1/* Copyright (C) 2011-2023 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
8
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library; if not, see
16 <https://www.gnu.org/licenses/>. */
17
18
19/* __ieee754_atanh(x)
20 Method :
21 1.Reduced x to positive by atanh(-x) = -atanh(x)
22 2.For x>=0.5
23 1 2x x
24 atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
25 2 1 - x 1 - x
26
27 For x<0.5
28 atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
29
30 Special cases:
31 atanh(x) is NaN if |x| > 1 with signal;
32 atanh(NaN) is that NaN with no signal;
33 atanh(+-1) is +-INF with signal.
34
35 */
36
37#include <float.h>
38#include <inttypes.h>
39#include <math.h>
40#include <math-barriers.h>
41#include <math_private.h>
42#include <math-underflow.h>
43#include <libm-alias-finite.h>
44
45static const float huge = 1e30;
46
47float
48__ieee754_atanhf (float x)
49{
50 float xa = fabsf (x);
51 float t;
52 if (isless (xa, 0.5f))
53 {
54 if (__glibc_unlikely (xa < 0x1.0p-28f))
55 {
56 math_force_eval (huge + x);
57 math_check_force_underflow (x);
58 return x;
59 }
60
61 t = xa + xa;
62 t = 0.5f * __log1pf (t + t * xa / (1.0f - xa));
63 }
64 else if (__glibc_likely (isless (xa, 1.0f)))
65 t = 0.5f * __log1pf ((xa + xa) / (1.0f - xa));
66 else
67 {
68 if (isgreater (xa, 1.0f))
69 return (x - x) / (x - x);
70
71 return x / 0.0f;
72 }
73
74 return copysignf (t, x);
75}
76libm_alias_finite (__ieee754_atanhf, __atanhf)
77