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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"
void
fmpz_factor(fmpz_factor_t factor, const fmpz_t n)
{
ulong exp;
ulong p;
mpz_ptr xsrc;
nn_ptr xd;
slong xsize;
slong found;
slong trial_start, trial_stop;
TMP_INIT;
if (!COEFF_IS_MPZ(*n))
{
fmpz_factor_si(factor, *n);
return;
}
_fmpz_factor_set_length(factor, 0);
/* Get sign and size */
xsrc = COEFF_TO_PTR(*n);
if (xsrc->_mp_size < 0)
{
xsize = -(xsrc->_mp_size);
factor->sign = -1;
}
else
{
xsize = xsrc->_mp_size;
factor->sign = 1;
}
/* Just a single limb */
if (xsize == 1)
{
_fmpz_factor_extend_factor_ui(factor, xsrc->_mp_d[0]);
return;
}
/* Create a temporary copy to be mutated */
TMP_START;
xd = TMP_ALLOC(xsize * sizeof(ulong));
flint_mpn_copyi(xd, xsrc->_mp_d, xsize);
/* Factor out powers of two */
xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
if (exp != 0)
_fmpz_factor_append_ui(factor, UWORD(2), exp);
trial_start = 1;
trial_stop = 1000;
while (xsize > 1)
{
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 = trial_start + 1000;
continue;
}
else
{
fmpz_t n2;
mpz_ptr data;
fmpz_init2(n2, xsize);
data = _fmpz_promote(n2);
flint_mpn_copyi(data->_mp_d, xd, xsize);
data->_mp_size = xsize;
fmpz_factor_no_trial(factor, n2);
fmpz_clear(n2);
goto cleanup;
}
}
/* Any single-limb factor left? */
if (xd[0] != 1)
_fmpz_factor_extend_factor_ui(factor, xd[0]);
cleanup:
TMP_END;
return;
}