1 | /* @(#)s_tanh.c 5.1 93/09/24 */ |
2 | /* |
3 | * ==================================================== |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | * |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
7 | * Permission to use, copy, modify, and distribute this |
8 | * software is freely granted, provided that this notice |
9 | * is preserved. |
10 | * ==================================================== |
11 | */ |
12 | |
13 | #if defined(LIBM_SCCS) && !defined(lint) |
14 | static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $" ; |
15 | #endif |
16 | |
17 | /* Tanh(x) |
18 | * Return the Hyperbolic Tangent of x |
19 | * |
20 | * Method : |
21 | * x -x |
22 | * e - e |
23 | * 0. tanh(x) is defined to be ----------- |
24 | * x -x |
25 | * e + e |
26 | * 1. reduce x to non-negative by tanh(-x) = -tanh(x). |
27 | * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) |
28 | * -t |
29 | * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
30 | * t + 2 |
31 | * 2 |
32 | * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
33 | * t + 2 |
34 | * 22.0 < x <= INF : tanh(x) := 1. |
35 | * |
36 | * Special cases: |
37 | * tanh(NaN) is NaN; |
38 | * only tanh(0)=0 is exact for finite argument. |
39 | */ |
40 | |
41 | #include <float.h> |
42 | #include <math.h> |
43 | #include <math_private.h> |
44 | #include <libm-alias-double.h> |
45 | |
46 | static const double one = 1.0, two = 2.0, tiny = 1.0e-300; |
47 | |
48 | double |
49 | __tanh (double x) |
50 | { |
51 | double t, z; |
52 | int32_t jx, ix, lx; |
53 | |
54 | /* High word of |x|. */ |
55 | EXTRACT_WORDS (jx, lx, x); |
56 | ix = jx & 0x7fffffff; |
57 | |
58 | /* x is INF or NaN */ |
59 | if (ix >= 0x7ff00000) |
60 | { |
61 | if (jx >= 0) |
62 | return one / x + one; /* tanh(+-inf)=+-1 */ |
63 | else |
64 | return one / x - one; /* tanh(NaN) = NaN */ |
65 | } |
66 | |
67 | /* |x| < 22 */ |
68 | if (ix < 0x40360000) /* |x|<22 */ |
69 | { |
70 | if ((ix | lx) == 0) |
71 | return x; /* x == +-0 */ |
72 | if (ix < 0x3c800000) /* |x|<2**-55 */ |
73 | { |
74 | math_check_force_underflow (x); |
75 | return x * (one + x); /* tanh(small) = small */ |
76 | } |
77 | if (ix >= 0x3ff00000) /* |x|>=1 */ |
78 | { |
79 | t = __expm1 (two * fabs (x)); |
80 | z = one - two / (t + two); |
81 | } |
82 | else |
83 | { |
84 | t = __expm1 (-two * fabs (x)); |
85 | z = -t / (t + two); |
86 | } |
87 | /* |x| > 22, return +-1 */ |
88 | } |
89 | else |
90 | { |
91 | z = one - tiny; /* raised inexact flag */ |
92 | } |
93 | return (jx >= 0) ? z : -z; |
94 | } |
95 | libm_alias_double (__tanh, tanh) |
96 | |