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/*
Copyright (C) 2015 Vladimir Glazachev
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "aprcl.h"
int
aprcl_is_prime_final_division(const fmpz_t n, const fmpz_t s, ulong r)
{
int result = 1;
ulong i;
fmpz_t npow, nmul, rem;
fmpz_init(rem);
fmpz_init_set(npow, n);
fmpz_mod(npow, npow, s); /* npow = n mod s */
fmpz_init_set(nmul, npow);
for (i = 1; i <= r; i++)
{
if (fmpz_is_one(npow))
break;
fmpz_mod(rem, n, npow);
/* if npow | n */
if (fmpz_is_zero(rem))
{
/* if npow != n and npow != 1 */
if (!fmpz_equal(n, npow) && !fmpz_is_one(npow))
{
/* npow | n, so n is composite */
result = 0;
break;
}
}
/* npow = n^i mod s */
fmpz_mul(npow, npow, nmul);
fmpz_mod(npow, npow, s);
}
fmpz_clear(npow);
fmpz_clear(nmul);
fmpz_clear(rem);
return result;
}