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)
18static 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 <math-underflow.h>
49#include <libm-alias-ldouble.h>
50
51static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
52
53long double __tanhl(long double x)
54{
55 long double t,z;
56 int32_t se;
57 uint32_t j0,j1,ix;
58
59 /* High word of |x|. */
60 GET_LDOUBLE_WORDS(se,j0,j1,x);
61 ix = se&0x7fff;
62
63 /* x is INF or NaN */
64 if(ix==0x7fff) {
65 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
66 if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
67 else return one/x+one; /* tanhl(+inf)=+1 */
68 }
69
70 /* |x| < 23 */
71 if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
72 if ((ix|j0|j1) == 0)
73 return x; /* x == +- 0 */
74 if (ix<0x3fc8) /* |x|<2**-55 */
75 {
76 math_check_force_underflow (x);
77 return x*(one+tiny); /* tanh(small) = small */
78 }
79 if (ix>=0x3fff) { /* |x|>=1 */
80 t = __expm1l(two*fabsl(x));
81 z = one - two/(t+two);
82 } else {
83 t = __expm1l(-two*fabsl(x));
84 z= -t/(t+two);
85 }
86 /* |x| > 23, return +-1 */
87 } else {
88 z = one - tiny; /* raised inexact flag */
89 }
90 return (se&0x8000)? -z: z;
91}
92libm_alias_ldouble (__tanh, tanh)
93