1 | /* s_tanhl.c -- long double version of s_tanh.c. |
2 | * Conversion to long double 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 | #if defined(LIBM_SCCS) && !defined(lint) |
18 | static char rcsid[] = "$NetBSD: $" ; |
19 | #endif |
20 | |
21 | /* tanhl(x) |
22 | * Return the Hyperbolic Tangent of x |
23 | * |
24 | * Method : |
25 | * x -x |
26 | * e - e |
27 | * 0. tanhl(x) is defined to be ----------- |
28 | * x -x |
29 | * e + e |
30 | * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). |
31 | * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) |
32 | * -t |
33 | * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) |
34 | * t + 2 |
35 | * 2 |
36 | * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) |
37 | * t + 2 |
38 | * 23.0 < x <= INF : tanhl(x) := 1. |
39 | * |
40 | * Special cases: |
41 | * tanhl(NaN) is NaN; |
42 | * only tanhl(0)=0 is exact for finite argument. |
43 | */ |
44 | |
45 | #include <float.h> |
46 | #include <math.h> |
47 | #include <math_private.h> |
48 | #include <libm-alias-ldouble.h> |
49 | |
50 | static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; |
51 | |
52 | long double __tanhl(long double x) |
53 | { |
54 | long double t,z; |
55 | int32_t se; |
56 | uint32_t j0,j1,ix; |
57 | |
58 | /* High word of |x|. */ |
59 | GET_LDOUBLE_WORDS(se,j0,j1,x); |
60 | ix = se&0x7fff; |
61 | |
62 | /* x is INF or NaN */ |
63 | if(ix==0x7fff) { |
64 | /* for NaN it's not important which branch: tanhl(NaN) = NaN */ |
65 | if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ |
66 | else return one/x+one; /* tanhl(+inf)=+1 */ |
67 | } |
68 | |
69 | /* |x| < 23 */ |
70 | if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */ |
71 | if ((ix|j0|j1) == 0) |
72 | return x; /* x == +- 0 */ |
73 | if (ix<0x3fc8) /* |x|<2**-55 */ |
74 | { |
75 | math_check_force_underflow (x); |
76 | return x*(one+tiny); /* tanh(small) = small */ |
77 | } |
78 | if (ix>=0x3fff) { /* |x|>=1 */ |
79 | t = __expm1l(two*fabsl(x)); |
80 | z = one - two/(t+two); |
81 | } else { |
82 | t = __expm1l(-two*fabsl(x)); |
83 | z= -t/(t+two); |
84 | } |
85 | /* |x| > 23, return +-1 */ |
86 | } else { |
87 | z = one - tiny; /* raised inexact flag */ |
88 | } |
89 | return (se&0x8000)? -z: z; |
90 | } |
91 | libm_alias_ldouble (__tanh, tanh) |
92 | |