108 lines
3.0 KiB
C
108 lines
3.0 KiB
C
/* mpz_millerrabin(n,reps) -- An implementation of the probabilistic primality
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test found in Knuth's Seminumerical Algorithms book. If the function
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mpz_millerrabin() returns 0 then n is not prime. If it returns 1, then n is
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'probably' prime. The probability of a false positive is (1/4)**reps, where
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reps is the number of internal passes of the probabilistic algorithm. Knuth
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indicates that 25 passes are reasonable.
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THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
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CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
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FUTURE GNU MP RELEASES.
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Copyright 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2005 Free
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Software Foundation, Inc. Contributed by John Amanatides.
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Copyright 2011, Brian Gladman
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "mpir.h"
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#include "gmp-impl.h"
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static int
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mill_rab (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
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mpz_srcptr q, mpir_ui k)
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{
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unsigned long int i;
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mpz_powm (y, x, q, n);
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if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0)
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return 1;
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for (i = 1; i < k; i++)
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{
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mpz_powm_ui (y, y, 2L, n);
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if (mpz_cmp (y, nm1) == 0)
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return 1;
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if (mpz_cmp_ui (y, 1L) == 0)
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return 0;
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}
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return 0;
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}
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int
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mpz_miller_rabin (mpz_srcptr n, int reps, gmp_randstate_t rnd)
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{
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int r;
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mpz_t nm1, nm3, x, y, q;
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unsigned long int k;
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int is_prime;
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TMP_DECL;
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TMP_MARK;
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MPZ_TMP_INIT (nm1, SIZ (n) + 1);
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mpz_sub_ui (nm1, n, 1L);
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MPZ_TMP_INIT (x, SIZ (n) + 1);
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MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */
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/* Perform a Fermat test. */
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mpz_set_ui (x, 210L);
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mpz_powm (y, x, nm1, n);
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if (mpz_cmp_ui (y, 1L) != 0)
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{
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TMP_FREE;
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return 0;
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}
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MPZ_TMP_INIT (q, SIZ (n));
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/* Find q and k, where q is odd and n = 1 + 2**k * q. */
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k = mpz_scan1 (nm1, 0L);
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mpz_tdiv_q_2exp (q, nm1, k);
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/* n-3 */
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MPZ_TMP_INIT (nm3, SIZ (n) + 1);
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mpz_sub_ui (nm3, n, 3L);
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ASSERT (mpz_cmp_ui (nm3, 1L) >= 0);
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is_prime = 1;
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for (r = 0; r < reps && is_prime; r++)
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{
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/* 2 to n-2 inclusive, don't want 1, 0 or -1 */
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mpz_urandomm (x, rnd, nm3);
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mpz_add_ui (x, x, 2L);
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is_prime = mill_rab (n, nm1, x, y, q, k);
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}
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TMP_FREE;
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return is_prime;
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}
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