s_tanh.c revision 8870 
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#ifndef lint
14static char rcsid[] = "$Id: s_tanh.c,v 1.1.1.1 1994/08/19 09:39:53 jkh 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**-55 : tanh(x) := x*(one+x)
28 *					        -t
29 *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
30 *					       t + 2
31 *						     2
32 *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
33 *						   t + 2
34 *	    22.0   <  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 "math.h"
42#include "math_private.h"
43
44#ifdef __STDC__
45static const double one=1.0, two=2.0, tiny = 1.0e-300;
46#else
47static double one=1.0, two=2.0, tiny = 1.0e-300;
48#endif
49
50#ifdef __STDC__
51	double tanh(double x)
52#else
53	double tanh(x)
54	double x;
55#endif
56{
57	double t,z;
58	int32_t jx,ix;
59
60    /* High word of |x|. */
61	GET_HIGH_WORD(jx,x);
62	ix = jx&0x7fffffff;
63
64    /* x is INF or NaN */
65	if(ix>=0x7ff00000) {
66	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
67	    else       return one/x-one;    /* tanh(NaN) = NaN */
68	}
69
70    /* |x| < 22 */
71	if (ix < 0x40360000) {		/* |x|<22 */
72	    if (ix<0x3c800000) 		/* |x|<2**-55 */
73		return x*(one+x);    	/* tanh(small) = small */
74	    if (ix>=0x3ff00000) {	/* |x|>=1  */
75		t = expm1(two*fabs(x));
76		z = one - two/(t+two);
77	    } else {
78	        t = expm1(-two*fabs(x));
79	        z= -t/(t+two);
80	    }
81    /* |x| > 22, return +-1 */
82	} else {
83	    z = one - tiny;		/* raised inexact flag */
84	}
85	return (jx>=0)? z: -z;
86}
87