134 lines
4.0 KiB
C
134 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) 2010 Fredrik Johansson
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "mpn_extras.h"
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#include "ulong_extras.h"
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int
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fmpz_factor_trial_range(fmpz_factor_t factor, const fmpz_t n, ulong start, ulong num_primes)
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{
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ulong exp;
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mp_limb_t p;
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mpz_t x;
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mp_ptr xd;
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mp_size_t xsize;
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slong found;
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slong trial_start, trial_stop;
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int ret = 1;
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if (!COEFF_IS_MPZ(*n))
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{
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fmpz_factor_si(factor, *n);
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return ret;
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}
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_fmpz_factor_set_length(factor, 0);
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/* Make an mpz_t copy whose limbs will be mutated */
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mpz_init(x);
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fmpz_get_mpz(x, n);
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if (x->_mp_size < 0)
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{
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x->_mp_size = -(x->_mp_size);
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factor->sign = -1;
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}
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else
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{
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factor->sign = 1;
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}
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xd = x->_mp_d;
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xsize = x->_mp_size;
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/* Factor out powers of two */
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if (start == 0)
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{
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xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
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if (exp != 0)
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_fmpz_factor_append_ui(factor, UWORD(2), exp);
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}
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trial_start = FLINT_MAX(1, start);
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trial_stop = FLINT_MIN(start + 1000, start + num_primes);
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do
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{
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found = flint_mpn_factor_trial(xd, xsize, trial_start, trial_stop);
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if (found)
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{
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p = n_primes_arr_readonly(found+1)[found];
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exp = 1;
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xsize = flint_mpn_divexact_1(xd, xsize, p);
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/* Check if p^2 divides n */
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if (flint_mpn_divisible_1_p(xd, xsize, p))
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{
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/* TODO: when searching for squarefree numbers
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(Moebius function, etc), we can abort here. */
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xsize = flint_mpn_divexact_1(xd, xsize, p);
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exp = 2;
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}
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/* If we're up to cubes, then maybe there are higher powers */
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if (exp == 2 && flint_mpn_divisible_1_p(xd, xsize, p))
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{
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xsize = flint_mpn_divexact_1(xd, xsize, p);
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xsize = flint_mpn_remove_power_ascending(xd, xsize, &p, 1, &exp);
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exp += 3;
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}
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_fmpz_factor_append_ui(factor, p, exp);
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/* flint_printf("added %wu %wu\n", p, exp); */
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/* Continue using only trial division whilst it is successful.
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This allows quickly factoring huge highly composite numbers
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such as factorials, which can arise in some applications. */
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trial_start = found + 1;
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trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
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continue;
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}
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else
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{
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/* Insert primality test, perfect power test, other factoring
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algorithms here... */
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trial_start = trial_stop;
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trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
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}
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} while ((xsize > 1 || xd[0] != 1) && trial_start != trial_stop);
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/* Any factor left? */
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if (xsize > 1 || xd[0] != 1)
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ret = 0;
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mpz_clear(x);
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return ret;
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}
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