3 * Finding and testing prime numbers
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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.
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.
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,
28 /*----- Header files ------------------------------------------------------*/
36 /*----- Main code ---------------------------------------------------------*/
38 /* --- @smallenough@ --- *
40 * Arguments: @mp *m@ = integer to test
42 * Returns: One of the @PGEN@ result codes.
44 * Use: Assuming that @m@ has been tested by trial division on every
45 * prime in the small-primes array, this function will return
46 * @PGEN_DONE@ if the number is less than the square of the
47 * largest small prime.
50 static int smallenough(mp *m)
56 max = mp_fromuint(MP_NEW, MAXPRIME);
57 max = mp_sqr(max, max);
58 max->a->n--; /* Permanent allocation */
60 if (MP_CMP(m, <=, MP_ONE))
62 else 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])
98 /* --- Check for small primes --- */
109 /* --- @pfilt_create@ --- *
111 * Arguments: @pfilt *p@ = pointer to prime filtering context
112 * @mp *m@ = pointer to initial number to test
114 * Returns: One of the @PGEN@ result codes.
116 * Use: Tests an initial number for primality by computing its
117 * residue modulo various small prime numbers. This is fairly
118 * quick, but not particularly certain. If a @PGEN_TRY@
119 * result is returned, perform Rabin-Miller tests to confirm.
122 int pfilt_create(pfilt *p, mp *m)
126 size_t sz = MP_LEN(m);
127 mparena *a = m->a ? m->a : MPARENA_GLOBAL;
128 mpw *v = mpalloc(a, sz);
130 /* --- Take a copy of the number --- */
135 /* --- Fill in the residues --- */
137 for (i = 0; i < NPRIME; i++) {
138 p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
139 if (!p->r[i] && rc == PGEN_TRY) {
140 if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
147 /* --- Check for small primes --- */
158 /* --- @pfilt_destroy@ --- *
160 * Arguments: @pfilt *p@ = pointer to prime filtering context
164 * Use: Discards a context and all the resources it holds.
167 void pfilt_destroy(pfilt *p)
172 /* --- @pfilt_step@ --- *
174 * Arguments: @pfilt *p@ = pointer to prime filtering context
175 * @mpw step@ = how much to step the number
177 * Returns: One of the @PGEN@ result codes.
179 * Use: Steps a number by a small amount. Stepping is much faster
180 * than initializing with a new number. The test performed is
181 * the same simple one used by @primetab_create@, so @PGEN_TRY@
182 * results should be followed up by a Rabin-Miller test.
185 int pfilt_step(pfilt *p, mpw step)
190 /* --- Add the step on to the number --- */
192 p->m = mp_split(p->m);
193 mp_ensure(p->m, MP_LEN(p->m) + 1);
194 mpx_uaddn(p->m->v, p->m->vl, step);
197 /* --- Update the residue table --- */
199 for (i = 0; i < NPRIME; i++) {
200 p->r[i] = (p->r[i] + step) % primetab[i];
201 if (!p->r[i] && rc == PGEN_TRY) {
202 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
209 /* --- Check for small primes --- */
212 rc = smallenough(p->m);
219 /* --- @pfilt_muladd@ --- *
221 * Arguments: @pfilt *p@ = destination prime filtering context
222 * @const pfilt *q@ = source prime filtering context
223 * @mpw m@ = number to multiply by
224 * @mpw a@ = number to add
226 * Returns: One of the @PGEN@ result codes.
228 * Use: Multiplies the number in a prime filtering context by a
229 * small value and then adds a small value. The destination
230 * should either be uninitialized or the same as the source.
232 * Common things to do include multiplying by 2 and adding 0 to
233 * turn a prime into a jump for finding other primes with @q@ as
234 * a factor of @p - 1@, or multiplying by 2 and adding 1.
237 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
242 /* --- Multiply the big number --- */
245 mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
246 mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
247 mpx_uaddn(d->v, d->vl, a);
254 /* --- Gallivant through the residue table --- */
256 for (i = 0; i < NPRIME; i++) {
257 p->r[i] = (q->r[i] * m + a) % primetab[i];
258 if (!p->r[i] && rc == PGEN_TRY) {
259 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
266 /* --- Check for small primes --- */
269 rc = smallenough(p->m);
271 /* --- Finished --- */
276 /* --- @pfilt_jump@ --- *
278 * Arguments: @pfilt *p@ = pointer to prime filtering context
279 * @const pfilt *j@ = pointer to another filtering context
281 * Returns: One of the @PGEN@ result codes.
283 * Use: Steps a number by a large amount. Even so, jumping is much
284 * faster than initializing a new number. The test peformed is
285 * the same simple one used by @primetab_create@, so @PGEN_TRY@
286 * results should be followed up by a Rabin-Miller test.
288 * Note that the number stored in the @j@ context is probably
289 * better off being even than prime. The important thing is
290 * that all of the residues for the number have already been
294 int pfilt_jump(pfilt *p, const pfilt *j)
299 /* --- Add the step on --- */
301 p->m = mp_add(p->m, p->m, j->m);
303 /* --- Update the residue table --- */
305 for (i = 0; i < NPRIME; i++) {
306 p->r[i] = p->r[i] + j->r[i];
307 if (p->r[i] >= primetab[i])
308 p->r[i] -= primetab[i];
309 if (!p->r[i] && rc == PGEN_TRY) {
310 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
317 /* --- Check for small primes --- */
320 rc = smallenough(p->m);
327 /*----- That's all, folks -------------------------------------------------*/