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/*=============================================================================
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) 2012 William Hart
******************************************************************************/
#define ulong ulongxx /* prevent clash with stdlib */
#include <stdio.h>
#undef ulong
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#define n_pp1_set(x1, y1, x2, y2) \
do { \
x1 = x2; \
y1 = y2; \
} while (0)
#define n_pp1_set_ui(x, norm, c) \
do { \
x = (c << norm); \
} while (0)
void n_pp1_print(mp_limb_t x, mp_limb_t y, ulong norm)
{
if (norm)
{
x >>= norm;
y >>= norm;
}
flint_printf("[%wu, %wu]", x, y);
}
#define n_pp1_2k(x, y, n, ninv, x0, norm) \
do { \
const mp_limb_t two = (UWORD(2) << norm); \
y = n_mulmod_preinv(y, x, n, ninv, norm); \
y = n_submod(y, x0, n); \
x = n_mulmod_preinv(x, x, n, ninv, norm); \
x = n_submod(x, two, n); \
} while (0)
#define n_pp1_2kp1(x, y, n, ninv, x0, norm) \
do { \
const mp_limb_t two = (UWORD(2) << norm); \
x = n_mulmod_preinv(x, y, n, ninv, norm); \
x = n_submod(x, x0, n); \
y = n_mulmod_preinv(y, y, n, ninv, norm); \
y = n_submod(y, two, n); \
} while (0)
void n_pp1_pow_ui(mp_limb_t * x, mp_limb_t * y, ulong exp,
mp_limb_t n, mp_limb_t ninv, ulong norm)
{
const mp_limb_t x0 = *x;
const mp_limb_t two = (UWORD(2) << norm);
ulong bit = ((UWORD(1) << FLINT_BIT_COUNT(exp)) >> 2);
(*y) = n_mulmod_preinv(*x, *x, n, ninv, norm);
(*y) = n_submod(*y, two, n);
while (bit)
{
if (exp & bit)
n_pp1_2kp1(*x, *y, n, ninv, x0, norm);
else
n_pp1_2k(*x, *y, n, ninv, x0, norm);
bit >>= 1;
}
}
mp_limb_t n_pp1_factor(mp_limb_t n, mp_limb_t x, ulong norm)
{
if (norm)
{
n >>= norm;
x >>= norm;
}
x = n_submod(x, 2, n);
if (x == 0)
return 0;
return n_gcd(n, x);
}
mp_limb_t n_pp1_find_power(mp_limb_t * x, mp_limb_t * y,
ulong p, mp_limb_t n, mp_limb_t ninv, ulong norm)
{
mp_limb_t factor;
do
{
n_pp1_pow_ui(x, y, p, n, ninv, norm);
factor = n_pp1_factor(n, *x, norm);
} while (factor == 1);
return factor;
}
mp_limb_t n_factor_pp1(mp_limb_t n, ulong B1, ulong c)
{
slong i, j;
mp_limb_t factor = 0;
mp_limb_t x, y = 0, oldx, oldy, ninv;
ulong pr, oldpr, sqrt, bits0, norm;
n_primes_t iter;
if ((n % 2) == 0)
return 2;
n_primes_init(iter);
sqrt = n_sqrt(B1);
bits0 = FLINT_BIT_COUNT(B1);
count_leading_zeros(norm, n);
n <<= norm;
ninv = n_preinvert_limb(n);
n_pp1_set_ui(x, norm, c);
/* mul by various prime powers */
pr = 0;
oldpr = 0;
for (i = 0; pr < B1; )
{
j = i + 1024;
oldpr = pr;
n_pp1_set(oldx, oldy, x, y);
for ( ; i < j; i++)
{
pr = n_primes_next(iter);
if (pr < sqrt)
{
ulong bits = FLINT_BIT_COUNT(pr);
ulong exp = bits0 / bits;
n_pp1_pow_ui(&x, &y, n_pow(pr, exp), n, ninv, norm);
} else
n_pp1_pow_ui(&x, &y, pr, n, ninv, norm);
}
factor = n_pp1_factor(n, x, norm);
if (factor == 0)
break;
if (factor != 1)
goto cleanup;
}
if (pr < B1) /* factor = 0 */
{
n_primes_jump_after(iter, oldpr);
n_pp1_set(x, y, oldx, oldy);
do
{
pr = n_primes_next(iter);
n_pp1_set(oldx, oldy, x, y);
if (pr < sqrt)
{
ulong bits = FLINT_BIT_COUNT(pr);
ulong exp = bits0 / bits;
n_pp1_pow_ui(&x, &y, n_pow(pr, exp), n, ninv, norm);
} else
n_pp1_pow_ui(&x, &y, pr, n, ninv, norm);
factor = n_pp1_factor(n, x, norm);
if (factor == 0)
break;
if (factor != 1)
goto cleanup;
} while (1);
} else
goto cleanup;
/* factor still 0 */
factor = n_pp1_find_power(&oldx, &oldy, pr, n, ninv, norm);
cleanup:
n_primes_clear(iter);
return factor;
}
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