i += 6; |
| 273 | if (n % i == 0) |
| 274 | break; |
| 275 | if (n / i < i) |
| 276 | return n; |
| 277 | |
| 278 | i += 4; |
| 279 | if (n % i == 0) |
| 280 | break; |
| 281 | if (n / i < i) |
| 282 | return n; |
| 283 | |
| 284 | i += 2; |
| 285 | if (n % i == 0) |
| 286 | break; |
| 287 | if (n / i < i) |
| 288 | return n; |
| 289 | |
| 290 | i += 6; |
| 291 | if (n % i == 0) |
| 292 | break; |
| 293 | if (n / i < i) |
| 294 | return n; |
| 295 | |
| 296 | i += 4; |
| 297 | if (n % i == 0) |
| 298 | break; |
| 299 | if (n / i < i) |
| 300 | return n; |
| 301 | |
| 302 | i += 6; |
| 303 | if (n % i == 0) |
| 304 | break; |
| 305 | if (n / i < i) |
| 306 | return n; |
| 307 | |
| 308 | i += 8; |
| 309 | if (n % i == 0) |
| 310 | break; |
| 311 | if (n / i < i) |
| 312 | return n; |
| 313 | |
| 314 | i += 4; |
| 315 | if (n % i == 0) |
| 316 | break; |
| 317 | if (n / i < i) |
| 318 | return n; |
| 319 | |
| 320 | i += 2; |
| 321 | if (n % i == 0) |
| 322 | break; |
| 323 | if (n / i < i) |
| 324 | return n; |
| 325 | |
| 326 | i += 4; |
| 327 | if (n % i == 0) |
| 328 | break; |
| 329 | if (n / i < i) |
| 330 | return n; |
| 331 | |
| 332 | i += 2; |
| 333 | if (n % i == 0) |
| 334 | break; |
| 335 | if (n / i < i) |
| 336 | return n; |
| 337 | |
| 338 | i += 4; |
| 339 | if (n % i == 0) |
| 340 | break; |
| 341 | if (n / i < i) |
| 342 | return n; |
| 343 | |
| 344 | i += 8; |
| 345 | if (n % i == 0) |
| 346 | break; |
| 347 | if (n / i < i) |
| 348 | return n; |
| 349 | |
| 350 | i += 6; |
| 351 | if (n % i == 0) |
| 352 | break; |
| 353 | if (n / i < i) |
| 354 | return n; |
| 355 | |
| 356 | i += 4; |
| 357 | if (n % i == 0) |
| 358 | break; |
| 359 | if (n / i < i) |
| 360 | return n; |
| 361 | |
| 362 | i += 6; |
| 363 | if (n % i == 0) |
| 364 | break; |
| 365 | if (n / i < i) |
| 366 | return n; |
| 367 | |
| 368 | i += 2; |
| 369 | if (n % i == 0) |
| 370 | break; |
| 371 | if (n / i < i) |
| 372 | return n; |
| 373 | |
| 374 | i += 4; |
| 375 | if (n % i == 0) |
| 376 | break; |
| 377 | if (n / i < i) |
| 378 | return n; |
| 379 | |
| 380 | i += 6; |
| 381 | if (n % i == 0) |
| 382 | break; |
| 383 | if (n / i < i) |
| 384 | return n; |
| 385 | |
| 386 | i += 2; |
| 387 | if (n % i == 0) |
| 388 | break; |
| 389 | if (n / i < i) |
| 390 | return n; |
| 391 | |
| 392 | i += 6; |
| 393 | if (n % i == 0) |
| 394 | break; |
| 395 | if (n / i < i) |
| 396 | return n; |
| 397 | |
| 398 | i += 6; |
| 399 | if (n % i == 0) |
| 400 | break; |
| 401 | if (n / i < i) |
| 402 | return n; |
| 403 | |
| 404 | i += 4; |
| 405 | if (n % i == 0) |
| 406 | break; |
| 407 | if (n / i < i) |
| 408 | return n; |
| 409 | |
| 410 | i += 2; |
| 411 | if (n % i == 0) |
| 412 | break; |
| 413 | if (n / i < i) |
| 414 | return n; |
| 415 | |
| 416 | i += 4; |
| 417 | if (n % i == 0) |
| 418 | break; |
| 419 | if (n / i < i) |
| 420 | return n; |
| 421 | |
| 422 | i += 6; |
| 423 | if (n % i == 0) |
| 424 | break; |
| 425 | if (n / i < i) |
| 426 | return n; |
| 427 | |
| 428 | i += 2; |
| 429 | if (n % i == 0) |
| 430 | break; |
| 431 | if (n / i < i) |
| 432 | return n; |
| 433 | |
| 434 | i += 6; |
| 435 | if (n % i == 0) |
| 436 | break; |
| 437 | if (n / i < i) |
| 438 | return n; |
| 439 | |
| 440 | i += 4; |
| 441 | if (n % i == 0) |
| 442 | break; |
| 443 | if (n / i < i) |
| 444 | return n; |
| 445 | |
| 446 | i += 2; |
| 447 | if (n % i == 0) |
| 448 | break; |
| 449 | if (n / i < i) |
| 450 | return n; |
| 451 | |
| 452 | i += 4; |
| 453 | if (n % i == 0) |
| 454 | break; |
| 455 | if (n / i < i) |
| 456 | return n; |
| 457 | |
| 458 | i += 2; |
| 459 | if (n % i == 0) |
| 460 | break; |
| 461 | if (n / i < i) |
| 462 | return n; |
| 463 | |
| 464 | i += 10; |
| 465 | if (n % i == 0) |
| 466 | break; |
| 467 | if (n / i < i) |
| 468 | return n; |
| 469 | |
| 470 | // This will loop i to the next "plane" of potential primes |
| 471 | i += 2; |
| 472 | } |
| 473 | } |
| 474 | next: |
| 475 | // n is not prime. Increment n to next potential prime. |
| 476 | if (++in == M) |
| 477 | { |
| 478 | ++k0; |
| 479 | in = 0; |
| 480 | } |
| 481 | n = L * k0 + indices[in]; |
| 482 | } |
| 483 | } |
| 484 | |
| 485 | _LIBCPP_END_NAMESPACE_STD |