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 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $");
16 #endif
17
18 /* Tanh(x)
19 * Return the Hyperbolic Tangent of x
20 *
21 * Method :
22 * x -x
23 * e - e
24 * 0. tanh(x) is defined to be -----------
25 * x -x
26 * e + e
27 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
28 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
29 * -t
30 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
31 * t + 2
32 * 2
33 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
34 * t + 2
35 * 22.0 < x <= INF : tanh(x) := 1.
36 *
37 * Special cases:
38 * tanh(NaN) is NaN;
39 * only tanh(0)=0 is exact for finite argument.
40 */
41
42 #include "math.h"
43 #include "math_private.h"
44
45 static const double one=1.0, two=2.0, tiny = 1.0e-300;
46
47 double
tanh(double x)48 tanh(double x)
49 {
50 double t,z;
51 int32_t jx,ix;
52
53 /* High word of |x|. */
54 GET_HIGH_WORD(jx,x);
55 ix = jx&0x7fffffff;
56
57 /* x is INF or NaN */
58 if(ix>=0x7ff00000) {
59 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
60 else return one/x-one; /* tanh(NaN) = NaN */
61 }
62
63 /* |x| < 22 */
64 if (ix < 0x40360000) { /* |x|<22 */
65 if (ix<0x3c800000) /* |x|<2**-55 */
66 return x*(one+x); /* tanh(small) = small */
67 if (ix>=0x3ff00000) { /* |x|>=1 */
68 t = expm1(two*fabs(x));
69 z = one - two/(t+two);
70 } else {
71 t = expm1(-two*fabs(x));
72 z= -t/(t+two);
73 }
74 /* |x| > 22, return +-1 */
75 } else {
76 z = one - tiny; /* raised inexact flag */
77 }
78 return (jx>=0)? z: -z;
79 }
80