3 * $Id: pfilt.c,v 1.6 2004/04/08 01:36:15 mdw Exp $
5 * Finding and testing prime numbers
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Header files ------------------------------------------------------*/
38 /*----- Main code ---------------------------------------------------------*/
40 /* --- @smallenough@ --- *
42 * Arguments: @mp *m@ = integer to test
44 * Returns: One of the @PGEN@ result codes.
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.
52 static int smallenough(mp *m)
58 max = mp_fromuint(MP_NEW, MAXPRIME);
59 max = mp_sqr(max, max);
60 max->a->n--; /* Permanent allocation */
62 if (MP_CMP(m, <, max))
67 /* --- @pfilt_smallfactor@ --- *
69 * Arguments: @mp *m@ = integer to test
71 * Returns: One of the @PGEN@ result codes.
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.
78 int pfilt_smallfactor(mp *m)
82 size_t sz = MP_LEN(m);
83 mparena *a = m->a ? m->a : MPARENA_GLOBAL;
84 mpw *v = mpalloc(a, sz);
86 /* --- Fill in the residues --- */
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])
97 /* --- Check for small primes --- */
108 /* --- @pfilt_create@ --- *
110 * Arguments: @pfilt *p@ = pointer to prime filtering context
111 * @mp *m@ = pointer to initial number to test
113 * Returns: One of the @PGEN@ result codes.
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.
121 int pfilt_create(pfilt *p, mp *m)
125 size_t sz = MP_LEN(m);
126 mparena *a = m->a ? m->a : MPARENA_GLOBAL;
127 mpw *v = mpalloc(a, sz);
129 /* --- Take a copy of the number --- */
134 /* --- Fill in the residues --- */
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])
146 /* --- Check for small primes --- */
157 /* --- @pfilt_destroy@ --- *
159 * Arguments: @pfilt *p@ = pointer to prime filtering context
163 * Use: Discards a context and all the resources it holds.
166 void pfilt_destroy(pfilt *p)
171 /* --- @pfilt_step@ --- *
173 * Arguments: @pfilt *p@ = pointer to prime filtering context
174 * @mpw step@ = how much to step the number
176 * Returns: One of the @PGEN@ result codes.
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.
184 int pfilt_step(pfilt *p, mpw step)
189 /* --- Add the step on to the number --- */
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);
196 /* --- Update the residue table --- */
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])
208 /* --- Check for small primes --- */
211 rc = smallenough(p->m);
218 /* --- @pfilt_muladd@ --- *
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
225 * Returns: One of the @PGEN@ result codes.
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.
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.
236 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
241 /* --- Multiply the big number --- */
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);
253 /* --- Gallivant through the residue table --- */
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])
265 /* --- Check for small primes --- */
268 rc = smallenough(p->m);
270 /* --- Finished --- */
275 /* --- @pfilt_jump@ --- *
277 * Arguments: @pfilt *p@ = pointer to prime filtering context
278 * @const pfilt *j@ = pointer to another filtering context
280 * Returns: One of the @PGEN@ result codes.
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.
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
293 int pfilt_jump(pfilt *p, const pfilt *j)
298 /* --- Add the step on --- */
300 p->m = mp_add(p->m, p->m, j->m);
302 /* --- Update the residue table --- */
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])
316 /* --- Check for small primes --- */
319 rc = smallenough(p->m);
326 /*----- That's all, folks -------------------------------------------------*/