Return to millerrabin.c CVS log

Up to [local] / OpenXM_contrib / gmp / mpz

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

1.1       ohara       1: /* mpz_millerrabin(n,reps) -- An implementation of the probabilistic primality
                      2:    test found in Knuth's Seminumerical Algorithms book.  If the function
                      3:    mpz_millerrabin() returns 0 then n is not prime.  If it returns 1, then n is
                      4:    'probably' prime.  The probability of a false positive is (1/4)**reps, where
                      5:    reps is the number of internal passes of the probabilistic algorithm.  Knuth
                      6:    indicates that 25 passes are reasonable.
                      7:
                      8:    THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
                      9:    CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
                     10:    FUTURE GNU MP RELEASES.
                     11:
                     12: Copyright 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000, 2001 Free Software
                     13: Foundation, Inc.  Contributed by John Amanatides.
                     14:
                     15: This file is part of the GNU MP Library.
                     16:
                     17: The GNU MP Library is free software; you can redistribute it and/or modify
                     18: it under the terms of the GNU Lesser General Public License as published by
                     19: the Free Software Foundation; either version 2.1 of the License, or (at your
                     20: option) any later version.
                     21:
                     22: The GNU MP Library is distributed in the hope that it will be useful, but
                     23: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     24: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
                     25: License for more details.
                     26:
                     27: You should have received a copy of the GNU Lesser General Public License
                     28: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
                     29: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     30: MA 02111-1307, USA. */
                     31:
                     32: #include "gmp.h"
                     33: #include "gmp-impl.h"
                     34:
                     35: static int millerrabin _PROTO ((mpz_srcptr n, mpz_srcptr nm1,
                     36:                                 mpz_ptr x, mpz_ptr y,
                     37:                                 mpz_srcptr q, unsigned long int k));
                     38:
                     39: int
                     40: mpz_millerrabin (mpz_srcptr n, int reps)
                     41: {
                     42:   int r;
                     43:   mpz_t nm1, x, y, q;
                     44:   unsigned long int k;
                     45:   gmp_randstate_t rstate;
                     46:   int is_prime;
                     47:   TMP_DECL (marker);
                     48:   TMP_MARK (marker);
                     49:
                     50:   MPZ_TMP_INIT (nm1, SIZ (n) + 1);
                     51:   mpz_sub_ui (nm1, n, 1L);
                     52:
                     53:   MPZ_TMP_INIT (x, SIZ (n));
                     54:   MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */
                     55:
                     56:   /* Perform a Fermat test.  */
                     57:   mpz_set_ui (x, 210L);
                     58:   mpz_powm (y, x, nm1, n);
                     59:   if (mpz_cmp_ui (y, 1L) != 0)
                     60:     {
                     61:       TMP_FREE (marker);
                     62:       return 0;
                     63:     }
                     64:
                     65:   MPZ_TMP_INIT (q, SIZ (n));
                     66:
                     67:   /* Find q and k, where q is odd and n = 1 + 2**k * q.  */
                     68:   k = mpz_scan1 (nm1, 0L);
                     69:   mpz_tdiv_q_2exp (q, nm1, k);
                     70:
                     71:   gmp_randinit (rstate, GMP_RAND_ALG_DEFAULT, 32L);
                     72:
                     73:   is_prime = 1;
                     74:   for (r = 0; r < reps && is_prime; r++)
                     75:     {
                     76:       do
                     77:        mpz_urandomb (x, rstate, mpz_sizeinbase (n, 2) - 1);
                     78:       while (mpz_cmp_ui (x, 1L) <= 0);
                     79:
                     80:       is_prime = millerrabin (n, nm1, x, y, q, k);
                     81:     }
                     82:
                     83:   gmp_randclear (rstate);
                     84:
                     85:   TMP_FREE (marker);
                     86:   return is_prime;
                     87: }
                     88:
                     89: static int
                     90: millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
                     91:              mpz_srcptr q, unsigned long int k)
                     92: {
                     93:   unsigned long int i;
                     94:
                     95:   mpz_powm (y, x, q, n);
                     96:
                     97:   if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0)
                     98:     return 1;
                     99:
                    100:   for (i = 1; i < k; i++)
                    101:     {
                    102:       mpz_powm_ui (y, y, 2L, n);
                    103:       if (mpz_cmp (y, nm1) == 0)
                    104:        return 1;
                    105:       if (mpz_cmp_ui (y, 1L) == 0)
                    106:        return 0;
                    107:     }
                    108:   return 0;
                    109: }