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/* Copyright (C) 2011-2021 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
/* __ieee754_atanh(x)
Method :
1.Reduced x to positive by atanh(-x) = -atanh(x)
2.For x>=0.5
1 2x x
atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
2 1 - x 1 - x
For x<0.5
atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
Special cases:
atanh(x) is NaN if |x| > 1 with signal;
atanh(NaN) is that NaN with no signal;
atanh(+-1) is +-INF with signal.
*/
#include <float.h>
#include <inttypes.h>
#include <math.h>
#include <math-barriers.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>
static const double huge = 1e300;
double
__ieee754_atanh (double x)
{
double xa = fabs (x);
double t;
if (isless (xa, 0.5))
{
if (__glibc_unlikely (xa < 0x1.0p-28))
{
math_force_eval (huge + x);
math_check_force_underflow (x);
return x;
}
t = xa + xa;
t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
}
else if (__glibc_likely (isless (xa, 1.0)))
t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
else
{
if (isgreater (xa, 1.0))
return (x - x) / (x - x);
return x / 0.0;
}
return copysign (t, x);
}
libm_alias_finite (__ieee754_atanh, __atanh)
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