109 lines
2.7 KiB
C
109 lines
2.7 KiB
C
/* mpz_probab_prime_p --
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An implementation of the probabilistic primality test found in Knuth's
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Seminumerical Algorithms book. If the function mpz_probab_prime_p()
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returns 0 then n is not prime. If it returns 1, then n is 'probably'
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prime. The probability of a false positive is (1/4)**reps, where
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reps is the number of internal passes of the probabilistic algorithm.
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Knuth indicates that 25 passes are reasonable.
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Copyright (C) 1991 Free Software Foundation, Inc.
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Contributed by John Amanatides.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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The GNU MP Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with the GNU MP Library; see the file COPYING. If not, write to
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the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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static int
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possibly_prime (n, n_minus_1, x, y, q, k)
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MP_INT *n, *n_minus_1, *x, *y, *q;
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int k;
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{
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int i;
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/* find random x s.t. 1 < x < n */
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do
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{
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mpz_random (x, mpz_size (n));
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mpz_mmod (x, x, n);
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}
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while (mpz_cmp_ui (x, 1) <= 0);
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mpz_powm (y, x, q, n);
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if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, n_minus_1) == 0)
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return 1;
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for (i = 1; i < k; i++)
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{
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mpz_powm_ui (y, y, 2, n);
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if (mpz_cmp (y, n_minus_1) == 0)
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return 1;
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if (mpz_cmp_ui (y, 1) == 0)
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return 0;
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}
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return 0;
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}
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int
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mpz_probab_prime_p (m, reps)
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const MP_INT *m;
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int reps;
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{
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MP_INT n, n_minus_1, x, y, q;
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int i, k, is_prime;
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mpz_init (&n);
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/* Take the absolute value of M, to handle positive and negative primes. */
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mpz_abs (&n, m);
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if (mpz_cmp_ui (&n, 3) <= 0)
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{
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if (mpz_cmp_ui (&n, 1) <= 0)
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return 0; /* smallest prime is 2 */
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else
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return 1;
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}
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if ((mpz_get_ui (&n) & 1) == 0)
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return 0; /* even */
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mpz_init (&n_minus_1);
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mpz_sub_ui (&n_minus_1, &n, 1);
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mpz_init (&x);
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mpz_init (&y);
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/* find q and k, s.t. n = 1 + 2**k * q */
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mpz_init_set (&q, &n_minus_1);
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k = 0;
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while ((mpz_get_ui (&q) & 1) == 0)
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{
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k++;
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mpz_div_2exp (&q, &q, 1);
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}
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is_prime = 1;
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for (i = 0; i < reps && is_prime; i++)
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is_prime &= possibly_prime (&n, &n_minus_1, &x, &y, &q, k);
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mpz_clear (&n_minus_1);
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mpz_clear (&n);
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mpz_clear (&x);
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mpz_clear (&y);
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mpz_clear (&q);
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return is_prime;
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}
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