+++ /dev/null
-/* -*-c-*-
- *
- * $Id: pfilt.c,v 1.6 2004/04/08 01:36:15 mdw Exp $
- *
- * Finding and testing prime numbers
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "mp.h"
-#include "mpint.h"
-#include "pfilt.h"
-#include "pgen.h"
-#include "primetab.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @smallenough@ --- *
- *
- * Arguments: @mp *m@ = integer to test
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Assuming that @m@ has been tested by trial division on every
- * prime in the small-primes array, this function will return
- * @PGEN_DONE@ if the number is less than the square of the
- * largest small prime.
- */
-
-static int smallenough(mp *m)
-{
- static mp *max = 0;
- int rc = PGEN_TRY;
-
- if (!max) {
- max = mp_fromuint(MP_NEW, MAXPRIME);
- max = mp_sqr(max, max);
- max->a->n--; /* Permanent allocation */
- }
- if (MP_CMP(m, <=, MP_ONE))
- rc = PGEN_FAIL;
- else if (MP_CMP(m, <, max))
- rc = PGEN_DONE;
- return (rc);
-}
-
-/* --- @pfilt_smallfactor@ --- *
- *
- * Arguments: @mp *m@ = integer to test
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Tests a number by dividing by a number of small primes. This
- * is a useful first step if you're testing random primes; for
- * sequential searches, @pfilt_create@ works better.
- */
-
-int pfilt_smallfactor(mp *m)
-{
- int rc = PGEN_TRY;
- int i;
- size_t sz = MP_LEN(m);
- mparena *a = m->a ? m->a : MPARENA_GLOBAL;
- mpw *v = mpalloc(a, sz);
-
- /* --- Fill in the residues --- */
-
- for (i = 0; i < NPRIME; i++) {
- if (!mpx_udivn(v, v + sz, m->v, m->vl, primetab[i])) {
- if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
- rc = PGEN_DONE;
- else
- rc = PGEN_FAIL;
- break;
- }
- }
-
- /* --- Check for small primes --- */
-
- if (rc == PGEN_TRY)
- rc = smallenough(m);
-
- /* --- Done --- */
-
- mpfree(a, v);
- return (rc);
-}
-
-/* --- @pfilt_create@ --- *
- *
- * Arguments: @pfilt *p@ = pointer to prime filtering context
- * @mp *m@ = pointer to initial number to test
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Tests an initial number for primality by computing its
- * residue modulo various small prime numbers. This is fairly
- * quick, but not particularly certain. If a @PGEN_TRY@
- * result is returned, perform Rabin-Miller tests to confirm.
- */
-
-int pfilt_create(pfilt *p, mp *m)
-{
- int rc = PGEN_TRY;
- int i;
- size_t sz = MP_LEN(m);
- mparena *a = m->a ? m->a : MPARENA_GLOBAL;
- mpw *v = mpalloc(a, sz);
-
- /* --- Take a copy of the number --- */
-
- mp_shrink(m);
- p->m = MP_COPY(m);
-
- /* --- Fill in the residues --- */
-
- for (i = 0; i < NPRIME; i++) {
- p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
- if (!p->r[i] && rc == PGEN_TRY) {
- if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
- rc = PGEN_DONE;
- else
- rc = PGEN_FAIL;
- }
- }
-
- /* --- Check for small primes --- */
-
- if (rc == PGEN_TRY)
- rc = smallenough(m);
-
- /* --- Done --- */
-
- mpfree(a, v);
- return (rc);
-}
-
-/* --- @pfilt_destroy@ --- *
- *
- * Arguments: @pfilt *p@ = pointer to prime filtering context
- *
- * Returns: ---
- *
- * Use: Discards a context and all the resources it holds.
- */
-
-void pfilt_destroy(pfilt *p)
-{
- mp_drop(p->m);
-}
-
-/* --- @pfilt_step@ --- *
- *
- * Arguments: @pfilt *p@ = pointer to prime filtering context
- * @mpw step@ = how much to step the number
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Steps a number by a small amount. Stepping is much faster
- * than initializing with a new number. The test performed is
- * the same simple one used by @primetab_create@, so @PGEN_TRY@
- * results should be followed up by a Rabin-Miller test.
- */
-
-int pfilt_step(pfilt *p, mpw step)
-{
- int rc = PGEN_TRY;
- int i;
-
- /* --- Add the step on to the number --- */
-
- p->m = mp_split(p->m);
- mp_ensure(p->m, MP_LEN(p->m) + 1);
- mpx_uaddn(p->m->v, p->m->vl, step);
- mp_shrink(p->m);
-
- /* --- Update the residue table --- */
-
- for (i = 0; i < NPRIME; i++) {
- p->r[i] = (p->r[i] + step) % primetab[i];
- if (!p->r[i] && rc == PGEN_TRY) {
- if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
- rc = PGEN_DONE;
- else
- rc = PGEN_FAIL;
- }
- }
-
- /* --- Check for small primes --- */
-
- if (rc == PGEN_TRY)
- rc = smallenough(p->m);
-
- /* --- Done --- */
-
- return (rc);
-}
-
-/* --- @pfilt_muladd@ --- *
- *
- * Arguments: @pfilt *p@ = destination prime filtering context
- * @const pfilt *q@ = source prime filtering context
- * @mpw m@ = number to multiply by
- * @mpw a@ = number to add
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Multiplies the number in a prime filtering context by a
- * small value and then adds a small value. The destination
- * should either be uninitialized or the same as the source.
- *
- * Common things to do include multiplying by 2 and adding 0 to
- * turn a prime into a jump for finding other primes with @q@ as
- * a factor of @p - 1@, or multiplying by 2 and adding 1.
- */
-
-int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
-{
- int rc = PGEN_TRY;
- int i;
-
- /* --- Multiply the big number --- */
-
- {
- mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
- mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
- mpx_uaddn(d->v, d->vl, a);
- if (p == q)
- mp_drop(p->m);
- mp_shrink(d);
- p->m = d;
- }
-
- /* --- Gallivant through the residue table --- */
-
- for (i = 0; i < NPRIME; i++) {
- p->r[i] = (q->r[i] * m + a) % primetab[i];
- if (!p->r[i] && rc == PGEN_TRY) {
- if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
- rc = PGEN_DONE;
- else
- rc = PGEN_FAIL;
- }
- }
-
- /* --- Check for small primes --- */
-
- if (rc == PGEN_TRY)
- rc = smallenough(p->m);
-
- /* --- Finished --- */
-
- return (rc);
-}
-
-/* --- @pfilt_jump@ --- *
- *
- * Arguments: @pfilt *p@ = pointer to prime filtering context
- * @const pfilt *j@ = pointer to another filtering context
- *
- * Returns: One of the @PGEN@ result codes.
- *
- * Use: Steps a number by a large amount. Even so, jumping is much
- * faster than initializing a new number. The test peformed is
- * the same simple one used by @primetab_create@, so @PGEN_TRY@
- * results should be followed up by a Rabin-Miller test.
- *
- * Note that the number stored in the @j@ context is probably
- * better off being even than prime. The important thing is
- * that all of the residues for the number have already been
- * computed.
- */
-
-int pfilt_jump(pfilt *p, const pfilt *j)
-{
- int rc = PGEN_TRY;
- int i;
-
- /* --- Add the step on --- */
-
- p->m = mp_add(p->m, p->m, j->m);
-
- /* --- Update the residue table --- */
-
- for (i = 0; i < NPRIME; i++) {
- p->r[i] = p->r[i] + j->r[i];
- if (p->r[i] > primetab[i])
- p->r[i] -= primetab[i];
- if (!p->r[i] && rc == PGEN_TRY) {
- if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
- rc = PGEN_DONE;
- else
- rc = PGEN_FAIL;
- }
- }
-
- /* --- Check for small primes --- */
-
- if (rc == PGEN_TRY)
- rc = smallenough(p->m);
-
- /* --- Done --- */
-
- return (rc);
-}
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff