1/* Copyright (C) 2011-2020 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3 Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19
20/* __ieee754_atanh(x)
21 Method :
22 1.Reduced x to positive by atanh(-x) = -atanh(x)
23 2.For x>=0.5
24 1 2x x
25 atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
26 2 1 - x 1 - x
27
28 For x<0.5
29 atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
30
31 Special cases:
32 atanh(x) is NaN if |x| > 1 with signal;
33 atanh(NaN) is that NaN with no signal;
34 atanh(+-1) is +-INF with signal.
35
36 */
37
38#include <float.h>
39#include <inttypes.h>
40#include <math.h>
41#include <math-barriers.h>
42#include <math_private.h>
43#include <math-underflow.h>
44#include <libm-alias-finite.h>
45
46static const double huge = 1e300;
47
48double
49__ieee754_atanh (double x)
50{
51 double xa = fabs (x);
52 double t;
53 if (isless (xa, 0.5))
54 {
55 if (__glibc_unlikely (xa < 0x1.0p-28))
56 {
57 math_force_eval (huge + x);
58 math_check_force_underflow (x);
59 return x;
60 }
61
62 t = xa + xa;
63 t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
64 }
65 else if (__glibc_likely (isless (xa, 1.0)))
66 t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
67 else
68 {
69 if (isgreater (xa, 1.0))
70 return (x - x) / (x - x);
71
72 return x / 0.0;
73 }
74
75 return copysign (t, x);
76}
77libm_alias_finite (__ieee754_atanh, __atanh)
78