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, <, max))
  63     rc = PGEN_DONE;
  64   return (rc);
  65 }
  66
  67 /* --- @pfilt_smallfactor@ --- *
  68  *
  69  * Arguments:   @mp *m@ = integer to test
  70  *
  71  * Returns:     One of the @PGEN@ result codes.
  72  *
  73  * Use:         Tests a number by dividing by a number of small primes.  This
  74  *              is a useful first step if you're testing random primes; for
  75  *              sequential searches, @pfilt_create@ works better.
  76  */
  77
  78 int pfilt_smallfactor(mp *m)
  79 {
  80   int rc = PGEN_TRY;
  81   int i;
  82   size_t sz = MP_LEN(m);
  83   mparena *a = m->a ? m->a : MPARENA_GLOBAL;
  84   mpw *v = mpalloc(a, sz);
  85
  86   /* --- Fill in the residues --- */
  87
  88   for (i = 0; i < NPRIME; i++) {
  89     if (!mpx_udivn(v, v + sz, m->v, m->vl, primetab[i])) {
  90       if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
  91         rc = PGEN_DONE;
  92       else
  93         rc = PGEN_FAIL;
  94     }
  95   }
  96
  97   /* --- Check for small primes --- */
  98
  99   if (rc == PGEN_TRY)
 100     rc = smallenough(m);
 101
 102   /* --- Done --- */
 103
 104   mpfree(a, v);
 105   return (rc);
 106 }
 107
 108 /* --- @pfilt_create@ --- *
 109  *
 110  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 111  *              @mp *m@ = pointer to initial number to test
 112  *
 113  * Returns:     One of the @PGEN@ result codes.
 114  *
 115  * Use:         Tests an initial number for primality by computing its
 116  *              residue modulo various small prime numbers.  This is fairly
 117  *              quick, but not particularly certain.  If a @PGEN_TRY@
 118  *              result is returned, perform Rabin-Miller tests to confirm.
 119  */
 120
 121 int pfilt_create(pfilt *p, mp *m)
 122 {
 123   int rc = PGEN_TRY;
 124   int i;
 125   size_t sz = MP_LEN(m);
 126   mparena *a = m->a ? m->a : MPARENA_GLOBAL;
 127   mpw *v = mpalloc(a, sz);
 128
 129   /* --- Take a copy of the number --- */
 130
 131   mp_shrink(m);
 132   p->m = MP_COPY(m);
 133
 134   /* --- Fill in the residues --- */
 135
 136   for (i = 0; i < NPRIME; i++) {
 137     p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
 138     if (!p->r[i] && rc == PGEN_TRY) {
 139       if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
 140         rc = PGEN_DONE;
 141       else
 142         rc = PGEN_FAIL;
 143     }
 144   }
 145
 146   /* --- Check for small primes --- */
 147
 148   if (rc == PGEN_TRY)
 149     rc = smallenough(m);
 150
 151   /* --- Done --- */
 152
 153   mpfree(a, v);
 154   return (rc);
 155 }
 156
 157 /* --- @pfilt_destroy@ --- *
 158  *
 159  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 160  *
 161  * Returns:     ---
 162  *
 163  * Use:         Discards a context and all the resources it holds.
 164  */
 165
 166 void pfilt_destroy(pfilt *p)
 167 {
 168   mp_drop(p->m);
 169 }
 170
 171 /* --- @pfilt_step@ --- *
 172  *
 173  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 174  *              @mpw step@ = how much to step the number
 175  *
 176  * Returns:     One of the @PGEN@ result codes.
 177  *
 178  * Use:         Steps a number by a small amount.  Stepping is much faster
 179  *              than initializing with a new number.  The test performed is
 180  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 181  *              results should be followed up by a Rabin-Miller test.
 182  */
 183
 184 int pfilt_step(pfilt *p, mpw step)
 185 {
 186   int rc = PGEN_TRY;
 187   int i;
 188
 189   /* --- Add the step on to the number --- */
 190
 191   p->m = mp_split(p->m);
 192   mp_ensure(p->m, MP_LEN(p->m) + 1);
 193   mpx_uaddn(p->m->v, p->m->vl, step);
 194   mp_shrink(p->m);
 195
 196   /* --- Update the residue table --- */
 197
 198   for (i = 0; i < NPRIME; i++) {
 199     p->r[i] = (p->r[i] + step) % primetab[i];
 200     if (!p->r[i] && rc == PGEN_TRY) {
 201       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 202         rc = PGEN_DONE;
 203       else
 204         rc = PGEN_FAIL;
 205     }
 206   }
 207
 208   /* --- Check for small primes --- */
 209
 210   if (rc == PGEN_TRY)
 211     rc = smallenough(p->m);
 212
 213   /* --- Done --- */
 214
 215   return (rc);
 216 }
 217
 218 /* --- @pfilt_muladd@ --- *
 219  *
 220  * Arguments:   @pfilt *p@ = destination prime filtering context
 221  *              @const pfilt *q@ = source prime filtering context
 222  *              @mpw m@ = number to multiply by
 223  *              @mpw a@ = number to add
 224  *
 225  * Returns:     One of the @PGEN@ result codes.
 226  *
 227  * Use:         Multiplies the number in a prime filtering context by a
 228  *              small value and then adds a small value.  The destination
 229  *              should either be uninitialized or the same as the source.
 230  *
 231  *              Common things to do include multiplying by 2 and adding 0 to
 232  *              turn a prime into a jump for finding other primes with @q@ as
 233  *              a factor of @p - 1@, or multiplying by 2 and adding 1.
 234  */
 235
 236 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
 237 {
 238   int rc = PGEN_TRY;
 239   int i;
 240
 241   /* --- Multiply the big number --- */
 242
 243   {
 244     mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
 245     mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
 246     mpx_uaddn(d->v, d->vl, a);
 247     if (p == q)
 248       mp_drop(p->m);
 249     mp_shrink(d);
 250     p->m = d;
 251   }
 252
 253   /* --- Gallivant through the residue table --- */
 254
 255   for (i = 0; i < NPRIME; i++) {
 256     p->r[i] = (q->r[i] * m + a) % primetab[i];
 257     if (!p->r[i] && rc == PGEN_TRY) {
 258       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 259         rc = PGEN_DONE;
 260       else
 261         rc = PGEN_FAIL;
 262     }
 263   }
 264
 265   /* --- Check for small primes --- */
 266
 267   if (rc == PGEN_TRY)
 268     rc = smallenough(p->m);
 269
 270   /* --- Finished --- */
 271
 272   return (rc);
 273 }
 274
 275 /* --- @pfilt_jump@ --- *
 276  *
 277  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 278  *              @const pfilt *j@ = pointer to another filtering context
 279  *
 280  * Returns:     One of the @PGEN@ result codes.
 281  *
 282  * Use:         Steps a number by a large amount.  Even so, jumping is much
 283  *              faster than initializing a new number.  The test peformed is
 284  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 285  *              results should be followed up by a Rabin-Miller test.
 286  *
 287  *              Note that the number stored in the @j@ context is probably
 288  *              better off being even than prime.  The important thing is
 289  *              that all of the residues for the number have already been
 290  *              computed.
 291  */
 292
 293 int pfilt_jump(pfilt *p, const pfilt *j)
 294 {
 295   int rc = PGEN_TRY;
 296   int i;
 297
 298   /* --- Add the step on --- */
 299
 300   p->m = mp_add(p->m, p->m, j->m);
 301
 302   /* --- Update the residue table --- */
 303
 304   for (i = 0; i < NPRIME; i++) {
 305     p->r[i] = p->r[i] + j->r[i];
 306     if (p->r[i] > primetab[i])
 307       p->r[i] -= primetab[i];
 308     if (!p->r[i] && rc == PGEN_TRY) {
 309       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 310         rc = PGEN_DONE;
 311       else
 312         rc = PGEN_FAIL;
 313     }
 314   }
 315
 316   /* --- Check for small primes --- */
 317
 318   if (rc == PGEN_TRY)
 319     rc = smallenough(p->m);
 320
 321   /* --- Done --- */
 322
 323   return (rc);
 324 }
 325
 326 /*----- That's all, folks -------------------------------------------------*/