1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
|
/* Copyright (C) 2011, 2012 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
<http://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 <inttypes.h>
#include <math.h>
#include <math_private.h>
static const double huge = 1e300;
double
__ieee754_atanh (double x)
{
double xa = fabs (x);
double t;
if (isless (xa, 0.5))
{
if (__builtin_expect (xa < 0x1.0p-28, 0))
{
math_force_eval (huge + x);
return x;
}
t = xa + xa;
t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
}
else if (__builtin_expect (isless (xa, 1.0), 1))
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);
}
strong_alias (__ieee754_atanh, __atanh_finite)
|
