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/*
Copyright (C) 2017 Fredrik Johansson
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 "arb.h"
void
arb_sinc_pi(arb_t res, const arb_t x, slong prec)
{
mag_t m;
arb_t t;
if (!arb_is_finite(x))
{
if (arf_is_nan(arb_midref(x)))
arb_indeterminate(res);
else if (arb_contains_zero(x))
arb_zero_pm_one(res);
else
arb_zero(res);
return;
}
if (arb_is_int(x))
{
if (arb_is_zero(x))
arb_one(res);
else
arb_zero(res);
return;
}
mag_init(m);
arb_init(t);
arb_get_mag_lower(m, x);
if (mag_cmp_2exp_si(m, -1) > 0)
{
arb_const_pi(t, prec + 4);
arb_mul(t, t, x, prec + 4);
arb_sin_pi(res, x, prec + 4);
arb_div(res, res, t, prec);
}
else
{
arb_const_pi(t, prec + 4);
arb_mul(t, t, x, prec + 4);
arb_sinc(res, t, prec);
}
mag_clear(m);
arb_clear(t);
}