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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 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 General Public License as published by
+the Free Software Foundation; either version 2, 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 General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with the GNU MP Library; see the file COPYING. If not, write to
+the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+
+static int
+possibly_prime (n, n_minus_1, x, y, q, k)
+ MP_INT *n, *n_minus_1, *x, *y, *q;
+ int k;
+{
+ 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, 1) <= 0);
+
+ mpz_powm (y, x, q, n);
+
+ if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, n_minus_1) == 0)
+ return 1;
+
+ for (i = 1; i < k; i++)
+ {
+ mpz_powm_ui (y, y, 2, n);
+ if (mpz_cmp (y, n_minus_1) == 0)
+ return 1;
+ if (mpz_cmp_ui (y, 1) == 0)
+ return 0;
+ }
+ return 0;
+}
+
+int
+mpz_probab_prime_p (m, reps)
+ const MP_INT *m;
+ int reps;
+{
+ MP_INT n, n_minus_1, x, y, q;
+ int i, k, is_prime;
+
+ mpz_init (&n);
+ /* Take the absolute value of M, to handle positive and negative primes. */
+ mpz_abs (&n, m);
+
+ if (mpz_cmp_ui (&n, 3) <= 0)
+ {
+ if (mpz_cmp_ui (&n, 1) <= 0)
+ return 0; /* smallest prime is 2 */
+ else
+ return 1;
+ }
+ if ((mpz_get_ui (&n) & 1) == 0)
+ return 0; /* even */
+
+ mpz_init (&n_minus_1);
+ mpz_sub_ui (&n_minus_1, &n, 1);
+ 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 = 0;
+ while ((mpz_get_ui (&q) & 1) == 0)
+ {
+ k++;
+ mpz_div_2exp (&q, &q, 1);
+ }
+
+ 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;
+}
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