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Diffstat (limited to 'ghc/runtime/gmp/mpz_pprime_p.c')
-rw-r--r-- | ghc/runtime/gmp/mpz_pprime_p.c | 108 |
1 files changed, 108 insertions, 0 deletions
diff --git a/ghc/runtime/gmp/mpz_pprime_p.c b/ghc/runtime/gmp/mpz_pprime_p.c new file mode 100644 index 0000000000..9d08803dbc --- /dev/null +++ b/ghc/runtime/gmp/mpz_pprime_p.c @@ -0,0 +1,108 @@ +/* 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; +} |