github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpz/millerrabin.c (about)

     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, 1996-2002, 2005, 2014 Free Software
    13  Foundation, Inc.
    14  
    15  Contributed by John Amanatides.
    16  
    17  This file is part of the GNU MP Library.
    18  
    19  The GNU MP Library is free software; you can redistribute it and/or modify
    20  it under the terms of either:
    21  
    22    * the GNU Lesser General Public License as published by the Free
    23      Software Foundation; either version 3 of the License, or (at your
    24      option) any later version.
    25  
    26  or
    27  
    28    * the GNU General Public License as published by the Free Software
    29      Foundation; either version 2 of the License, or (at your option) any
    30      later version.
    31  
    32  or both in parallel, as here.
    33  
    34  The GNU MP Library is distributed in the hope that it will be useful, but
    35  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    36  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    37  for more details.
    38  
    39  You should have received copies of the GNU General Public License and the
    40  GNU Lesser General Public License along with the GNU MP Library.  If not,
    41  see https://www.gnu.org/licenses/.  */
    42  
    43  #include "gmp.h"
    44  #include "gmp-impl.h"
    45  
    46  static int millerrabin (mpz_srcptr, mpz_srcptr,
    47  			mpz_ptr, mpz_ptr,
    48  			mpz_srcptr, unsigned long int);
    49  
    50  int
    51  mpz_millerrabin (mpz_srcptr n, int reps)
    52  {
    53    int r;
    54    mpz_t nm1, nm3, x, y, q;
    55    unsigned long int k;
    56    gmp_randstate_t rstate;
    57    int is_prime;
    58    TMP_DECL;
    59    TMP_MARK;
    60  
    61    MPZ_TMP_INIT (nm1, SIZ (n) + 1);
    62    mpz_sub_ui (nm1, n, 1L);
    63  
    64    MPZ_TMP_INIT (x, SIZ (n) + 1);
    65    MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */
    66  
    67    /* Perform a Fermat test.  */
    68    mpz_set_ui (x, 210L);
    69    mpz_powm (y, x, nm1, n);
    70    if (mpz_cmp_ui (y, 1L) != 0)
    71      {
    72        TMP_FREE;
    73        return 0;
    74      }
    75  
    76    MPZ_TMP_INIT (q, SIZ (n));
    77  
    78    /* Find q and k, where q is odd and n = 1 + 2**k * q.  */
    79    k = mpz_scan1 (nm1, 0L);
    80    mpz_tdiv_q_2exp (q, nm1, k);
    81  
    82    /* n-3 */
    83    MPZ_TMP_INIT (nm3, SIZ (n) + 1);
    84    mpz_sub_ui (nm3, n, 3L);
    85    ASSERT (mpz_cmp_ui (nm3, 1L) >= 0);
    86  
    87    gmp_randinit_default (rstate);
    88  
    89    is_prime = 1;
    90    for (r = 0; r < reps && is_prime; r++)
    91      {
    92        /* 2 to n-2 inclusive, don't want 1, 0 or -1 */
    93        mpz_urandomm (x, rstate, nm3);
    94        mpz_add_ui (x, x, 2L);
    95  
    96        is_prime = millerrabin (n, nm1, x, y, q, k);
    97      }
    98  
    99    gmp_randclear (rstate);
   100  
   101    TMP_FREE;
   102    return is_prime;
   103  }
   104  
   105  static int
   106  millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
   107  	     mpz_srcptr q, unsigned long int k)
   108  {
   109    unsigned long int i;
   110  
   111    mpz_powm (y, x, q, n);
   112  
   113    if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0)
   114      return 1;
   115  
   116    for (i = 1; i < k; i++)
   117      {
   118        mpz_powm_ui (y, y, 2L, n);
   119        if (mpz_cmp (y, nm1) == 0)
   120  	return 1;
   121        /* y == 1 means that the previous y was a non-trivial square root
   122  	 of 1 (mod n). y == 0 means that n is a power of the base.
   123  	 In either case, n is not prime. */
   124        if (mpz_cmp_ui (y, 1L) <= 0)
   125  	return 0;
   126      }
   127    return 0;
   128  }