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**-57 : tanh(x) := x*(one+x) |
28 | * -t |
29 | * 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
30 | * t + 2 |
31 | * 2 |
32 | * 1 <= x <= 40.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
33 | * t + 2 |
34 | * 40.0 < 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 <math-underflow.h> |
45 | #include <math_ldbl_opt.h> |
46 | |
47 | static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L; |
48 | |
49 | long double __tanhl(long double x) |
50 | { |
51 | long double t,z; |
52 | int64_t jx,ix; |
53 | double xhi; |
54 | |
55 | /* High word of |x|. */ |
56 | xhi = ldbl_high (x); |
57 | EXTRACT_WORDS64 (jx, xhi); |
58 | ix = jx&0x7fffffffffffffffLL; |
59 | |
60 | /* x is INF or NaN */ |
61 | if(ix>=0x7ff0000000000000LL) { |
62 | if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
63 | else return one/x-one; /* tanh(NaN) = NaN */ |
64 | } |
65 | |
66 | /* |x| < 40 */ |
67 | if (ix < 0x4044000000000000LL) { /* |x|<40 */ |
68 | if (ix == 0) |
69 | return x; /* x == +-0 */ |
70 | if (ix<0x3c60000000000000LL) /* |x|<2**-57 */ |
71 | { |
72 | math_check_force_underflow (x); |
73 | return x; /* tanh(small) = small */ |
74 | } |
75 | if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */ |
76 | t = __expm1l(x: two*fabsl(x: x)); |
77 | z = one - two/(t+two); |
78 | } else { |
79 | t = __expm1l(x: -two*fabsl(x: x)); |
80 | z= -t/(t+two); |
81 | } |
82 | /* |x| > 40, return +-1 */ |
83 | } else { |
84 | z = one - tiny; /* raised inexact flag */ |
85 | } |
86 | return (jx>=0)? z: -z; |
87 | } |
88 | long_double_symbol (libm, __tanhl, tanhl); |
89 | |