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
|
/* s_tanhl.c -- long double version of s_tanh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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: $";
#endif
/* tanhl(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanhl(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
* 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
* -t
* 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
* t + 2
* 2
* 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
* t + 2
* 23.0 < x <= INF : tanhl(x) := 1.
*
* Special cases:
* tanhl(NaN) is NaN;
* only tanhl(0)=0 is exact for finite argument.
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
long double __tanhl(long double x)
{
long double t,z;
int32_t se;
u_int32_t j0,j1,ix;
/* High word of |x|. */
GET_LDOUBLE_WORDS(se,j0,j1,x);
ix = se&0x7fff;
/* x is INF or NaN */
if(ix==0x7fff) {
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
else return one/x+one; /* tanhl(+inf)=+1 */
}
/* |x| < 23 */
if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
if ((ix|j0|j1) == 0)
return x; /* x == +- 0 */
if (ix<0x3fc8) /* |x|<2**-55 */
{
if (fabsl (x) < LDBL_MIN)
{
long double force_underflow = x * x;
math_force_eval (force_underflow);
}
return x*(one+tiny); /* tanh(small) = small */
}
if (ix>=0x3fff) { /* |x|>=1 */
t = __expm1l(two*fabsl(x));
z = one - two/(t+two);
} else {
t = __expm1l(-two*fabsl(x));
z= -t/(t+two);
}
/* |x| > 23, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (se&0x8000)? -z: z;
}
weak_alias (__tanhl, tanhl)
|
