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/*
Copyright (C) 2013 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_sech(arb_t res, const arb_t x, slong prec)
{
if (arf_cmpabs_2exp_si(arb_midref(x), 0) > 0)
{
arb_t t;
arb_init(t);
if (arf_sgn(arb_midref(x)) > 0)
{
arb_neg(t, x);
arb_exp(t, t, prec + 4);
}
else
{
arb_exp(t, x, prec + 4);
}
arb_mul(res, t, t, prec + 4);
arb_add_ui(res, res, 1, prec + 4);
arb_div(res, t, res, prec);
arb_mul_2exp_si(res, res, 1);
arb_clear(t);
}
else
{
arb_cosh(res, x, prec + 4);
arb_inv(res, res, prec);
}
}