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Annotation of OpenXM_contrib/gmp/mpz/pprime_p.c, Revision 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: }