109 lines
2.7 KiB
C
109 lines
2.7 KiB
C
|
/* mpz_probab_prime_p --
|
||
|
|
An implementation of the probabilistic primality test found in Knuth's
|
||
|
|
Seminumerical Algorithms book. If the function mpz_probab_prime_p()
|
||
|
|
returns 0 then n is not prime. If it returns 1, then n is 'probably'
|
||
|
|
prime. The probability of a false positive is (1/4)**reps, where
|
||
|
|
reps is the number of internal passes of the probabilistic algorithm.
|
||
|
|
Knuth indicates that 25 passes are reasonable.
|
||
|
|
|
||
|
|
Copyright (C) 1991 Free Software Foundation, Inc.
|
||
|
|
Contributed by John Amanatides.
|
||
|
|
|
||
|
|
This file is part of the GNU MP Library.
|
||
|
|
|
||
|
|
The GNU MP Library is free software; you can redistribute it and/or modify
|
||
|
|
it under the terms of the GNU General Public License as published by
|
||
|
|
the Free Software Foundation; either version 2, or (at your option)
|
||
|
|
any later version.
|
||
|
|
|
||
|
|
The GNU MP Library is distributed in the hope that it will be useful,
|
||
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||
|
|
GNU General Public License for more details.
|
||
|
|
|
||
|
|
You should have received a copy of the GNU General Public License
|
||
|
|
along with the GNU MP Library; see the file COPYING. If not, write to
|
||
|
|
the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
|
||
|
|
|
||
|
|
#include "gmp.h"
|
||
|
|
#include "gmp-impl.h"
|
||
|
|
|
||
|
|
static int
|
||
|
|
possibly_prime (n, n_minus_1, x, y, q, k)
|
||
|
|
MP_INT *n, *n_minus_1, *x, *y, *q;
|
||
|
|
int k;
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
|
||
|
|
/* find random x s.t. 1 < x < n */
|
||
|
|
do
|
||
|
|
{
|
||
|
|
mpz_random (x, mpz_size (n));
|
||
|
|
mpz_mmod (x, x, n);
|
||
|
|
}
|
||
|
|
while (mpz_cmp_ui (x, 1) <= 0);
|
||
|
|
|
||
|
|
mpz_powm (y, x, q, n);
|
||
|
|
|
||
|
|
if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, n_minus_1) == 0)
|
||
|
|
return 1;
|
||
|
|
|
||
|
|
for (i = 1; i < k; i++)
|
||
|
|
{
|
||
|
|
mpz_powm_ui (y, y, 2, n);
|
||
|
|
if (mpz_cmp (y, n_minus_1) == 0)
|
||
|
|
return 1;
|
||
|
|
if (mpz_cmp_ui (y, 1) == 0)
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
mpz_probab_prime_p (m, reps)
|
||
|
|
const MP_INT *m;
|
||
|
|
int reps;
|
||
|
|
{
|
||
|
|
MP_INT n, n_minus_1, x, y, q;
|
||
|
|
int i, k, is_prime;
|
||
|
|
|
||
|
|
mpz_init (&n);
|
||
|
|
/* Take the absolute value of M, to handle positive and negative primes. */
|
||
|
|
mpz_abs (&n, m);
|
||
|
|
|
||
|
|
if (mpz_cmp_ui (&n, 3) <= 0)
|
||
|
|
{
|
||
|
|
if (mpz_cmp_ui (&n, 1) <= 0)
|
||
|
|
return 0; /* smallest prime is 2 */
|
||
|
|
else
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
if ((mpz_get_ui (&n) & 1) == 0)
|
||
|
|
return 0; /* even */
|
||
|
|
|
||
|
|
mpz_init (&n_minus_1);
|
||
|
|
mpz_sub_ui (&n_minus_1, &n, 1);
|
||
|
|
mpz_init (&x);
|
||
|
|
mpz_init (&y);
|
||
|
|
|
||
|
|
/* find q and k, s.t. n = 1 + 2**k * q */
|
||
|
|
mpz_init_set (&q, &n_minus_1);
|
||
|
|
k = 0;
|
||
|
|
while ((mpz_get_ui (&q) & 1) == 0)
|
||
|
|
{
|
||
|
|
k++;
|
||
|
|
mpz_div_2exp (&q, &q, 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
is_prime = 1;
|
||
|
|
for (i = 0; i < reps && is_prime; i++)
|
||
|
|
is_prime &= possibly_prime (&n, &n_minus_1, &x, &y, &q, k);
|
||
|
|
|
||
|
|
mpz_clear (&n_minus_1);
|
||
|
|
mpz_clear (&n);
|
||
|
|
mpz_clear (&x);
|
||
|
|
mpz_clear (&y);
|
||
|
|
mpz_clear (&q);
|
||
|
|
return is_prime;
|
||
|
|
}
|