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/*
Copyright (C) 2016 William Hart
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 <gmp.h>
#include "fmpz.h"
#include "fmpz_factor.h"
#include "ulong_extras.h"
#include "qsieve.h"
void
fmpz_factor_no_trial(fmpz_factor_t factor, const fmpz_t n)
{
int exp, i;
fmpz_t root;
if (fmpz_is_prime(n))
{
_fmpz_factor_append(factor, n, 1);
return;
}
fmpz_init(root);
exp = fmpz_is_perfect_power(root, n);
if (exp != 0)
{
fmpz_factor_t fac;
fmpz_factor_init(fac);
fmpz_factor_no_trial(fac, root);
_fmpz_factor_concat(factor, fac, exp);
fmpz_factor_clear(fac);
}
else
{
fmpz_factor_t fac, fac2, fac3;
slong bits = fmpz_sizeinbase(n, 2);
int done;
fmpz_factor_init(fac3);
done = fmpz_factor_smooth(fac3, n, FLINT_MAX(bits/3 - 17, 2), 1);
if (!done)
{
fmpz_t n2;
slong exp2;
fmpz_init(n2);
/* take out cofactor and factor it */
fmpz_set(n2, fac3->p + fac3->num - 1);
exp = fac3->exp[fac3->num - 1];
fac3->exp[fac3->num - 1] = 0;
fac3->num--;
fmpz_factor_init(fac);
/* qsieve can't factor perfect powers */
exp2 = fmpz_is_perfect_power(root, n2);
if (exp2)
{
_fmpz_factor_append(fac, root, exp2);
}
else
{
#if FLINT_BITS == 64
slong bits = fmpz_bits(n2);
if (bits <= 80)
{
slong squfof_iters;
ulong nhi, nlo, f1 = 0;
if (bits <= 69)
squfof_iters = 50000;
else if (bits <= 72)
squfof_iters = 150000;
else
squfof_iters = 200000;
fmpz_get_uiui(&nhi, &nlo, n2);
f1 = n_ll_factor_SQUFOF(nhi, nlo, squfof_iters);
/* SQUFOF has a small chance of failing with a fixed number
of iterations, so we need qsieve as a fallback. */
if (f1 == 0)
{
qsieve_factor(fac, n2);
}
else
{
fmpz_t t, f;
ulong expf;
fmpz_init(t);
fmpz_init_set_ui(f, f1);
expf = fmpz_remove(t, n2, f);
FLINT_ASSERT(expf >= 1);
_fmpz_factor_append(fac, f, expf);
_fmpz_factor_append(fac, t, 1);
fmpz_clear(t);
fmpz_clear(f);
}
}
else
{
qsieve_factor(fac, n2);
}
#else
qsieve_factor(fac, n2);
#endif
}
for (i = 0; i < fac->num; i++)
{
fmpz_factor_init(fac2);
fmpz_factor_no_trial(fac2, fac->p + i);
_fmpz_factor_concat(fac3, fac2, exp*fac->exp[i]);
fmpz_factor_clear(fac2);
}
fmpz_factor_clear(fac);
fmpz_clear(n2);
}
_fmpz_factor_concat(factor, fac3, 1);
fmpz_factor_clear(fac3);
}
fmpz_clear(root);
}