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authortege <tege@gmplib.org>1996-05-08 09:10:48 +0200
committertege <tege@gmplib.org>1996-05-08 09:10:48 +0200
commitc6d715868f53b08c62a129ffd77fb585fd89c43b (patch)
tree82f36d2d8cbe7e07ad3e18d5c6e047e8796d861e /mpz/pprime_p.c
downloadgmp-c6d715868f53b08c62a129ffd77fb585fd89c43b.tar.gz
Initial revision
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+/* mpz_probab_prime_p --
+ An implementation of the probabilistic primality test found in Knuth's
+ Seminumerical Algorithms book. If the function mpz_probab_prime_p()
+ returns 0 then n is not prime. If it returns 1, then n is 'probably'
+ prime. The probability of a false positive is (1/4)**reps, where
+ reps is the number of internal passes of the probabilistic algorithm.
+ Knuth indicates that 25 passes are reasonable.
+
+Copyright (C) 1991, 1993, 1994 Free Software Foundation, Inc.
+Contributed by John Amanatides.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library 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.
+
+The GNU MP Library 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 the GNU MP Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include "gmp.h"
+
+static int
+possibly_prime (n, n_minus_1, x, y, q, k)
+ mpz_srcptr n;
+ mpz_srcptr n_minus_1;
+ mpz_ptr x;
+ mpz_ptr y;
+ mpz_srcptr q;
+ unsigned long int k;
+{
+ unsigned long int i;
+
+ /* find random x s.t. 1 < x < n */
+ do
+ {
+ mpz_random (x, mpz_size (n));
+ mpz_mmod (x, x, n);
+ }
+ while (mpz_cmp_ui (x, 1L) <= 0);
+
+ mpz_powm (y, x, q, n);
+
+ if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, n_minus_1) == 0)
+ return 1;
+
+ for (i = 1; i < k; i++)
+ {
+ mpz_powm_ui (y, y, 2L, n);
+ if (mpz_cmp (y, n_minus_1) == 0)
+ return 1;
+ if (mpz_cmp_ui (y, 1L) == 0)
+ return 0;
+ }
+ return 0;
+}
+
+int
+#if __STDC__
+mpz_probab_prime_p (mpz_srcptr m, int reps)
+#else
+mpz_probab_prime_p (m, reps)
+ mpz_srcptr m;
+ int reps;
+#endif
+{
+ mpz_t n, n_minus_1, x, y, q;
+ int i, is_prime;
+ unsigned long int k;
+
+ mpz_init (n);
+ /* Take the absolute value of M, to handle positive and negative primes. */
+ mpz_abs (n, m);
+
+ if (mpz_cmp_ui (n, 3L) <= 0)
+ {
+ mpz_clear (n);
+ return mpz_cmp_ui (n, 1L) > 0;
+ }
+
+ if ((mpz_get_ui (n) & 1) == 0)
+ {
+ mpz_clear (n);
+ return 0; /* even */
+ }
+
+ mpz_init (n_minus_1);
+ mpz_sub_ui (n_minus_1, n, 1L);
+ mpz_init (x);
+ mpz_init (y);
+
+ /* find q and k, s.t. n = 1 + 2**k * q */
+ mpz_init_set (q, n_minus_1);
+ k = mpz_scan1 (q, 0);
+ mpz_tdiv_q_2exp (q, q, k);
+
+ is_prime = 1;
+ for (i = 0; i < reps && is_prime; i++)
+ is_prime &= possibly_prime (n, n_minus_1, x, y, q, k);
+
+ mpz_clear (n_minus_1);
+ mpz_clear (n);
+ mpz_clear (x);
+ mpz_clear (y);
+ mpz_clear (q);
+ return is_prime;
+}