| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Prime generation glue |
| 4 | * |
| 5 | * (c) 1999 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include <assert.h> |
| 31 | #include <stdio.h> |
| 32 | #include <stdlib.h> |
| 33 | #include <string.h> |
| 34 | |
| 35 | #include "fibrand.h" |
| 36 | #include "grand.h" |
| 37 | #include "mp.h" |
| 38 | #include "mprand.h" |
| 39 | #include "pgen.h" |
| 40 | #include "pfilt.h" |
| 41 | #include "rabin.h" |
| 42 | |
| 43 | /*----- Standard prime filter ---------------------------------------------*/ |
| 44 | |
| 45 | /* --- @pgen_filter@ --- */ |
| 46 | |
| 47 | int pgen_filter(int rq, pgen_event *ev, void *p) |
| 48 | { |
| 49 | pgen_filterctx *f = p; |
| 50 | int rc = PGEN_FAIL; |
| 51 | |
| 52 | switch (rq) { |
| 53 | case PGEN_BEGIN: |
| 54 | rc = pfilt_create(&f->f, ev->m); |
| 55 | mp_drop(ev->m); |
| 56 | break; |
| 57 | case PGEN_TRY: |
| 58 | mp_drop(ev->m); |
| 59 | break; |
| 60 | case PGEN_DONE: |
| 61 | pfilt_destroy(&f->f); |
| 62 | return (PGEN_DONE); |
| 63 | default: |
| 64 | rc = PGEN_ABORT; |
| 65 | break; |
| 66 | } |
| 67 | |
| 68 | if (rc == PGEN_FAIL && !((f->step | f->f.m->v[0]) & 1)) |
| 69 | rc = pfilt_step(&f->f, 1); |
| 70 | while (rc == PGEN_FAIL) |
| 71 | rc = pfilt_step(&f->f, f->step); |
| 72 | ev->m = MP_COPY(f->f.m); |
| 73 | return (rc); |
| 74 | } |
| 75 | |
| 76 | /* --- @pgen_jump@ --- * |
| 77 | * |
| 78 | * Similar to the standard @pgen_filter@, but jumps in large steps rather |
| 79 | * than small ones. |
| 80 | */ |
| 81 | |
| 82 | int pgen_jump(int rq, pgen_event *ev, void *p) |
| 83 | { |
| 84 | pgen_jumpctx *f = p; |
| 85 | int rc = PGEN_ABORT; |
| 86 | |
| 87 | switch (rq) { |
| 88 | case PGEN_BEGIN: { |
| 89 | mp *g = MP_NEW; |
| 90 | mp_gcd(&g, 0, 0, ev->m, f->j->m); |
| 91 | if (MP_CMP(g, >, MP_ONE)) { |
| 92 | mp_drop(g); |
| 93 | return (PGEN_ABORT); |
| 94 | } |
| 95 | mp_drop(g); |
| 96 | rc = pfilt_create(&f->f, ev->m); |
| 97 | mp_drop(ev->m); |
| 98 | } break; |
| 99 | case PGEN_TRY: |
| 100 | mp_drop(ev->m); |
| 101 | rc = pfilt_jump(&f->f, f->j); |
| 102 | break; |
| 103 | case PGEN_DONE: |
| 104 | pfilt_destroy(&f->f); |
| 105 | return (PGEN_DONE); |
| 106 | } |
| 107 | |
| 108 | while (rc == PGEN_FAIL) |
| 109 | rc = pfilt_jump(&f->f, f->j); |
| 110 | ev->m = MP_COPY(f->f.m); |
| 111 | return (rc); |
| 112 | } |
| 113 | |
| 114 | /*----- Standard prime test -----------------------------------------------*/ |
| 115 | |
| 116 | /* --- @pgen_test@ --- */ |
| 117 | |
| 118 | int pgen_test(int rq, pgen_event *ev, void *p) |
| 119 | { |
| 120 | rabin *r = p; |
| 121 | mp *a = MP_NEW; |
| 122 | int rc = PGEN_ABORT; |
| 123 | |
| 124 | switch (rq) { |
| 125 | case PGEN_BEGIN: |
| 126 | rabin_create(r, ev->m); |
| 127 | rc = PGEN_TRY; |
| 128 | break; |
| 129 | case PGEN_TRY: |
| 130 | a = mprand_range(a, ev->m, ev->r, 0); |
| 131 | rc = rabin_rtest(r, a); |
| 132 | break; |
| 133 | case PGEN_DONE: |
| 134 | rabin_destroy(r); |
| 135 | rc = PGEN_DONE; |
| 136 | break; |
| 137 | } |
| 138 | |
| 139 | mp_drop(a); |
| 140 | return (rc); |
| 141 | } |
| 142 | |
| 143 | /* --- @pgen_bailliepswtest@ --- */ |
| 144 | |
| 145 | int pgen_bailliepswtest(int rq, pgen_event *ev, void *p) |
| 146 | { |
| 147 | rabin r; |
| 148 | int rc; |
| 149 | |
| 150 | switch (rq) { |
| 151 | case PGEN_BEGIN: |
| 152 | if (ev->tests != 2) rc = PGEN_ABORT; |
| 153 | else rc = PGEN_TRY; |
| 154 | break; |
| 155 | |
| 156 | case PGEN_DONE: |
| 157 | rc = PGEN_DONE; |
| 158 | break; |
| 159 | |
| 160 | case PGEN_TRY: |
| 161 | switch (ev->tests) { |
| 162 | case 2: |
| 163 | rabin_create(&r, ev->m); |
| 164 | rc = rabin_test(&r, MP_TWO); |
| 165 | rabin_destroy(&r); |
| 166 | break; |
| 167 | case 1: |
| 168 | rc = pgen_granfrob(ev->m, 0, 0); |
| 169 | break; |
| 170 | default: |
| 171 | rc = PGEN_ABORT; |
| 172 | break; |
| 173 | } |
| 174 | break; |
| 175 | |
| 176 | default: |
| 177 | rc = PGEN_ABORT; |
| 178 | break; |
| 179 | } |
| 180 | |
| 181 | return (rc); |
| 182 | } |
| 183 | |
| 184 | /*----- The main driver ---------------------------------------------------*/ |
| 185 | |
| 186 | /* --- @pgen@ --- * |
| 187 | * |
| 188 | * Arguments: @const char *name@ = name of the value being searched for |
| 189 | * @mp *d@ = destination for the result integer |
| 190 | * @mp *m@ = start value to pass to stepper |
| 191 | * @pgen_proc *event@ = event handler function |
| 192 | * @void *ectx@ = context argument for event andler |
| 193 | * @unsigned steps@ = number of steps to take in search |
| 194 | * @pgen_proc *step@ = stepper function to use |
| 195 | * @void *sctx@ = context argument for stepper |
| 196 | * @unsigned tests@ = number of tests to make |
| 197 | * @pgen_proc *test@ = tester function to use |
| 198 | * @void *tctx@ = context argument for tester |
| 199 | * |
| 200 | * Returns: Pointer to final result, or null. |
| 201 | * |
| 202 | * Use: A generalized prime-number search skeleton. Yes, that's a |
| 203 | * scary number of arguments. |
| 204 | */ |
| 205 | |
| 206 | mp *pgen(const char *name, mp *d, mp *m, pgen_proc *event, void *ectx, |
| 207 | unsigned steps, pgen_proc *step, void *sctx, |
| 208 | unsigned tests, pgen_proc *test, void *tctx) |
| 209 | { |
| 210 | pgen_event ev; |
| 211 | int rq, rc; |
| 212 | pgen_proc *proc; |
| 213 | void *ctx; |
| 214 | int p; |
| 215 | |
| 216 | enum { P_STEP, P_TEST }; |
| 217 | |
| 218 | /* --- Set up the initial event block --- */ |
| 219 | |
| 220 | ev.name = name; |
| 221 | if (m) |
| 222 | ev.m = MP_COPY(m); |
| 223 | else |
| 224 | ev.m = 0; |
| 225 | ev.steps = steps; |
| 226 | ev.tests = tests; |
| 227 | ev.r = fibrand_create(0); |
| 228 | |
| 229 | /* --- Tell the event handler we're under way --- */ |
| 230 | |
| 231 | if (event && event(PGEN_BEGIN, &ev, ectx) == PGEN_ABORT) { |
| 232 | ev.r->ops->destroy(ev.r); |
| 233 | return (0); |
| 234 | } |
| 235 | |
| 236 | /* --- Set up for the initial call --- */ |
| 237 | |
| 238 | proc = step; ctx = sctx; p = P_STEP; rq = PGEN_BEGIN; |
| 239 | |
| 240 | /* --- Enter the great maelstrom of state transitions --- */ |
| 241 | |
| 242 | for (;;) { |
| 243 | unsigned act = 0; |
| 244 | |
| 245 | #define A_STEP 1u |
| 246 | #define A_TEST 2u |
| 247 | #define A_EVENT 4u |
| 248 | #define A_ENDTEST 8u |
| 249 | #define A_ENDSTEP 16u |
| 250 | #define A_DONE 32u |
| 251 | |
| 252 | /* --- Call the procedure and decide what to do next --- */ |
| 253 | |
| 254 | rc = proc(rq, &ev, ctx); |
| 255 | switch (rc) { |
| 256 | case PGEN_TRY: |
| 257 | if (p == P_TEST) |
| 258 | rq = PGEN_TRY; |
| 259 | else { |
| 260 | act |= A_EVENT; |
| 261 | proc = test; ctx = tctx; p = P_TEST; |
| 262 | rq = PGEN_BEGIN; |
| 263 | } |
| 264 | break; |
| 265 | case PGEN_PASS: |
| 266 | act |= A_TEST | A_EVENT; |
| 267 | if (p == P_TEST) |
| 268 | rq = PGEN_TRY; |
| 269 | else { |
| 270 | proc = test; ctx = tctx; p = P_TEST; |
| 271 | rq = PGEN_BEGIN; |
| 272 | } |
| 273 | break; |
| 274 | case PGEN_FAIL: |
| 275 | act |= A_STEP; |
| 276 | if (p == P_TEST) { |
| 277 | act |= A_ENDTEST | A_EVENT; |
| 278 | proc = step; ctx = sctx; p = P_STEP; |
| 279 | } |
| 280 | rq = PGEN_TRY; |
| 281 | break; |
| 282 | case PGEN_DONE: |
| 283 | act |= A_EVENT | A_DONE | A_ENDSTEP; |
| 284 | if (p == P_TEST) |
| 285 | act |= A_ENDTEST; |
| 286 | break; |
| 287 | case PGEN_ABORT: |
| 288 | act |= A_EVENT | A_DONE; |
| 289 | if (p == P_TEST || rq == PGEN_TRY) |
| 290 | act |= A_ENDSTEP; |
| 291 | if (p == P_TEST && rq != PGEN_BEGIN) |
| 292 | act |= A_ENDTEST; |
| 293 | break; |
| 294 | default: |
| 295 | assert(((void)"Invalid response from function", 0)); |
| 296 | break; |
| 297 | } |
| 298 | |
| 299 | /* --- If decrementing counters is requested, do that --- */ |
| 300 | |
| 301 | if ((act & A_STEP) && steps) { |
| 302 | ev.steps--; |
| 303 | if (!ev.steps) { |
| 304 | act |= A_EVENT | A_ENDSTEP | A_DONE; |
| 305 | rc = PGEN_ABORT; |
| 306 | } |
| 307 | ev.tests = tests; |
| 308 | } |
| 309 | |
| 310 | if ((act & A_TEST) && tests) { |
| 311 | ev.tests--; |
| 312 | if (!ev.tests) { |
| 313 | act |= A_ENDTEST | A_ENDSTEP | A_DONE; |
| 314 | rc = PGEN_DONE; |
| 315 | } |
| 316 | } |
| 317 | |
| 318 | /* --- Report an event if so directed --- */ |
| 319 | |
| 320 | if ((act & A_EVENT) && event && event(rc, &ev, ectx) == PGEN_ABORT) { |
| 321 | rc = PGEN_ABORT; |
| 322 | if (!(act & A_DONE)) { |
| 323 | act |= A_ENDSTEP | A_DONE; |
| 324 | if (p == P_TEST && rq != PGEN_BEGIN) |
| 325 | act |= A_ENDTEST; |
| 326 | } |
| 327 | } |
| 328 | |
| 329 | /* --- Close down tester and stepper functions --- */ |
| 330 | |
| 331 | if (act & A_ENDTEST) |
| 332 | test(PGEN_DONE, &ev, tctx); |
| 333 | if (act & A_ENDSTEP) |
| 334 | step(PGEN_DONE, &ev, sctx); |
| 335 | |
| 336 | /* --- Stop the entire test if necessary --- */ |
| 337 | |
| 338 | if (act & A_DONE) |
| 339 | break; |
| 340 | } |
| 341 | |
| 342 | /* --- Tidy up and return --- */ |
| 343 | |
| 344 | if (rc == PGEN_ABORT) { |
| 345 | mp_drop(ev.m); |
| 346 | ev.m = 0; |
| 347 | } |
| 348 | ev.r->ops->destroy(ev.r); |
| 349 | mp_drop(d); |
| 350 | |
| 351 | return (ev.m); |
| 352 | } |
| 353 | |
| 354 | /* --- @pgen_primep@ --- * |
| 355 | * |
| 356 | * Arguments: @mp *p@ = a number to check |
| 357 | * @grand *gr@ = a random number source |
| 358 | * |
| 359 | * Returns: Nonzero if @p@ is really prime. |
| 360 | * |
| 361 | * Use: Checks the primality of @p@. If @p@ is prime, then this |
| 362 | * function returns nonzero; if @p@ is really composite then it |
| 363 | * %%\emph{probably}%% returns zero, but might not. |
| 364 | * |
| 365 | * Currently, this function uses the Baillie--PSW test, which |
| 366 | * combines a single Miller--Rabin test with witness 2 with a |
| 367 | * single Frobenius test with parameters chosen using |
| 368 | * Selfridge's `Method A'. No composites are known which pass |
| 369 | * this test, though it's conjectured that infinitely many |
| 370 | * exist. |
| 371 | */ |
| 372 | |
| 373 | int pgen_primep(mp *p, grand *gr) |
| 374 | { |
| 375 | rabin r; |
| 376 | int rc; |
| 377 | |
| 378 | if (MP_NEGP(p)) return (0); |
| 379 | switch (pfilt_smallfactor(p)) { |
| 380 | case PGEN_DONE: return (1); |
| 381 | case PGEN_FAIL: return (0); |
| 382 | } |
| 383 | rabin_create(&r, p); rc = rabin_test(&r, MP_TWO); rabin_destroy(&r); |
| 384 | if (rc == PGEN_FAIL) return (0); |
| 385 | rc = pgen_granfrob(p, 0, 0); if (rc == PGEN_FAIL) return (0); |
| 386 | return (1); |
| 387 | } |
| 388 | |
| 389 | /*----- Test rig ----------------------------------------------------------*/ |
| 390 | |
| 391 | #ifdef TEST_RIG |
| 392 | |
| 393 | #include <mLib/testrig.h> |
| 394 | |
| 395 | static int t_primep(dstr *v) |
| 396 | { |
| 397 | mp *m = *(mp **)v[0].buf; |
| 398 | int e = *(int *)v[1].buf; |
| 399 | int r; |
| 400 | grand *rng; |
| 401 | int ok = 1; |
| 402 | |
| 403 | rng = fibrand_create(0); |
| 404 | r = pgen_primep(m, rng); |
| 405 | GR_DESTROY(rng); |
| 406 | if (e != r) { |
| 407 | fputs("\n*** primep failed", stderr); |
| 408 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
| 409 | fprintf(stderr, "\nexpected %d", e); |
| 410 | fprintf(stderr, "\nreported %d", r); |
| 411 | fputc('\n', stderr); |
| 412 | ok = 0; |
| 413 | } |
| 414 | |
| 415 | mp_drop(m); |
| 416 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 417 | return (ok); |
| 418 | } |
| 419 | |
| 420 | static int verify(dstr *v) |
| 421 | { |
| 422 | mp *m = *(mp **)v[0].buf; |
| 423 | mp *q = *(mp **)v[1].buf; |
| 424 | mp *p; |
| 425 | int ok = 1; |
| 426 | |
| 427 | pgen_filterctx pf; |
| 428 | rabin r; |
| 429 | |
| 430 | pf.step = 2; |
| 431 | p = pgen("p", MP_NEW, m, pgen_evspin, 0, 0, pgen_filter, &pf, |
| 432 | rabin_iters(mp_bits(m)), pgen_test, &r); |
| 433 | if (!p || !MP_EQ(p, q)) { |
| 434 | fputs("\n*** pgen failed", stderr); |
| 435 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
| 436 | fputs("\np = ", stderr); mp_writefile(p, stderr, 10); |
| 437 | fputs("\nq = ", stderr); mp_writefile(q, stderr, 10); |
| 438 | fputc('\n', stderr); |
| 439 | ok = 0; |
| 440 | } |
| 441 | |
| 442 | mp_drop(m); |
| 443 | mp_drop(q); |
| 444 | mp_drop(p); |
| 445 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 446 | return (ok); |
| 447 | } |
| 448 | |
| 449 | static test_chunk tests[] = { |
| 450 | { "pgen", verify, { &type_mp, &type_mp, 0 } }, |
| 451 | { "primep", t_primep, { &type_mp, &type_int, 0 } }, |
| 452 | { 0, 0, { 0 } } |
| 453 | }; |
| 454 | |
| 455 | int main(int argc, char *argv[]) |
| 456 | { |
| 457 | sub_init(); |
| 458 | test_run(argc, argv, tests, SRCDIR "/t/pgen"); |
| 459 | return (0); |
| 460 | } |
| 461 | #endif |
| 462 | |
| 463 | /*----- That's all, folks -------------------------------------------------*/ |