2018-01-01 00:32:25 +00:00
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/* Copyright (C) 2011-2018 Free Software Foundation, Inc.
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2011-10-12 15:27:51 +00:00
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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2012-02-09 23:18:22 +00:00
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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1996-03-05 21:41:30 +00:00
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/* __ieee754_atanh(x)
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2011-10-12 15:27:51 +00:00
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Method :
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1.Reduced x to positive by atanh(-x) = -atanh(x)
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2.For x>=0.5
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1 2x x
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atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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2 1 - x 1 - x
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For x<0.5
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atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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Special cases:
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atanh(x) is NaN if |x| > 1 with signal;
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atanh(NaN) is that NaN with no signal;
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atanh(+-1) is +-INF with signal.
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1996-03-05 21:41:30 +00:00
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*/
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2015-05-15 22:07:57 +00:00
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#include <float.h>
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2011-10-12 15:27:51 +00:00
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#include <inttypes.h>
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2012-03-09 19:29:16 +00:00
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#include <math.h>
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#include <math_private.h>
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1996-03-05 21:41:30 +00:00
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2011-10-12 15:27:51 +00:00
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static const double huge = 1e300;
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1996-03-05 21:41:30 +00:00
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2011-10-12 15:27:51 +00:00
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double
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__ieee754_atanh (double x)
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1996-03-05 21:41:30 +00:00
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{
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2011-10-12 15:27:51 +00:00
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double xa = fabs (x);
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double t;
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2012-02-19 10:20:18 +00:00
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if (isless (xa, 0.5))
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2011-10-12 15:27:51 +00:00
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{
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2014-02-10 13:45:42 +00:00
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if (__glibc_unlikely (xa < 0x1.0p-28))
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2011-10-25 14:52:45 +00:00
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{
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math_force_eval (huge + x);
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2015-09-23 22:42:30 +00:00
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math_check_force_underflow (x);
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2011-10-25 14:52:45 +00:00
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return x;
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}
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2011-10-12 15:27:51 +00:00
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t = xa + xa;
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t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
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}
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2014-02-10 13:45:42 +00:00
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else if (__glibc_likely (isless (xa, 1.0)))
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2011-10-12 15:27:51 +00:00
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t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
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else
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{
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2012-02-19 10:20:18 +00:00
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if (isgreater (xa, 1.0))
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2011-10-12 15:27:51 +00:00
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return (x - x) / (x - x);
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return x / 0.0;
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}
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return __copysign (t, x);
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1996-03-05 21:41:30 +00:00
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}
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2011-10-12 15:27:51 +00:00
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strong_alias (__ieee754_atanh, __atanh_finite)
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