git.distorted.org.uk Git - u/mdw/catacomb/blob - pfilt.c

   1 /* -*-c-*-
   2  *
   3  * $Id: pfilt.c,v 1.6 2004/04/08 01:36:15 mdw Exp $
   4  *
   5  * Finding and testing prime numbers
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33 #include "mpint.h"
  34 #include "pfilt.h"
  35 #include "pgen.h"
  36 #include "primetab.h"
  37
  38 /*----- Main code ---------------------------------------------------------*/
  39
  40 /* --- @smallenough@ --- *
  41  *
  42  * Arguments:   @mp *m@ = integer to test
  43  *
  44  * Returns:     One of the @PGEN@ result codes.
  45  *
  46  * Use:         Assuming that @m@ has been tested by trial division on every
  47  *              prime in the small-primes array, this function will return
  48  *              @PGEN_DONE@ if the number is less than the square of the
  49  *              largest small prime.
  50  */
  51
  52 static int smallenough(mp *m)
  53 {
  54   static mp *max = 0;
  55   int rc = PGEN_TRY;
  56
  57   if (!max) {
  58     max = mp_fromuint(MP_NEW, MAXPRIME);
  59     max = mp_sqr(max, max);
  60     max->a->n--; /* Permanent allocation */
  61   }
  62   if (MP_CMP(m, <=, MP_ONE))
  63     rc = PGEN_FAIL;
  64   else if (MP_CMP(m, <, max))
  65     rc = PGEN_DONE;
  66   return (rc);
  67 }
  68
  69 /* --- @pfilt_smallfactor@ --- *
  70  *
  71  * Arguments:   @mp *m@ = integer to test
  72  *
  73  * Returns:     One of the @PGEN@ result codes.
  74  *
  75  * Use:         Tests a number by dividing by a number of small primes.  This
  76  *              is a useful first step if you're testing random primes; for
  77  *              sequential searches, @pfilt_create@ works better.
  78  */
  79
  80 int pfilt_smallfactor(mp *m)
  81 {
  82   int rc = PGEN_TRY;
  83   int i;
  84   size_t sz = MP_LEN(m);
  85   mparena *a = m->a ? m->a : MPARENA_GLOBAL;
  86   mpw *v = mpalloc(a, sz);
  87
  88   /* --- Fill in the residues --- */
  89
  90   for (i = 0; i < NPRIME; i++) {
  91     if (!mpx_udivn(v, v + sz, m->v, m->vl, primetab[i])) {
  92       if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
  93         rc = PGEN_DONE;
  94       else
  95         rc = PGEN_FAIL;
  96       break;
  97     }
  98   }
  99
 100   /* --- Check for small primes --- */
 101
 102   if (rc == PGEN_TRY)
 103     rc = smallenough(m);
 104
 105   /* --- Done --- */
 106
 107   mpfree(a, v);
 108   return (rc);
 109 }
 110
 111 /* --- @pfilt_create@ --- *
 112  *
 113  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 114  *              @mp *m@ = pointer to initial number to test
 115  *
 116  * Returns:     One of the @PGEN@ result codes.
 117  *
 118  * Use:         Tests an initial number for primality by computing its
 119  *              residue modulo various small prime numbers.  This is fairly
 120  *              quick, but not particularly certain.  If a @PGEN_TRY@
 121  *              result is returned, perform Rabin-Miller tests to confirm.
 122  */
 123
 124 int pfilt_create(pfilt *p, mp *m)
 125 {
 126   int rc = PGEN_TRY;
 127   int i;
 128   size_t sz = MP_LEN(m);
 129   mparena *a = m->a ? m->a : MPARENA_GLOBAL;
 130   mpw *v = mpalloc(a, sz);
 131
 132   /* --- Take a copy of the number --- */
 133
 134   mp_shrink(m);
 135   p->m = MP_COPY(m);
 136
 137   /* --- Fill in the residues --- */
 138
 139   for (i = 0; i < NPRIME; i++) {
 140     p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
 141     if (!p->r[i] && rc == PGEN_TRY) {
 142       if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
 143         rc = PGEN_DONE;
 144       else
 145         rc = PGEN_FAIL;
 146     }
 147   }
 148
 149   /* --- Check for small primes --- */
 150
 151   if (rc == PGEN_TRY)
 152     rc = smallenough(m);
 153
 154   /* --- Done --- */
 155
 156   mpfree(a, v);
 157   return (rc);
 158 }
 159
 160 /* --- @pfilt_destroy@ --- *
 161  *
 162  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 163  *
 164  * Returns:     ---
 165  *
 166  * Use:         Discards a context and all the resources it holds.
 167  */
 168
 169 void pfilt_destroy(pfilt *p)
 170 {
 171   mp_drop(p->m);
 172 }
 173
 174 /* --- @pfilt_step@ --- *
 175  *
 176  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 177  *              @mpw step@ = how much to step the number
 178  *
 179  * Returns:     One of the @PGEN@ result codes.
 180  *
 181  * Use:         Steps a number by a small amount.  Stepping is much faster
 182  *              than initializing with a new number.  The test performed is
 183  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 184  *              results should be followed up by a Rabin-Miller test.
 185  */
 186
 187 int pfilt_step(pfilt *p, mpw step)
 188 {
 189   int rc = PGEN_TRY;
 190   int i;
 191
 192   /* --- Add the step on to the number --- */
 193
 194   p->m = mp_split(p->m);
 195   mp_ensure(p->m, MP_LEN(p->m) + 1);
 196   mpx_uaddn(p->m->v, p->m->vl, step);
 197   mp_shrink(p->m);
 198
 199   /* --- Update the residue table --- */
 200
 201   for (i = 0; i < NPRIME; i++) {
 202     p->r[i] = (p->r[i] + step) % primetab[i];
 203     if (!p->r[i] && rc == PGEN_TRY) {
 204       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 205         rc = PGEN_DONE;
 206       else
 207         rc = PGEN_FAIL;
 208     }
 209   }
 210
 211   /* --- Check for small primes --- */
 212
 213   if (rc == PGEN_TRY)
 214     rc = smallenough(p->m);
 215
 216   /* --- Done --- */
 217
 218   return (rc);
 219 }
 220
 221 /* --- @pfilt_muladd@ --- *
 222  *
 223  * Arguments:   @pfilt *p@ = destination prime filtering context
 224  *              @const pfilt *q@ = source prime filtering context
 225  *              @mpw m@ = number to multiply by
 226  *              @mpw a@ = number to add
 227  *
 228  * Returns:     One of the @PGEN@ result codes.
 229  *
 230  * Use:         Multiplies the number in a prime filtering context by a
 231  *              small value and then adds a small value.  The destination
 232  *              should either be uninitialized or the same as the source.
 233  *
 234  *              Common things to do include multiplying by 2 and adding 0 to
 235  *              turn a prime into a jump for finding other primes with @q@ as
 236  *              a factor of @p - 1@, or multiplying by 2 and adding 1.
 237  */
 238
 239 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
 240 {
 241   int rc = PGEN_TRY;
 242   int i;
 243
 244   /* --- Multiply the big number --- */
 245
 246   {
 247     mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
 248     mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
 249     mpx_uaddn(d->v, d->vl, a);
 250     if (p == q)
 251       mp_drop(p->m);
 252     mp_shrink(d);
 253     p->m = d;
 254   }
 255
 256   /* --- Gallivant through the residue table --- */
 257
 258   for (i = 0; i < NPRIME; i++) {
 259     p->r[i] = (q->r[i] * m + a) % primetab[i];
 260     if (!p->r[i] && rc == PGEN_TRY) {
 261       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 262         rc = PGEN_DONE;
 263       else
 264         rc = PGEN_FAIL;
 265     }
 266   }
 267
 268   /* --- Check for small primes --- */
 269
 270   if (rc == PGEN_TRY)
 271     rc = smallenough(p->m);
 272
 273   /* --- Finished --- */
 274
 275   return (rc);
 276 }
 277
 278 /* --- @pfilt_jump@ --- *
 279  *
 280  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 281  *              @const pfilt *j@ = pointer to another filtering context
 282  *
 283  * Returns:     One of the @PGEN@ result codes.
 284  *
 285  * Use:         Steps a number by a large amount.  Even so, jumping is much
 286  *              faster than initializing a new number.  The test peformed is
 287  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 288  *              results should be followed up by a Rabin-Miller test.
 289  *
 290  *              Note that the number stored in the @j@ context is probably
 291  *              better off being even than prime.  The important thing is
 292  *              that all of the residues for the number have already been
 293  *              computed.
 294  */
 295
 296 int pfilt_jump(pfilt *p, const pfilt *j)
 297 {
 298   int rc = PGEN_TRY;
 299   int i;
 300
 301   /* --- Add the step on --- */
 302
 303   p->m = mp_add(p->m, p->m, j->m);
 304
 305   /* --- Update the residue table --- */
 306
 307   for (i = 0; i < NPRIME; i++) {
 308     p->r[i] = p->r[i] + j->r[i];
 309     if (p->r[i] > primetab[i])
 310       p->r[i] -= primetab[i];
 311     if (!p->r[i] && rc == PGEN_TRY) {
 312       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 313         rc = PGEN_DONE;
 314       else
 315         rc = PGEN_FAIL;
 316     }
 317   }
 318
 319   /* --- Check for small primes --- */
 320
 321   if (rc == PGEN_TRY)
 322     rc = smallenough(p->m);
 323
 324   /* --- Done --- */
 325
 326   return (rc);
 327 }
 328
 329 /*----- That's all, folks -------------------------------------------------*/