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 -- __float128 version of s_tanh.c.
* Conversion to __float128 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.
* ====================================================
*/
/* Changes for 128-bit __float128 contributed by
Stephen L. Moshier <moshier@na-net.ornl.gov> */
/* 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**-57 : tanhl(x) := x*(one+x)
* -t
* 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
* t + 2
* 2
* 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
* t + 2
* 40.0 < x <= INF : tanhl(x) := 1.
*
* Special cases:
* tanhl(NaN) is NaN;
* only tanhl(0)=0 is exact for finite argument.
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q;
__float128
tanhq (__float128 x)
{
__float128 t, z;
uint32_t jx, ix;
ieee854_float128 u;
/* Words of |x|. */
u.value = x;
jx = u.words32.w0;
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7fff0000)
{
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
if (jx & 0x80000000)
return one / x - one; /* tanhl(-inf)= -1; */
else
return one / x + one; /* tanhl(+inf)=+1 */
}
/* |x| < 40 */
if (ix < 0x40044000)
{
if (u.value == 0)
return x; /* x == +- 0 */
if (ix < 0x3fc60000) /* |x| < 2^-57 */
return x * (one + tiny); /* tanh(small) = small */
u.words32.w0 = ix; /* Absolute value of x. */
if (ix >= 0x3fff0000)
{ /* |x| >= 1 */
t = expm1q (two * u.value);
z = one - two / (t + two);
}
else
{
t = expm1q (-two * u.value);
z = -t / (t + two);
}
/* |x| > 40, return +-1 */
}
else
{
z = one - tiny; /* raised inexact flag */
}
return (jx & 0x80000000) ? -z : z;
}
|
