/* 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; }