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 1.9 1999/07/02 15:37:43 simonb 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
45static const double one=1.0, two=2.0, tiny = 1.0e-300;
46
47double
48tanh(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