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Annotation of OpenXM_contrib/gmp/mpz/pprime_p.c, Revision 1.1.1.1

1.1       maekawa     1: /* mpz_probab_prime_p --
                      2:    An implementation of the probabilistic primality test found in Knuth's
                      3:    Seminumerical Algorithms book.  If the function mpz_probab_prime_p()
                      4:    returns 0 then n is not prime.  If it returns 1, then n is 'probably'
                      5:    prime.  The probability of a false positive is (1/4)**reps, where
                      6:    reps is the number of internal passes of the probabilistic algorithm.
                      7:    Knuth indicates that 25 passes are reasonable.
                      8:
                      9: Copyright (C) 1991, 1993, 1994 Free Software Foundation, Inc.
                     10: Contributed by John Amanatides.
                     11:
                     12: This file is part of the GNU MP Library.
                     13:
                     14: The GNU MP Library is free software; you can redistribute it and/or modify
                     15: it under the terms of the GNU Library General Public License as published by
                     16: the Free Software Foundation; either version 2 of the License, or (at your
                     17: option) any later version.
                     18:
                     19: The GNU MP Library is distributed in the hope that it will be useful, but
                     20: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     21: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
                     22: License for more details.
                     23:
                     24: You should have received a copy of the GNU Library General Public License
                     25: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
                     26: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     27: MA 02111-1307, USA. */
                     28:
                     29: #include "gmp.h"
                     30:
                     31: static int
                     32: possibly_prime (n, n_minus_1, x, y, q, k)
                     33:      mpz_srcptr n;
                     34:      mpz_srcptr n_minus_1;
                     35:      mpz_ptr x;
                     36:      mpz_ptr y;
                     37:      mpz_srcptr q;
                     38:      unsigned long int k;
                     39: {
                     40:   unsigned long int i;
                     41:
                     42:   /* find random x s.t. 1 < x < n */
                     43:   do
                     44:     {
                     45:       mpz_random (x, mpz_size (n));
                     46:       mpz_mmod (x, x, n);
                     47:     }
                     48:   while (mpz_cmp_ui (x, 1L) <= 0);
                     49:
                     50:   mpz_powm (y, x, q, n);
                     51:
                     52:   if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, n_minus_1) == 0)
                     53:     return 1;
                     54:
                     55:   for (i = 1; i < k; i++)
                     56:     {
                     57:       mpz_powm_ui (y, y, 2L, n);
                     58:       if (mpz_cmp (y, n_minus_1) == 0)
                     59:        return 1;
                     60:       if (mpz_cmp_ui (y, 1L) == 0)
                     61:        return 0;
                     62:     }
                     63:   return 0;
                     64: }
                     65:
                     66: int
                     67: #if __STDC__
                     68: mpz_probab_prime_p (mpz_srcptr m, int reps)
                     69: #else
                     70: mpz_probab_prime_p (m, reps)
                     71:      mpz_srcptr m;
                     72:      int reps;
                     73: #endif
                     74: {
                     75:   mpz_t n, n_minus_1, x, y, q;
                     76:   int i, is_prime;
                     77:   unsigned long int k;
                     78:
                     79:   mpz_init (n);
                     80:   /* Take the absolute value of M, to handle positive and negative primes.  */
                     81:   mpz_abs (n, m);
                     82:
                     83:   if (mpz_cmp_ui (n, 3L) <= 0)
                     84:     {
                     85:       mpz_clear (n);
                     86:       return mpz_cmp_ui (n, 1L) > 0;
                     87:     }
                     88:
                     89:   if ((mpz_get_ui (n) & 1) == 0)
                     90:     {
                     91:       mpz_clear (n);
                     92:       return 0;                        /* even */
                     93:     }
                     94:
                     95:   mpz_init (n_minus_1);
                     96:   mpz_sub_ui (n_minus_1, n, 1L);
                     97:   mpz_init (x);
                     98:   mpz_init (y);
                     99:
                    100:   /* find q and k, s.t.  n = 1 + 2**k * q */
                    101:   mpz_init_set (q, n_minus_1);
                    102:   k = mpz_scan1 (q, 0);
                    103:   mpz_tdiv_q_2exp (q, q, k);
                    104:
                    105:   is_prime = 1;
                    106:   for (i = 0; i < reps && is_prime; i++)
                    107:     is_prime &= possibly_prime (n, n_minus_1, x, y, q, k);
                    108:
                    109:   mpz_clear (n_minus_1);
                    110:   mpz_clear (n);
                    111:   mpz_clear (x);
                    112:   mpz_clear (y);
                    113:   mpz_clear (q);
                    114:   return is_prime;
                    115: }