mdw@git.distorted.org.uk Git - catacomb/blob - math/pgen.c

   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   int rc = PGEN_ABORT;
 122
 123   switch (rq) {
 124     case PGEN_BEGIN:
 125       rabin_create(r, ev->m);
 126       rc = PGEN_TRY;
 127       break;
 128     case PGEN_TRY:
 129       if (!ev->tests)
 130         rc = rabin_rtest(r, MP_TWO);
 131       else {
 132         mp *a = mprand_range(MP_NEW, ev->m, ev->r, 0);
 133         rc = rabin_rtest(r, a);
 134         mp_drop(a);
 135       }
 136       break;
 137     case PGEN_DONE:
 138       rabin_destroy(r);
 139       rc = PGEN_DONE;
 140       break;
 141   }
 142
 143   return (rc);
 144 }
 145
 146 /*----- The main driver ---------------------------------------------------*/
 147
 148 /* --- @pgen@ --- *
 149  *
 150  * Arguments:   @const char *name@ = name of the value being searched for
 151  *              @mp *d@ = destination for the result integer
 152  *              @mp *m@ = start value to pass to stepper
 153  *              @pgen_proc *event@ = event handler function
 154  *              @void *ectx@ = context argument for event andler
 155  *              @unsigned steps@ = number of steps to take in search
 156  *              @pgen_proc *step@ = stepper function to use
 157  *              @void *sctx@ = context argument for stepper
 158  *              @unsigned tests@ = number of tests to make
 159  *              @pgen_proc *test@ = tester function to use
 160  *              @void *tctx@ = context argument for tester
 161  *
 162  * Returns:     Pointer to final result, or null.
 163  *
 164  * Use:         A generalized prime-number search skeleton.  Yes, that's a
 165  *              scary number of arguments.
 166  */
 167
 168 mp *pgen(const char *name, mp *d, mp *m, pgen_proc *event, void *ectx,
 169          unsigned steps, pgen_proc *step, void *sctx,
 170          unsigned tests, pgen_proc *test, void *tctx)
 171 {
 172   pgen_event ev;
 173   int rq, rc;
 174   pgen_proc *proc;
 175   void *ctx;
 176   int p;
 177
 178   enum { P_STEP, P_TEST };
 179
 180   /* --- Set up the initial event block --- */
 181
 182   ev.name = name;
 183   if (m)
 184     ev.m = MP_COPY(m);
 185   else
 186     ev.m = 0;
 187   ev.steps = 0;
 188   ev.tests = 0;
 189   ev.r = fibrand_create(0);
 190
 191   /* --- Tell the event handler we're under way --- */
 192
 193   if (event && event(PGEN_BEGIN, &ev, ectx) == PGEN_ABORT) {
 194     ev.r->ops->destroy(ev.r);
 195     return (0);
 196   }
 197
 198   /* --- Set up for the initial call --- */
 199
 200   proc = step; ctx = sctx; p = P_STEP; rq = PGEN_BEGIN;
 201
 202   /* --- Enter the great maelstrom of state transitions --- */
 203
 204   for (;;) {
 205     unsigned act = 0;
 206
 207 #define A_STEP 1u
 208 #define A_TEST 2u
 209 #define A_EVENT 4u
 210 #define A_ENDTEST 8u
 211 #define A_ENDSTEP 16u
 212 #define A_DONE 32u
 213
 214     /* --- Call the procedure and decide what to do next --- */
 215
 216     rc = proc(rq, &ev, ctx);
 217     switch (rc) {
 218       case PGEN_TRY:
 219         if (p == P_TEST)
 220           rq = PGEN_TRY;
 221         else {
 222           act |= A_EVENT;
 223           proc = test; ctx = tctx; p = P_TEST;
 224           rq = PGEN_BEGIN;
 225         }
 226         break;
 227       case PGEN_PASS:
 228         act |= A_TEST | A_EVENT;
 229         if (p == P_TEST)
 230           rq = PGEN_TRY;
 231         else {
 232           proc = test; ctx = tctx; p = P_TEST;
 233           rq = PGEN_BEGIN;
 234         }
 235         break;
 236       case PGEN_FAIL:
 237         act |= A_STEP;
 238         if (p == P_TEST) {
 239           act |= A_ENDTEST | A_EVENT;
 240           proc = step; ctx = sctx; p = P_STEP;
 241         }
 242         rq = PGEN_TRY;
 243         break;
 244       case PGEN_DONE:
 245         act |= A_EVENT | A_DONE | A_ENDSTEP;
 246         if (p == P_TEST)
 247           act |= A_ENDTEST;
 248         break;
 249       case PGEN_ABORT:
 250         act |= A_EVENT | A_DONE;
 251         if (p == P_TEST || rq == PGEN_TRY)
 252           act |= A_ENDSTEP;
 253         if (p == P_TEST && rq != PGEN_BEGIN)
 254           act |= A_ENDTEST;
 255         break;
 256       default:
 257         assert(((void)"Invalid response from function", 0));
 258         break;
 259     }
 260
 261     /* --- If decrementing counters is requested, do that --- */
 262
 263     if ((act & A_STEP) && steps) {
 264       ev.steps++;
 265       if (ev.steps == steps) {
 266         act |= A_EVENT | A_ENDSTEP | A_DONE;
 267         rc = PGEN_ABORT;
 268       }
 269       ev.tests = 0;
 270     }
 271
 272     if ((act & A_TEST) && tests) {
 273       ev.tests++;
 274       if (ev.tests == tests) {
 275         act |= A_ENDTEST | A_ENDSTEP | A_DONE;
 276         rc = PGEN_DONE;
 277       }
 278     }
 279
 280     /* --- Report an event if so directed --- */
 281
 282     if ((act & A_EVENT) && event && event(rc, &ev, ectx) == PGEN_ABORT) {
 283       rc = PGEN_ABORT;
 284       if (!(act & A_DONE)) {
 285         act |= A_ENDSTEP | A_DONE;
 286         if (p == P_TEST && rq != PGEN_BEGIN)
 287           act |= A_ENDTEST;
 288       }
 289     }
 290
 291     /* --- Close down tester and stepper functions --- */
 292
 293     if (act & A_ENDTEST)
 294       test(PGEN_DONE, &ev, tctx);
 295     if (act & A_ENDSTEP)
 296       step(PGEN_DONE, &ev, sctx);
 297
 298     /* --- Stop the entire test if necessary --- */
 299
 300     if (act & A_DONE)
 301       break;
 302   }
 303
 304   /* --- Tidy up and return --- */
 305
 306   if (rc == PGEN_ABORT) {
 307     mp_drop(ev.m);
 308     ev.m = 0;
 309   }
 310   ev.r->ops->destroy(ev.r);
 311   mp_drop(d);
 312
 313   return (ev.m);
 314 }
 315
 316 /* --- @pgen_primep@ --- *
 317  *
 318  * Arguments:   @mp *p@ = a number to check
 319  *              @grand *gr@ = a random number source
 320  *
 321  * Returns:     Nonzero if @p@ is really prime.
 322  *
 323  * Use:         Checks the primality of @p@.  If @p@ is prime, then this
 324  *              function returns nonzero; if @p@ is really composite then it
 325  *              %%\emph{probably}%% returns zero, but might not.
 326  *
 327  *              Currently, this function uses the Baillie--PSW test, which
 328  *              combines a single Miller--Rabin test with witness 2 with a
 329  *              single Frobenius test with parameters chosen using
 330  *              Selfridge's `Method A'.  No composites are known which pass
 331  *              this test, though it's conjectured that infinitely many
 332  *              exist.
 333  */
 334
 335 int pgen_primep(mp *p, grand *gr)
 336 {
 337   rabin r;
 338   int rc;
 339
 340   if (MP_NEGP(p)) return (0);
 341   switch (pfilt_smallfactor(p)) {
 342     case PGEN_DONE: return (1);
 343     case PGEN_FAIL: return (0);
 344   }
 345   rabin_create(&r, p); rc = rabin_test(&r, MP_TWO); rabin_destroy(&r);
 346   if (rc == PGEN_FAIL) return (0);
 347   rc = pgen_granfrob(p, 0, 0); if (rc == PGEN_FAIL) return (0);
 348   return (1);
 349 }
 350
 351 /*----- Test rig ----------------------------------------------------------*/
 352
 353 #ifdef TEST_RIG
 354
 355 #include <mLib/testrig.h>
 356
 357 static int t_primep(dstr *v)
 358 {
 359   mp *m = *(mp **)v[0].buf;
 360   int e = *(int *)v[1].buf;
 361   int r;
 362   grand *rng;
 363   int ok = 1;
 364
 365   rng = fibrand_create(0);
 366   r = pgen_primep(m, rng);
 367   GR_DESTROY(rng);
 368   if (e != r) {
 369     fputs("\n*** primep failed", stderr);
 370     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 371     fprintf(stderr, "\nexpected %d", e);
 372     fprintf(stderr, "\nreported %d", r);
 373     fputc('\n', stderr);
 374     ok = 0;
 375   }
 376
 377   mp_drop(m);
 378   assert(mparena_count(MPARENA_GLOBAL) == 0);
 379   return (ok);
 380 }
 381
 382 static int verify(dstr *v)
 383 {
 384   mp *m = *(mp **)v[0].buf;
 385   mp *q = *(mp **)v[1].buf;
 386   mp *p;
 387   int ok = 1;
 388
 389   pgen_filterctx pf;
 390   rabin r;
 391
 392   pf.step = 2;
 393   p = pgen("p", MP_NEW, m, pgen_evspin, 0, 0, pgen_filter, &pf,
 394            rabin_iters(mp_bits(m)), pgen_test, &r);
 395   if (!p || !MP_EQ(p, q)) {
 396     fputs("\n*** pgen failed", stderr);
 397     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 398     fputs("\np = ", stderr); mp_writefile(p, stderr, 10);
 399     fputs("\nq = ", stderr); mp_writefile(q, stderr, 10);
 400     fputc('\n', stderr);
 401     ok = 0;
 402   }
 403
 404   mp_drop(m);
 405   mp_drop(q);
 406   mp_drop(p);
 407   assert(mparena_count(MPARENA_GLOBAL) == 0);
 408   return (ok);
 409 }
 410
 411 static test_chunk tests[] = {
 412   { "pgen", verify, { &type_mp, &type_mp, 0 } },
 413   { "primep", t_primep, { &type_mp, &type_int, 0 } },
 414   { 0, 0, { 0 } }
 415 };
 416
 417 int main(int argc, char *argv[])
 418 {
 419   sub_init();
 420   test_run(argc, argv, tests, SRCDIR "/t/pgen");
 421   return (0);
 422 }
 423 #endif
 424
 425 /*----- That's all, folks -------------------------------------------------*/