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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) 2014 William Hart
******************************************************************************/
#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#undef ulong
#define ulong mp_limb_t
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "fmpz.h"
#include "fmpz_vec.h"
void _fmpz_nm1_trial_factors(const fmpz_t n, mp_ptr pm1, slong * num_pm1, ulong limit)
{
slong i, num;
ulong ppi, p;
const ulong * primes;
const double * pinv;
*num_pm1 = 0;
/* number of primes multiplied that will fit in a word */
num = FLINT_BITS/FLINT_BIT_COUNT(limit);
/* compute remainders of n mod p for primes p up to limit (approx.) */
n_prime_pi_bounds(&ppi, &ppi, limit); /* precompute primes */
primes = n_primes_arr_readonly(ppi + FLINT_BITS);
pinv = n_prime_inverses_arr_readonly(ppi + FLINT_BITS);
while (primes[0] < limit)
{
/* multiply batch of primes */
p = primes[0];
for (i = 1; i < num; i++)
p *= primes[i];
/* multi-modular reduction */
p = fmpz_tdiv_ui(n, p);
/* check for factors */
for (i = 0; i < num; i++)
{
ulong r = n_mod2_precomp(p, primes[i], pinv[i]);
if (r == 1) /* n - 1 = 0 mod p */
pm1[(*num_pm1)++] = primes[i];
}
/* get next batch of primes */
primes += num;
pinv += num;
}
}
int fmpz_is_prime_pocklington(fmpz_t F, fmpz_t R, const fmpz_t n, mp_ptr pm1, slong num_pm1)
{
slong i, d, bits;
ulong a;
fmpz_t g, q, r, pow, pow2, ex, c, p;
fmpz_factor_t fac;
int res = 0, fac_found;
fmpz_init(p);
fmpz_init(q);
fmpz_init(r);
fmpz_init(g);
fmpz_init(pow);
fmpz_init(pow2);
fmpz_init(c);
fmpz_init(ex);
fmpz_factor_init(fac);
fmpz_sub_ui(R, n, 1); /* start with n - 1 */
bits = fmpz_bits(R);
for (i = 0; i < num_pm1; i++)
{
fmpz_set_ui(p, pm1[i]);
d = fmpz_remove(R, R, p);
_fmpz_factor_append_ui(fac, pm1[i], d);
}
srand(time(NULL));
if (!fmpz_is_probabprime_BPSW(R))
{
if (bits > 150 && (fac_found = fmpz_factor_pp1(p, R, bits + 1000, bits/20 + 1000, rand()%100 + 3)
&& fmpz_is_prime(p)))
{
d = fmpz_remove(R, R, p);
_fmpz_factor_append(fac, p, d);
if (fmpz_is_probabprime_BPSW(R)) /* fast test first */
{
if (fmpz_is_prime(R) == 1)
{
_fmpz_factor_append(fac, R, 1);
fmpz_set_ui(R, 1);
}
}
}
} else
{
if (fmpz_is_prime(R) == 1)
{
_fmpz_factor_append(fac, R, 1);
fmpz_set_ui(R, 1);
}
}
/* compute product F of found primes */
fmpz_set_ui(F, 1);
for (i = 0; i < fac->num; i++)
{
if (fac->exp[i] == 1)
fmpz_mul(F, F, fac->p + i);
else
{
fmpz_pow_ui(pow, fac->p + i, fac->exp[i]);
fmpz_mul(F, F, pow);
}
}
for (a = 2; ; a++)
{
/* compute a^((n-1)/F) mod n */
fmpz_set_ui(pow, a);
fmpz_powm(pow, pow, R, n);
/* check a^(n-1) = 1 mod n */
fmpz_powm(pow2, pow, F, n);
if (!fmpz_is_one(pow2))
{
res = 0;
goto cleanup;
}
fmpz_set_ui(c, 1);
/* find values a^((n-1)/q) - 1 for each prime q dividing F */
for (i = 0; i < fac->num; i++)
{
fmpz_tdiv_q(ex, F, fac->p + i);
fmpz_powm(pow2, pow, ex, n);
fmpz_sub_ui(pow2, pow2, 1);
if (fmpz_sgn(pow2) < 0)
fmpz_add(pow2, pow2, n);
if (!fmpz_is_zero(pow2))
{
fmpz_mul(c, c, pow2);
fmpz_mod(c, c, n);
} else
break;
}
if (i == fac->num) /* found valid base a */
break;
}
/* check for factors of n */
fmpz_gcd(g, n, c);
res = fmpz_is_one(g);
cleanup:
fmpz_factor_clear(fac);
fmpz_clear(pow);
fmpz_clear(pow2);
fmpz_clear(c);
fmpz_clear(ex);
fmpz_clear(p);
fmpz_clear(q);
fmpz_clear(r);
fmpz_clear(g);
return res;
}
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