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)
14static 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
47static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
48
49long 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}
88long_double_symbol (libm, __tanhl, tanhl);
89

source code of glibc/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c