--- /dev/null
+/* -*-c-*-
+ *
+ * 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