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pqc/external/flint-2.4.3/fmpz/is_prime_pseudosquare.c

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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) 2009, 2012 William Hart
******************************************************************************/
#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#include <stdio.h>
#undef ulong
#define ulong mp_limb_t
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "fmpz.h"
#ifndef FLINT64
mp_limb_t flint_fmpz_pseudosquares[][3] =
{
{ 17, 0, 0 },
{ 73, 0, 0 },
{ 241, 0, 0 },
{ 1009, 0, 0 },
{ 2641, 0, 0 },
{ 8089, 0, 0 },
{ 18001, 0, 0 },
{ 53881, 0, 0 },
{ 87481, 0, 0 },
{ 117049, 0, 0 },
{ 515761, 0, 0 },
{ 1083289, 0, 0 },
{ 3206641, 0, 0 },
{ 3818929, 0, 0 },
{ 9257329, 0, 0 },
{ 22000801, 0, 0 },
{ 48473881, 0, 0 },
{ 48473881, 0, 0 },
{ 175244281, 0, 0 },
{ 427733329, 0, 0 },
{ 427733329, 0, 0 },
{ 898716289u, 0, 0 },
{ 2805544681u, 0, 0 },
{ 2805544681u, 0, 0 },
{ 2805544681u, 0, 0 },
{ 1720328849u, 2u, 0 },
{ 2141495009u, 5u, 0 },
{ 3553231785u, 19u, 0 },
{ 3553231785u, 19u, 0 },
{ 2991566689u, 45u, 0 },
{ 2991566689u, 45u, 0 },
{ 2804689073u, 668u, 0 },
{ 2804689073u, 668u, 0 },
{ 2804689073u, 668u, 0 },
{ 46910577u, 6112u, 0 },
{ 46910577u, 6112u, 0 },
{ 1079027281u, 26178u, 0 },
{ 1079027281u, 26178u, 0 },
{ 1079027281u, 26178u, 0 },
{ 3590018425u, 41661u, 0 },
{ 3590018425u, 41661u, 0 },
{ 2746102297u, 162087u, 0 },
{ 2746102297u, 162087u, 0 },
{ 1936779721u, 664710u, 0 },
{ 1070451441u, 1501768u, 0 },
{ 1070451441u, 1501768u, 0 },
{ 2061289617u, 2710474u, 0 },
{ 2061289617u, 2710474u, 0 },
{ 4235760785u, 44382509u, 0 },
{ 2312776601u, 45783875u, 0 },
{ 2678348049u, 165920782u, 0 },
{ 3315991761u, 413007985u, 0 },
{ 1567179849u, 541956877u, 0 },
{ 2273104657u, 1486621767u, 0 },
{ 3796117489u, 1867116582u, 0 },
{ 2425538377u, 2374430322u, 0 },
{ 2425538377u, 2374430322u, 0 },
{ 2425538377u, 2374430322u, 0 },
{ 3763487577u, 3377920039u, 3u },
{ 2972093785u, 1402148275u, 11u },
{ 2785759393u, 3968325740u, 28u },
{ 551239041u, 3335735663u, 50u },
{ 551239041u, 3335735663u, 50u },
{ 732515297u, 554264481u, 116u },
{ 732515297u, 554264481u, 116u },
{ 732515297u, 554264481u, 116u },
{ 2681625681u, 3960593856u, 739u },
{ 2546105329u, 1679561907u, 1875u },
{ 533319201u, 2248012685u, 5393u },
{ 533319201u, 2248012685u, 5393u },
{ 996692113u, 2949507147u, 16011u },
{ 996692113u, 2949507147u, 16011u },
{ 2616068761u, 328479117u, 198156u },
{ 1411295841u, 761797252u, 229581u }
};
#else
mp_limb_t flint_fmpz_pseudosquares[][2] =
{
{ 17, 0 },
{ 73, 0 },
{ 241, 0 },
{ 1009, 0 },
{ 2641, 0 },
{ 8089, 0 },
{ 18001, 0 },
{ 53881, 0 },
{ 87481, 0 },
{ 117049, 0 },
{ 515761, 0 },
{ 1083289, 0 },
{ 3206641, 0 },
{ 3818929, 0 },
{ 9257329, 0 },
{ 22000801, 0 },
{ 48473881, 0 },
{ 48473881, 0 },
{ 175244281, 0 },
{ 427733329, 0 },
{ 427733329, 0 },
{ 898716289u, 0 },
{ 2805544681u, 0 },
{ 2805544681u, 0 },
{ 2805544681u, 0 },
{ 10310263441u, 0 },
{ 23616331489u, 0 },
{ 85157610409u, 0 },
{ 85157610409u, 0 },
{ 196265095009u, 0 },
{ 196265095009u, 0 },
{ 2871842842801u, 0 },
{ 2871842842801u, 0 },
{ 2871842842801u, 0 },
{ 26250887023729u, 0 },
{ 26250887023729u, 0 },
{ 112434732901969u, 0 },
{ 112434732901969u, 0 },
{ 112434732901969u, 0 },
{ 178936222537081u, 0 },
{ 178936222537081u, 0 },
{ 696161110209049u, 0 },
{ 696161110209049u, 0 },
{ 2854909648103881u, 0 },
{ 6450045516630769u, 0 },
{ 6450045516630769u, 0 },
{ 11641399247947921u, 0 },
{ 11641399247947921u, 0 },
{ 190621428905186449u, 0 },
{ 196640248121928601u, 0 },
{ 712624335095093521u, 0 },
{ 1773855791877850321u, 0 },
{ 2327687064124474441u, 0 },
{ 6384991873059836689u, 0 },
{ 8019204661305419761u, 0 },
{ 10198100582046287689u, 0 },
{ 10198100582046287689u, 0 },
{ 10198100582046287689u, 0 },
{ 14508056099771532121u, 3u },
{ 6022180988239908185u, 11u },
{ 17043829275960758433u, 28u },
{ 14326875581237116289u, 50u },
{ 14326875581237116289u, 50u },
{ 2380547819961928673u, 116u },
{ 2380547819961928673u, 116u },
{ 2380547819961928673u, 116u },
{ 17010621086940159057u, 739u },
{ 7213663464718498801u, 1875u },
{ 9655140963601468961u, 5393u },
{ 9655140963601468961u, 5393u },
{ 12668036736679956625u, 16011u },
{ 12668036736679956625u, 16011u },
{ 1410807067550026393u, 198156u },
{ 3271894284933966433u, 229581u }
};
#endif
#define FLINT_NUM_FMPZ_PSEUDOSQUARES 74
void fmpz_set_pseudosquare(fmpz_t f, unsigned int i)
{
#ifndef FLINT64
if (i < 25)
fmpz_set_ui(f, flint_fmpz_pseudosquares[i][0]);
else if (i < 58)
{
fmpz_set_ui(f, flint_fmpz_pseudosquares[i][1]);
fmpz_mul_2exp(f, f, 32);
fmpz_add_ui(f, f, flint_fmpz_pseudosquares[i][0]);
} else if (i < FLINT_NUM_FMPZ_PSEUDOSQUARES)
{
fmpz_set_ui(f, flint_fmpz_pseudosquares[i][2]);
fmpz_mul_2exp(f, f, 32);
fmpz_add_ui(f, f, flint_fmpz_pseudosquares[i][1]);
fmpz_mul_2exp(f, f, 32);
fmpz_add_ui(f, f, flint_fmpz_pseudosquares[i][1]);
}
#else
if (i < 58)
fmpz_set_ui(f, flint_fmpz_pseudosquares[i][0]);
else if (i < FLINT_NUM_FMPZ_PSEUDOSQUARES)
{
fmpz_set_ui(f, flint_fmpz_pseudosquares[i][1]);
fmpz_mul_2exp(f, f, 64);
fmpz_add_ui(f, f, flint_fmpz_pseudosquares[i][0]);
}
#endif
else
{
flint_printf("Exception (fmpz_set_pseudosquare). Index too large.\n");
abort();
}
}
int fmpz_is_prime_pseudosquare(const fmpz_t n)
{
unsigned int i, j, m1;
mp_limb_t p, B, mod8;
fmpz_t NB, f, exp, mod, nm1;
int ret;
const mp_limb_t * primes;
if (fmpz_sgn(n) <= 0)
return 0;
if (fmpz_size(n) == 1)
return n_is_prime_pseudosquare(fmpz_get_ui(n));
primes = n_primes_arr_readonly(FLINT_PSEUDOSQUARES_CUTOFF + 1);
for (i = 0; i < FLINT_PSEUDOSQUARES_CUTOFF; i++)
{
p = primes[i];
if (fmpz_fdiv_ui(n, p) == 0)
return 0;
}
fmpz_init(NB);
fmpz_init(f);
fmpz_init(exp);
fmpz_init(mod);
fmpz_init(nm1);
B = primes[FLINT_PSEUDOSQUARES_CUTOFF];
fmpz_sub_ui(nm1, n, 1);
fmpz_fdiv_q_ui(NB, nm1, B);
fmpz_add_ui(NB, NB, 1);
m1 = 0;
for (i = 0; i < FLINT_NUM_FMPZ_PSEUDOSQUARES; i++)
{
fmpz_set_pseudosquare(f, i);
if (fmpz_cmp(f, NB) > 0)
break;
}
if (i == FLINT_NUM_FMPZ_PSEUDOSQUARES)
{
ret = -1;
goto cleanup;
}
fmpz_fdiv_q_2exp(exp, nm1, 1);
for (j = 0; j <= i; j++)
{
fmpz_set_ui(mod, primes[j]);
fmpz_powm(mod, mod, exp, n);
if (!fmpz_is_one(mod) && fmpz_cmp(mod, nm1) != 0)
{
ret = 0;
goto cleanup;
}
if (fmpz_cmp(mod, nm1) == 0)
m1 = 1;
}
mod8 = fmpz_fdiv_ui(n, 8);
if ((mod8 == 3) || (mod8 == 7))
{
ret = 1;
goto cleanup;
}
if (mod8 == 5)
{
fmpz_set_ui(mod, 2);
fmpz_powm(mod, mod, exp, n);
if (fmpz_cmp(mod, nm1) == 0)
{
ret = 1;
goto cleanup;
}
flint_printf("Whoah, ");
fmpz_print(n);
flint_printf("is a probable prime, but not prime, please report!!\n");
abort();
}
else
{
if (m1)
{
ret = 1;
goto cleanup;
}
for (j = i + 1; j < FLINT_NUM_FMPZ_PSEUDOSQUARES + 1; j++)
{
fmpz_set_ui(mod, primes[j]);
fmpz_powm(mod, mod, exp, n);
if (fmpz_cmp(mod, nm1) == 0)
{
ret = 1;
goto cleanup;
}
if (!fmpz_is_one(mod))
{
flint_printf("Whoah, ");
fmpz_print(n);
flint_printf("is a probable prime, but not prime, please report!!\n");
abort();
}
}
flint_printf("Whoah, ");
fmpz_print(n);
flint_printf("is a probable prime, but not prime, please report!!\n");
abort();
}
cleanup:
fmpz_clear(NB);
fmpz_clear(f);
fmpz_clear(exp);
fmpz_clear(mod);
fmpz_clear(nm1);
return ret;
}
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