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87969c8c | 1 | /* s_tanhl.c -- __float128 version of s_tanh.c. |
2 | * Conversion to __float128 by Ulrich Drepper, | |
3 | * Cygnus Support, drepper@cygnus.com. | |
4 | */ | |
5 | ||
6 | /* | |
7 | * ==================================================== | |
8 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
9 | * | |
10 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
11 | * Permission to use, copy, modify, and distribute this | |
12 | * software is freely granted, provided that this notice | |
13 | * is preserved. | |
14 | * ==================================================== | |
15 | */ | |
16 | ||
17 | /* Changes for 128-bit __float128 contributed by | |
18 | Stephen L. Moshier <moshier@na-net.ornl.gov> */ | |
19 | ||
20 | /* tanhl(x) | |
21 | * Return the Hyperbolic Tangent of x | |
22 | * | |
23 | * Method : | |
24 | * x -x | |
25 | * e - e | |
26 | * 0. tanhl(x) is defined to be ----------- | |
27 | * x -x | |
28 | * e + e | |
29 | * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). | |
30 | * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) | |
31 | * -t | |
32 | * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) | |
33 | * t + 2 | |
34 | * 2 | |
35 | * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) | |
36 | * t + 2 | |
37 | * 40.0 < x <= INF : tanhl(x) := 1. | |
38 | * | |
39 | * Special cases: | |
40 | * tanhl(NaN) is NaN; | |
41 | * only tanhl(0)=0 is exact for finite argument. | |
42 | */ | |
43 | ||
44 | #include "quadmath-imp.h" | |
45 | ||
46 | static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q; | |
47 | ||
48 | __float128 | |
49 | tanhq (__float128 x) | |
50 | { | |
51 | __float128 t, z; | |
52 | uint32_t jx, ix; | |
53 | ieee854_float128 u; | |
54 | ||
55 | /* Words of |x|. */ | |
56 | u.value = x; | |
57 | jx = u.words32.w0; | |
58 | ix = jx & 0x7fffffff; | |
59 | /* x is INF or NaN */ | |
60 | if (ix >= 0x7fff0000) | |
61 | { | |
62 | /* for NaN it's not important which branch: tanhl(NaN) = NaN */ | |
63 | if (jx & 0x80000000) | |
64 | return one / x - one; /* tanhl(-inf)= -1; */ | |
65 | else | |
66 | return one / x + one; /* tanhl(+inf)=+1 */ | |
67 | } | |
68 | ||
69 | /* |x| < 40 */ | |
70 | if (ix < 0x40044000) | |
71 | { | |
72 | if (u.value == 0) | |
73 | return x; /* x == +- 0 */ | |
74 | if (ix < 0x3fc60000) /* |x| < 2^-57 */ | |
75 | return x * (one + tiny); /* tanh(small) = small */ | |
76 | u.words32.w0 = ix; /* Absolute value of x. */ | |
77 | if (ix >= 0x3fff0000) | |
78 | { /* |x| >= 1 */ | |
79 | t = expm1q (two * u.value); | |
80 | z = one - two / (t + two); | |
81 | } | |
82 | else | |
83 | { | |
84 | t = expm1q (-two * u.value); | |
85 | z = -t / (t + two); | |
86 | } | |
87 | /* |x| > 40, return +-1 */ | |
88 | } | |
89 | else | |
90 | { | |
91 | z = one - tiny; /* raised inexact flag */ | |
92 | } | |
93 | return (jx & 0x80000000) ? -z : z; | |
94 | } |