129 lines
4.0 KiB
C
129 lines
4.0 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2009 William Hart
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******************************************************************************/
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#define ulong ulongxx /* interferes with system includes */
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#include <stdlib.h>
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#include <stdio.h>
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#undef ulong
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#include <gmp.h>
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#include "flint.h"
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#include "ulong_extras.h"
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mp_limb_t flint_pseudosquares[] = {17, 73, 241, 1009, 2641, 8089, 18001,
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53881, 87481, 117049, 515761, 1083289, 3206641, 3818929, 9257329,
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22000801, 48473881, 48473881, 175244281, 427733329, 427733329,
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898716289u, 2805544681u, 2805544681u, 2805544681u
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#ifndef FLINT64
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};
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#else
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, 10310263441u, 23616331489u, 85157610409u, 85157610409u,
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196265095009u, 196265095009u, 2871842842801u, 2871842842801u,
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2871842842801u, 26250887023729u, 26250887023729u, 112434732901969u,
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112434732901969u, 112434732901969u, 178936222537081u,
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178936222537081u, 696161110209049u, 696161110209049u,
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2854909648103881u, 6450045516630769u, 6450045516630769u,
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11641399247947921u, 11641399247947921u, 190621428905186449u,
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196640248121928601u, 712624335095093521u, 1773855791877850321u };
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#endif
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#if FLINT64
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#define FLINT_NUM_PSEUDOSQUARES 52
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#else
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#define FLINT_NUM_PSEUDOSQUARES 25
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#endif
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int n_is_prime_pseudosquare(mp_limb_t n)
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{
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unsigned int i, j, m1;
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mp_limb_t p, B, NB, exp, mod8;
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const mp_limb_t * primes;
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const double * inverses;
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if (n < UWORD(2)) return 0;
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if ((n & UWORD(1)) == UWORD(0))
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{
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return (n == UWORD(2));
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}
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primes = n_primes_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);
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inverses = n_prime_inverses_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF+1);
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for (i = 0; i < FLINT_PSEUDOSQUARES_CUTOFF; i++)
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{
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double ppre;
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p = primes[i];
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if (p*p > n) return 1;
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ppre = inverses[i];
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if (!n_mod2_precomp(n, p, ppre)) return 0;
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}
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B = primes[FLINT_PSEUDOSQUARES_CUTOFF];
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NB = (n - 1)/B + 1;
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m1 = 0;
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for (i = 0; i < FLINT_NUM_PSEUDOSQUARES; i++)
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{
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if (flint_pseudosquares[i] > NB) break;
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}
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exp = (n - 1)/2;
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for (j = 0; j <= i; j++)
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{
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mp_limb_t mod = n_powmod2(primes[j], exp, n);
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if ((mod != UWORD(1)) && (mod != n - 1)) return 0;
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if (mod == n - 1) m1 = 1;
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}
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mod8 = n % 8;
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if ((mod8 == 3) || (mod8 == 7)) return 1;
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if (mod8 == 5)
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{
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mp_limb_t mod = n_powmod2(UWORD(2), exp, n);
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if (mod == n - 1) return 1;
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flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
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abort();
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}
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else
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{
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if (m1) return 1;
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for (j = i + 1; j < FLINT_NUM_PSEUDOSQUARES + 1; j++)
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{
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mp_limb_t mod = n_powmod2(primes[j], exp, n);
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if (mod == n - 1) return 1;
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if (mod != 1)
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{
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flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
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abort();
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}
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}
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flint_printf("Whoah, %wu is a probable prime, but not prime, please report!!\n", n);
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abort();
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}
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}
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