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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_coth(arb_t y, const arb_t x, slong prec)
{
arb_t t, u;
int sign = arf_sgn(arb_midref(x)) < 0;
arb_init(t);
arb_init(u);
arb_mul_2exp_si(t, x, 1);
if (!sign)
arb_neg(t, t);
if (arf_cmpabs_2exp_si(arb_midref(x), 1) > 0)
{
/* coth(x) = 1 + 2 exp(-2x) / (1 - exp(-2x)) */
arb_exp(t, t, prec + 4);
arb_sub_ui(u, t, 1, prec + 4);
arb_div(y, t, u, prec + 4);
arb_mul_2exp_si(y, y, 1);
arb_sub_ui(y, y, 1, prec);
}
else
{
/* coth(x) = (exp(2x) + 1) / (exp(2x) - 1) */
arb_expm1(t, t, prec + 4);
arb_add_ui(y, t, 2, prec + 4);
arb_div(y, y, t, prec);
}
if (!sign)
arb_neg(y, y);
arb_clear(t);
arb_clear(u);
}
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