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
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
|
/* @(#)e_atanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/*
FUNCTION
<<atanh>>, <<atanhf>>---inverse hyperbolic tangent
INDEX
atanh
INDEX
atanhf
ANSI_SYNOPSIS
#include <math.h>
double atanh(double <[x]>);
float atanhf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double atanh(<[x]>)
double <[x]>;
float atanhf(<[x]>)
float <[x]>;
DESCRIPTION
<<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
<<atanhf>> is identical, other than taking and returning
<<float>> values.
RETURNS
<<atanh>> and <<atanhf>> return the calculated value.
If
@ifnottex
|<[x]>|
@end ifnottex
@tex
$|x|$
@end tex
is greater than 1, the global <<errno>> is set to <<EDOM>> and
the result is a NaN. A <<DOMAIN error>> is reported.
If
@ifnottex
|<[x]>|
@end ifnottex
@tex
$|x|$
@end tex
is 1, the global <<errno>> is set to <<EDOM>>; and the result is
infinity with the same sign as <<x>>. A <<SING error>> is reported.
You can modify the error handling for these routines using
<<matherr>>.
PORTABILITY
Neither <<atanh>> nor <<atanhf>> are ANSI C.
QUICKREF
atanh - pure
atanhf - pure
*/
/* 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 "fdlibm.h"
#ifndef _DOUBLE_IS_32BITS
#ifdef __STDC__
static const double one = 1.0, huge = 1e300;
#else
static double one = 1.0, huge = 1e300;
#endif
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
#ifdef __STDC__
double atanh(double x)
#else
double atanh(x)
double x;
#endif
{
double t;
__int32_t hx,ix;
__uint32_t lx;
EXTRACT_WORDS(hx,lx,x);
ix = hx&0x7fffffff;
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3ff00000)
return x/zero;
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
SET_HIGH_WORD(x,ix);
if(ix<0x3fe00000) { /* x < 0.5 */
t = x+x;
t = 0.5*log1p(t+t*x/(one-x));
} else
t = 0.5*log1p((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}
#endif /* defined(_DOUBLE_IS_32BITS) */
|