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, <=, MP_ONE))
64 else if (MP_CMP(m, <, max))
69 /* --- @pfilt_smallfactor@ --- *
71 * Arguments: @mp *m@ = integer to test
73 * Returns: One of the @PGEN@ result codes.
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.
80 int pfilt_smallfactor(mp *m)
84 size_t sz = MP_LEN(m);
85 mparena *a = m->a ? m->a : MPARENA_GLOBAL;
86 mpw *v = mpalloc(a, sz);
88 /* --- Fill in the residues --- */
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])
100 /* --- Check for small primes --- */
111 /* --- @pfilt_create@ --- *
113 * Arguments: @pfilt *p@ = pointer to prime filtering context
114 * @mp *m@ = pointer to initial number to test
116 * Returns: One of the @PGEN@ result codes.
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.
124 int pfilt_create(pfilt *p, mp *m)
128 size_t sz = MP_LEN(m);
129 mparena *a = m->a ? m->a : MPARENA_GLOBAL;
130 mpw *v = mpalloc(a, sz);
132 /* --- Take a copy of the number --- */
137 /* --- Fill in the residues --- */
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])
149 /* --- Check for small primes --- */
160 /* --- @pfilt_destroy@ --- *
162 * Arguments: @pfilt *p@ = pointer to prime filtering context
166 * Use: Discards a context and all the resources it holds.
169 void pfilt_destroy(pfilt *p)
174 /* --- @pfilt_step@ --- *
176 * Arguments: @pfilt *p@ = pointer to prime filtering context
177 * @mpw step@ = how much to step the number
179 * Returns: One of the @PGEN@ result codes.
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.
187 int pfilt_step(pfilt *p, mpw step)
192 /* --- Add the step on to the number --- */
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);
199 /* --- Update the residue table --- */
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])
211 /* --- Check for small primes --- */
214 rc = smallenough(p->m);
221 /* --- @pfilt_muladd@ --- *
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
228 * Returns: One of the @PGEN@ result codes.
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.
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.
239 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
244 /* --- Multiply the big number --- */
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);
256 /* --- Gallivant through the residue table --- */
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])
268 /* --- Check for small primes --- */
271 rc = smallenough(p->m);
273 /* --- Finished --- */
278 /* --- @pfilt_jump@ --- *
280 * Arguments: @pfilt *p@ = pointer to prime filtering context
281 * @const pfilt *j@ = pointer to another filtering context
283 * Returns: One of the @PGEN@ result codes.
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.
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
296 int pfilt_jump(pfilt *p, const pfilt *j)
301 /* --- Add the step on --- */
303 p->m = mp_add(p->m, p->m, j->m);
305 /* --- Update the residue table --- */
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])
319 /* --- Check for small primes --- */
322 rc = smallenough(p->m);
329 /*----- That's all, folks -------------------------------------------------*/