=================================================================== RCS file: /home/cvs/OpenXM_contrib/gmp/mpz/Attic/pprime_p.c,v retrieving revision 1.1.1.1 retrieving revision 1.1.1.2 diff -u -p -r1.1.1.1 -r1.1.1.2 --- OpenXM_contrib/gmp/mpz/Attic/pprime_p.c 2000/01/10 15:35:27 1.1.1.1 +++ OpenXM_contrib/gmp/mpz/Attic/pprime_p.c 2000/09/09 14:12:56 1.1.1.2 @@ -2,114 +2,241 @@ 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. + prime. If it returns 2, n is surely 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, 1993, 1994 Free Software Foundation, Inc. -Contributed by John Amanatides. +Copyright (C) 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000 Free Software +Foundation, Inc. Miller-Rabin code 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 Library General Public License as published by -the Free Software Foundation; either version 2 of the License, or (at your +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 of the License, 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 Library General Public +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. -You should have received a copy of the GNU Library General Public License +You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" -static int -possibly_prime (n, n_minus_1, x, y, q, k) +static int isprime _PROTO ((unsigned long int t)); +static int mpz_millerrabin _PROTO ((mpz_srcptr n, int reps)); + +int +#if __STDC__ +mpz_probab_prime_p (mpz_srcptr n, int reps) +#else +mpz_probab_prime_p (n, reps) mpz_srcptr n; - mpz_srcptr n_minus_1; - mpz_ptr x; - mpz_ptr y; - mpz_srcptr q; - unsigned long int k; + int reps; +#endif { - unsigned long int i; + mp_limb_t r; - /* find random x s.t. 1 < x < n */ - do + /* Handle small and negative n. */ + if (mpz_cmp_ui (n, 1000000L) <= 0) { - mpz_random (x, mpz_size (n)); - mpz_mmod (x, x, n); + int is_prime; + if (mpz_sgn (n) < 0) + { + /* Negative number. Negate and call ourselves. */ + mpz_t n2; + mpz_init (n2); + mpz_neg (n2, n); + is_prime = mpz_probab_prime_p (n2, reps); + mpz_clear (n2); + return is_prime; + } + is_prime = isprime (mpz_get_ui (n)); + return is_prime ? 2 : 0; } - while (mpz_cmp_ui (x, 1L) <= 0); - mpz_powm (y, x, q, n); + /* If n is now even, it is not a prime. */ + if ((mpz_get_ui (n) & 1) == 0) + return 0; - if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, n_minus_1) == 0) - return 1; + /* Check if n has small factors. */ + if (UDIV_TIME > (2 * UMUL_TIME + 6)) + r = mpn_preinv_mod_1 (PTR(n), SIZ(n), (mp_limb_t) PP, (mp_limb_t) PP_INVERTED); + else + r = mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) PP); + if (r % 3 == 0 || r % 5 == 0 || r % 7 == 0 || r % 11 == 0 || r % 13 == 0 + || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0 +#if BITS_PER_MP_LIMB == 64 + || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0 + || r % 47 == 0 || r % 53 == 0 +#endif + ) + { + return 0; + } - for (i = 1; i < k; i++) + /* Do more dividing. We collect small primes, using umul_ppmm, until we + overflow a single limb. We divide our number by the small primes product, + and look for factors in the remainder. */ + { + unsigned long int ln2; + unsigned long int q; + mp_limb_t p1, p0, p; + unsigned int primes[15]; + int nprimes; + + nprimes = 0; + p = 1; + ln2 = mpz_sizeinbase (n, 2) / 30; ln2 = ln2 * ln2; + for (q = BITS_PER_MP_LIMB == 64 ? 59 : 31; q < ln2; q += 2) + { + if (isprime (q)) + { + umul_ppmm (p1, p0, p, q); + if (p1 != 0) + { + r = mpn_mod_1 (PTR(n), SIZ(n), p); + while (--nprimes >= 0) + if (r % primes[nprimes] == 0) + { + if (mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) primes[nprimes]) != 0) + abort (); + return 0; + } + p = q; + nprimes = 0; + } + else + { + p = p0; + } + primes[nprimes++] = q; + } + } + } + + /* Perform a number of Miller-Rabin tests. */ + return mpz_millerrabin (n, reps); +} + +static int +#if __STDC__ +isprime (unsigned long int t) +#else +isprime (t) + unsigned long int t; +#endif +{ + unsigned long int q, r, d; + + if (t < 3 || (t & 1) == 0) + return t == 2; + + for (d = 3, r = 1; r != 0; d += 2) { - mpz_powm_ui (y, y, 2L, n); - if (mpz_cmp (y, n_minus_1) == 0) + q = t / d; + r = t - q * d; + if (q < d) return 1; - if (mpz_cmp_ui (y, 1L) == 0) - return 0; } return 0; } -int +static int millerrabin _PROTO ((mpz_srcptr n, mpz_srcptr nm1, + mpz_ptr x, mpz_ptr y, + mpz_srcptr q, unsigned long int k)); + +static int #if __STDC__ -mpz_probab_prime_p (mpz_srcptr m, int reps) +mpz_millerrabin (mpz_srcptr n, int reps) #else -mpz_probab_prime_p (m, reps) - mpz_srcptr m; +mpz_millerrabin (n, reps) + mpz_srcptr n; int reps; #endif { - mpz_t n, n_minus_1, x, y, q; - int i, is_prime; + int r; + mpz_t nm1, x, y, q; unsigned long int k; + gmp_randstate_t rstate; + int is_prime; + TMP_DECL (marker); + TMP_MARK (marker); - mpz_init (n); - /* Take the absolute value of M, to handle positive and negative primes. */ - mpz_abs (n, m); + MPZ_TMP_INIT (nm1, SIZ (n) + 1); + mpz_sub_ui (nm1, n, 1L); - if (mpz_cmp_ui (n, 3L) <= 0) - { - mpz_clear (n); - return mpz_cmp_ui (n, 1L) > 0; - } + MPZ_TMP_INIT (x, SIZ (n)); + MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */ - if ((mpz_get_ui (n) & 1) == 0) + /* Perform a Fermat test. */ + mpz_set_ui (x, 210L); + mpz_powm (y, x, nm1, n); + if (mpz_cmp_ui (y, 1L) != 0) { - mpz_clear (n); - return 0; /* even */ + return 0; + TMP_FREE (marker); } - mpz_init (n_minus_1); - mpz_sub_ui (n_minus_1, n, 1L); - mpz_init (x); - mpz_init (y); + MPZ_TMP_INIT (q, SIZ (n)); - /* find q and k, s.t. n = 1 + 2**k * q */ - mpz_init_set (q, n_minus_1); - k = mpz_scan1 (q, 0); - mpz_tdiv_q_2exp (q, q, k); + /* Find q and k, where q is odd and n = 1 + 2**k * q. */ + k = mpz_scan1 (nm1, 0L); + mpz_tdiv_q_2exp (q, nm1, k); + gmp_randinit (rstate, GMP_RAND_ALG_DEFAULT, 32L); + is_prime = 1; - for (i = 0; i < reps && is_prime; i++) - is_prime &= possibly_prime (n, n_minus_1, x, y, q, k); + for (r = 0; r < reps && is_prime; r++) + { + do + mpz_urandomb (x, rstate, mpz_sizeinbase (n, 2) - 1); + while (mpz_cmp_ui (x, 1L) <= 0); - mpz_clear (n_minus_1); - mpz_clear (n); - mpz_clear (x); - mpz_clear (y); - mpz_clear (q); + is_prime = millerrabin (n, nm1, x, y, q, k); + } + + gmp_randclear (rstate); + + TMP_FREE (marker); return is_prime; +} + +static int +#if __STDC__ +millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y, + mpz_srcptr q, unsigned long int k) +#else +millerrabin (n, nm1, x, y, q, k) + mpz_srcptr n; + mpz_srcptr nm1; + mpz_ptr x; + mpz_ptr y; + mpz_srcptr q; + unsigned long int k; +#endif +{ + unsigned long int i; + + mpz_powm (y, x, q, n); + + if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0) + return 1; + + for (i = 1; i < k; i++) + { + mpz_powm_ui (y, y, 2L, n); + if (mpz_cmp (y, nm1) == 0) + return 1; + if (mpz_cmp_ui (y, 1L) == 0) + return 0; + } + return 0; }