pqc/external/flint-2.4.3/ulong_extras/factor_lehman.c
2014-05-24 23:16:06 +02:00

80 lines
2.4 KiB
C

/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 William Hart
******************************************************************************/
#define ulong ulongxx /* interferes with system includes */
#include <math.h>
#undef ulong
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
mp_limb_t n_factor_lehman(mp_limb_t n)
{
double limit;
mp_limb_t cuberoot, k;
n_factor_t factors;
slong bound;
#if FLINT64 /* cannot compute enough primes */
if (n > UWORD(10000000000000000)) return n;
#endif
if ((n & 1) == 0) return 2;
limit = pow(n, 1.0/3.0);
cuberoot = (mp_limb_t) ceil(limit);
bound = n_prime_pi(cuberoot);
n_factor_init(&factors);
if (n_factor_trial_range(&factors, n, 0, bound) != n)
return factors.p[0];
if ((factors.p[0] = n_factor_one_line(n, FLINT_FACTOR_ONE_LINE_ITERS)))
if (factors.p[0] != n)
return factors.p[0];
for (k = 1; k <= cuberoot + 1; k++)
{
double low = 2.0*sqrt((double) k)*sqrt((double) n);
mp_limb_t x = (mp_limb_t) ceil(low - 0.0001);
mp_limb_t end = (mp_limb_t) floor(0.0001 + low + pow(n, 1.0/6.0)/((double) 4.0*sqrt((double) k)));
mp_limb_t sub = k*n*4;
for ( ; x <= end; x++)
{
mp_limb_t p, sq = x*x - sub;
if (n_is_square(sq))
{
sq = sqrt((double) sq);
p = n_gcd(n, x - sq);
if (p != 1)
return p;
}
}
}
return n;
}