--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: pgen.c,v 1.1 1999/11/19 13:17:57 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: pgen.c,v $
+ * Revision 1.1 1999/11/19 13:17:57 mdw
+ * Prime number generator and tester.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpmont.h"
+#include "pgen.h"
+#include "ptab.h"
+#include "rabin.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @pgen_create@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mp *m@ = pointer to initial number to test
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * 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_MAYBE@
+ * result is returned, perform Rabin-Miller tests to confirm.
+ */
+
+int pgen_create(pgen *p, mp *m)
+{
+ int rc = PGEN_MAYBE;
+ int i;
+ mp *r = MP_NEW;
+ mpw qw;
+ mp q;
+
+ /* --- Take a copy of the number --- */
+
+ mp_shrink(m);
+ p->m = MP_COPY(m);
+
+ /* --- Fill in the residues --- */
+
+ mp_build(&q, &qw, &qw + 1);
+ for (i = 0; i < NPRIME; i++) {
+ qw = ptab[i];
+ mp_div(0, &r, m, &q);
+ p->r[i] = r->v[0];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(m) == 1 && m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ mp_drop(r);
+ return (rc);
+}
+
+/* --- @pgen_destroy@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ *
+ * Returns: ---
+ *
+ * Use: Discards a context and all the resources it holds.
+ */
+
+void pgen_destroy(pgen *p)
+{
+ mp_drop(p->m);
+}
+
+/* --- @pgen_step@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @mpw step@ = how much to step the number
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * 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 @ptab_create@, so @PGEN_MAYBE@
+ * results should be followed up by a Rabin-Miller test.
+ */
+
+int pgen_step(pgen *p, mpw step)
+{
+ mp s;
+ int rc = PGEN_MAYBE;
+ int i;
+
+ /* --- Add the step on to the number --- */
+
+ mp_build(&s, &step, &step + 1);
+ p->m = mp_add(p->m, p->m, &s);
+
+ /* --- Update the residue table --- */
+
+ for (i = 0; i < NPRIME; i++) {
+ p->r[i] = (p->r[i] + step) % ptab[i];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ return (rc);
+}
+
+/* --- @pgen_jump@ --- *
+ *
+ * Arguments: @pgen *p@ = pointer to prime generation context
+ * @pgen *j@ = pointer to another generation context
+ *
+ * Returns: One of the @PGEN@ constants above.
+ *
+ * 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 @ptab_create@, so @PGEN_MAYBE@
+ * 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 pgen_jump(pgen *p, pgen *j)
+{
+ int rc = PGEN_MAYBE;
+ 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] > ptab[i])
+ p->r[i] -= ptab[i];
+ if (!p->r[i] && rc == PGEN_MAYBE) {
+ if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i])
+ rc = PGEN_PRIME;
+ else
+ rc = PGEN_COMPOSITE;
+ }
+ }
+
+ /* --- Done --- */
+
+ return (rc);
+}
+
+/*----- Test code ---------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include <mLib/testrig.h>
+
+static int verify(dstr *v)
+{
+ mp *m = *(mp **)v[0].buf;
+ mp *r = *(mp **)v[1].buf;
+ pgen p;
+ mpw gw;
+ mp g;
+ int rc;
+ static char baton[] = "/-\\|";
+ char *b = baton;
+ int ok = 1;
+
+ mp_build(&g, &gw, &gw + 1);
+ rc = pgen_create(&p, m);
+ for (;;) {
+ if (rc == PGEN_PRIME)
+ break;
+ if (rc == PGEN_MAYBE) {
+ int i;
+ rabin r;
+ rabin_create(&r, p.m);
+ for (i = 0; i < 5; i++) {
+ gw = rand();
+ if (rabin_test(&r, &g) == PGEN_COMPOSITE)
+ break;
+ }
+ rabin_destroy(&r);
+ if (i == 5)
+ break;
+ putc(*b++, stderr);
+ putc('\b', stderr);
+ if (!*b)
+ b = baton;
+ }
+ rc = pgen_step(&p, 2);
+ }
+
+ if (MP_CMP(p.m, !=, r)) {
+ fputs("\n*** failed.", stderr);
+ fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
+ fputs("\np = ", stderr); mp_writefile(p.m, stderr, 10);
+ fputs("\nr = ", stderr); mp_writefile(r, stderr, 10);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+
+ mp_drop(m);
+ mp_drop(r);
+ pgen_destroy(&p);
+ return (ok);
+}
+
+static test_chunk tests[] = {
+ { "pgen", verify, { &type_mp, &type_mp, 0 } },
+ { 0, 0, { 0 } }
+};
+
+int main(int argc, char *argv[])
+{
+ sub_init();
+ test_run(argc, argv, tests, SRCDIR "/tests/pgen");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff