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
|
/* @(#)s_tanh.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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
#endif
/* Tanh(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanh(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
* -t
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
* t + 2
* 2
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
* t + 2
* 22.0 < x <= INF : tanh(x) := 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
static const double one = 1.0, two = 2.0, tiny = 1.0e-300;
double
__tanh (double x)
{
double t, z;
int32_t jx, ix, lx;
/* High word of |x|. */
EXTRACT_WORDS (jx, lx, x);
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7ff00000)
{
if (jx >= 0)
return one / x + one; /* tanh(+-inf)=+-1 */
else
return one / x - one; /* tanh(NaN) = NaN */
}
/* |x| < 22 */
if (ix < 0x40360000) /* |x|<22 */
{
if ((ix | lx) == 0)
return x; /* x == +-0 */
if (ix < 0x3c800000) /* |x|<2**-55 */
{
math_check_force_underflow (x);
return x * (one + x); /* tanh(small) = small */
}
if (ix >= 0x3ff00000) /* |x|>=1 */
{
t = __expm1 (two * fabs (x));
z = one - two / (t + two);
}
else
{
t = __expm1 (-two * fabs (x));
z = -t / (t + two);
}
/* |x| > 22, return +-1 */
}
else
{
z = one - tiny; /* raised inexact flag */
}
return (jx >= 0) ? z : -z;
}
weak_alias (__tanh, tanh)
#ifdef NO_LONG_DOUBLE
strong_alias (__tanh, __tanhl)
weak_alias (__tanh, tanhl)
#endif
|
