/* check_all_small_numbers_long.c -- test the RQFT on a range of small numbers (GMP version)

*

* Copyright 2014 by Colin Benner <colin-software@yzhs.de>

*

* This file is part of frobenius-test.

*

* frobenius-test 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 3 of the License, or

* (at your option) any later version.

*

* frobenius-test 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 frobenius-test. If not, see <http://www.gnu.org/licenses/>.

*/

#include <stdio.h>

#include <stdlib.h>

#include <gmp.h>

#include "frobenius.h"

#include "helpers.h"

#include "helpers_int.h"

/*

* Uncomment the following to always select the smallest possible parameter c

* instead of using c = n-4.

*/

//#define SMALL_C

/*

* Run the randomized quadratic frobenius test to check whether [n] is a a

* prime. The Parameter [k] determines how many times the test will be run at

* most. If the test returns "composite", it will not be run again.

*/

int main(int argc, char *argv[])

{

Primality result;

#define VARS n, b, c, bb4c

mpz_t VARS;

uint64_t n_, b_ = 0, c_;

uint64_t false_positives = 0;

uint64_t lower_bound = 5, upper_bound = 1000000;

mpz_inits(VARS, NULL);

if (argc > 2)

lower_bound = strtoul(argv[1], NULL, 10);

if (argc > 1)

upper_bound = strtoul(argv[argc > 2 ? 2 : 1], NULL, 10);

printf("%lu to %lu\n", lower_bound, upper_bound);

for (n_ = lower_bound | 1; n_ <= upper_bound; n_+=2) {

mpz_set_ui(n, n_);

if (mpz_perfect_square_p(n) || mpz_probab_prime_p(n, 100))

continue;

#ifdef SMALL_C

for (c_ = 2; c_ < n_; c_++) {

if (jacobi(n_ - c_, n_) != 1)

continue;

#else

c_ = n_ - 4;

mpz_sub_ui(c, n, 4);

#endif

for (b_ = 1; b_ < n_; b_++) {

mpz_mul(bb4c, b, b);

mpz_addmul_ui(bb4c, c, 4);

mpz_mod(bb4c, bb4c, n);

if (mpz_jacobi(bb4c, n) == -1)

break;

if (b_ % 1000 == 999) {

fprintf(stderr, "Could not find a valid parameter pair (b, c)\n");

goto next_n;

}

}

#ifdef SMALL_C

break;

}

#endif

result = steps_3_4_5(n, b, c);

if (result != composite) {

false_positives++;

fflush(stdout);

printf("Found a false positive: n = %lu, b = %lu, c = %lu\n", n_, b_, c_);

}

if (n_ % 10000000 == 1) {

fprintf(stderr, ".");

fflush(stderr);

}

next_n:

;

}

printf("\nA total number of %lu false positives were found among the numbers %lu,...,%lu\n",

false_positives, lower_bound, upper_bound);

mpz_clears(VARS, NULL);

return 0;

}