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/*
Copyright (C) 2015 Arb authors
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "arb.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sinc....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t x, a;
slong prec, mag_bits;
prec = 2 + n_randint(state, 500);
mag_bits = 6 + n_randint(state, 500);
arb_init(x);
arb_randtest(x, state, 1 + n_randint(state, prec), mag_bits);
arb_init(a);
arb_sinc(a, x, prec);
/* sinc(x) approximately in [-2, 2] */
{
arb_t b;
arb_init(b);
arb_zero(b);
mag_set_d(arb_radref(b), 1.01);
mag_mul_2exp_si(arb_radref(b), arb_radref(b), 1);
if (!arb_contains(b, a))
{
flint_printf("FAIL: containment\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_abort();
}
arb_clear(b);
}
/* sinc(x) * x = sin(x) */
{
arb_t b, c;
arb_init(b);
arb_init(c);
arb_mul(b, a, x, prec);
arb_sin(c, x, prec);
if (!arb_overlaps(b, c))
{
flint_printf("FAIL: overlap (sin)\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_abort();
}
arb_clear(b);
arb_clear(c);
}
/* aliasing */
{
arb_t b;
arb_init(b);
arb_set(b, x);
arb_sinc(b, b, prec);
if (!arb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_abort();
}
arb_clear(b);
}
arb_clear(x);
arb_clear(a);
}
/* Check a few special intervals. */
{
arb_t x, y;
slong prec;
arb_init(x);
arb_init(y);
prec = 32;
arb_neg_inf(x);
arb_sinc(y, x, prec);
if (!arb_is_zero(y))
{
flint_printf("FAIL: negative infinity\n");
flint_printf("x = "); arb_printd(x, 30); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 30); flint_printf("\n\n");
flint_abort();
}
arb_pos_inf(x);
arb_sinc(y, x, prec);
if (!arb_is_zero(y))
{
flint_printf("FAIL: positive infinity\n");
flint_printf("x = "); arb_printd(x, 30); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 30); flint_printf("\n\n");
flint_abort();
}
arb_zero_pm_inf(x);
arb_sinc(y, x, prec);
if (!(arb_is_finite(y) &&
arb_contains_negative(y) &&
arb_contains_positive(y) &&
arb_contains_zero(y)))
{
flint_printf("FAIL: the whole extended real line\n");
flint_printf("x = "); arb_printd(x, 30); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 30); flint_printf("\n\n");
flint_abort();
}
arb_clear(x);
arb_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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