1/* s_tanhl.c -- long double version of s_tanh.c.
2 */
3
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15#if defined(LIBM_SCCS) && !defined(lint)
16static char rcsid[] = "$NetBSD: $";
17#endif
18
19/* tanhl(x)
20 * Return the Hyperbolic Tangent of x
21 *
22 * Method :
23 * x -x
24 * e - e
25 * 0. tanhl(x) is defined to be -----------
26 * x -x
27 * e + e
28 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
29 * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
30 * -t
31 * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
32 * t + 2
33 * 2
34 * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
35 * t + 2
36 * 23.0 < x <= INF : tanhl(x) := 1.
37 *
38 * Special cases:
39 * tanhl(NaN) is NaN;
40 * only tanhl(0)=0 is exact for finite argument.
41 */
42
43#include <float.h>
44#include <math.h>
45#include <math_private.h>
46#include <math-underflow.h>
47#include <libm-alias-ldouble.h>
48
49static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
50
51long double __tanhl(long double x)
52{
53 long double t,z;
54 int32_t se;
55 uint32_t j0,j1,ix;
56
57 /* High word of |x|. */
58 GET_LDOUBLE_WORDS(se,j0,j1,x);
59 ix = se&0x7fff;
60
61 /* x is INF or NaN */
62 if(ix==0x7fff) {
63 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
64 if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
65 else return one/x+one; /* tanhl(+inf)=+1 */
66 }
67
68 /* |x| < 23 */
69 if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
70 if ((ix|j0|j1) == 0)
71 return x; /* x == +- 0 */
72 if (ix<0x3fc8) /* |x|<2**-55 */
73 {
74 math_check_force_underflow (x);
75 return x*(one+tiny); /* tanh(small) = small */
76 }
77 if (ix>=0x3fff) { /* |x|>=1 */
78 t = __expm1l(two*fabsl(x));
79 z = one - two/(t+two);
80 } else {
81 t = __expm1l(-two*fabsl(x));
82 z= -t/(t+two);
83 }
84 /* |x| > 23, return +-1 */
85 } else {
86 z = one - tiny; /* raised inexact flag */
87 }
88 return (se&0x8000)? -z: z;
89}
90libm_alias_ldouble (__tanh, tanh)
91