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/*
Copyright (C) 2010 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
#include "mpn_extras.h"
#include "fmpz.h"
#include "fmpz_factor.h"
int
fmpz_factor_trial_range(fmpz_factor_t factor, const fmpz_t n, ulong start, ulong num_primes)
{
ulong exp;
ulong p;
mpz_t x;
nn_ptr xd;
slong xsize;
ulong found;
ulong trial_start, trial_stop;
int ret = 1;
if (!COEFF_IS_MPZ(*n))
{
fmpz_factor_si(factor, *n);
return ret;
}
_fmpz_factor_set_length(factor, 0);
/* Make an mpz_t copy whose limbs will be mutated */
mpz_init(x);
fmpz_get_mpz(x, n);
if (x->_mp_size < 0)
{
x->_mp_size = -(x->_mp_size);
factor->sign = -1;
}
else
{
factor->sign = 1;
}
xd = x->_mp_d;
xsize = x->_mp_size;
/* Factor out powers of two */
if (start == 0)
{
xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
if (exp != 0)
_fmpz_factor_append_ui(factor, UWORD(2), exp);
}
trial_start = FLINT_MAX(1, start);
trial_stop = FLINT_MIN(start + 1000, start + num_primes);
do
{
found = flint_mpn_factor_trial(xd, xsize, trial_start, trial_stop);
if (found)
{
p = n_primes_arr_readonly(found+1)[found];
exp = 1;
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
/* Check if p^2 divides n */
if (flint_mpn_divisible_1_odd(xd, xsize, p))
{
/* TODO: when searching for squarefree numbers
(Moebius function, etc), we can abort here. */
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
exp = 2;
}
/* If we're up to cubes, then maybe there are higher powers */
if (exp == 2 && flint_mpn_divisible_1_odd(xd, xsize, p))
{
mpn_divexact_1(xd, xd, xsize, p);
xsize -= (xd[xsize - 1] == 0);
xsize = flint_mpn_remove_power_ascending(xd, xsize, &p, 1, &exp);
exp += 3;
}
_fmpz_factor_append_ui(factor, p, exp);
/* flint_printf("added %wu %wu\n", p, exp); */
/* Continue using only trial division whilst it is successful.
This allows quickly factoring huge highly composite numbers
such as factorials, which can arise in some applications. */
trial_start = found + 1;
trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
continue;
}
else
{
/* Insert primality test, perfect power test, other factoring
algorithms here... */
trial_start = trial_stop;
trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
}
} while ((xsize > 1 || xd[0] != 1) && trial_start != trial_stop);
/* Any factor left? */
if (xsize > 1 || xd[0] != 1)
ret = 0;
mpz_clear(x);
return ret;
}