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