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/*
Copyright (C) 2009 William Hart
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 "test_helpers.h"
#include "gmpcompat.h"
#include "ulong_extras.h"
TEST_FUNCTION_START(n_is_probabprime_lucas, state)
{
int i, result;
ulong count = UWORD(0);
ulong d;
mpz_t d_m;
double test_multiplier = FLINT_MAX(1, flint_test_multiplier());
{
/* A selection of Lucas pseudoprimes. These are known composites for
which the Lucas test *should* claim PRIME, but which a buggy
implementation may claim COMPOSITE for spurious reasons. */
ulong pseudo[] = {
/* Initial entries from Dana Jacobsen's table (http://ntheory.org/pseudoprimes.html) */
323, 377, 1159, 1829, 3827, 5459, 5777, 9071, 9179, 10877, 11419, 11663,
13919, 14839, 16109, 16211, 18407, 18971, 19043, 22499, 23407, 24569,
25199, 25877, 26069, 27323, 32759, 34943, 35207, 39059, 39203, 39689,
/* Some bigger entries (24 bits) */
8711699, 10402139, 12124559, 13695947, 13826231,
/* Even bigger entries (32 bits) */
UWORD(2877330059), UWORD(3816635327), UWORD(3964016279),
#if FLINT_BITS == 64
/* Check that #2168 is fixed. */
UWORD(9508976851322519),
#endif
0
};
for (i = 0; (d = pseudo[i]) != 0; i++)
{
if (!n_is_probabprime_lucas(d))
TEST_FUNCTION_FAIL("Lucas pseudoprime %wu claimed composite by Lucas test\n", d);
}
}
for (i = 0; i < 10000 * test_multiplier; i++) /* Test that primes pass the test */
{
mpz_init(d_m);
do
{
d = n_randtest_not_zero(state);
flint_mpz_set_ui(d_m, d);
mpz_nextprime(d_m, d_m);
d = flint_mpz_get_ui(d_m);
} while (mpz_size(d_m) > 1);
result = n_is_probabprime_lucas(d);
if (!result)
TEST_FUNCTION_FAIL("d = %wu is declared composite\n", d);
mpz_clear(d_m);
}
for (i = 0; i < 10000 * test_multiplier; i++) /* Test that not too many composites pass */
{
mpz_init(d_m);
do
{
d = n_randtest(state);
flint_mpz_set_ui(d_m, d);
} while (mpz_probab_prime_p(d_m, 12));
if (n_is_probabprime_lucas(d) == 1) count++;
mpz_clear(d_m);
}
result = (count < 20 * test_multiplier);
if (!result)
TEST_FUNCTION_FAIL("%wu composites declared prime\n", count);
TEST_FUNCTION_END(state);
}