116 lines
2.9 KiB
C
116 lines
2.9 KiB
C
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/* 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, 1993, 1994 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 Library General Public License as published by
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the Free Software Foundation; either version 2 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
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License for more details.
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You should have received a copy of the GNU Library General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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MA 02111-1307, USA. */
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#include "gmp.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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mpz_srcptr n;
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mpz_srcptr n_minus_1;
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mpz_ptr x;
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mpz_ptr y;
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mpz_srcptr q;
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unsigned long int k;
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{
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unsigned long 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, 1L) <= 0);
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mpz_powm (y, x, q, n);
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if (mpz_cmp_ui (y, 1L) == 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, 2L, 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, 1L) == 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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#if __STDC__
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mpz_probab_prime_p (mpz_srcptr m, int reps)
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#else
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mpz_probab_prime_p (m, reps)
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mpz_srcptr m;
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int reps;
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#endif
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{
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mpz_t n, n_minus_1, x, y, q;
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int i, is_prime;
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unsigned long int k;
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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, 3L) <= 0)
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{
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mpz_clear (n);
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return mpz_cmp_ui (n, 1L) > 0;
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}
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if ((mpz_get_ui (n) & 1) == 0)
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{
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mpz_clear (n);
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return 0; /* even */
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}
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mpz_init (n_minus_1);
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mpz_sub_ui (n_minus_1, n, 1L);
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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 = mpz_scan1 (q, 0);
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mpz_tdiv_q_2exp (q, q, k);
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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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