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[] = "$FreeBSD: src/lib/msun/src/s_tanh.c,v 1.7 2002/05/28 18:15:04 alfred 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
44static const double one=1.0, two=2.0, tiny = 1.0e-300;
45
46double
47tanh(double x)
48{
49	double t,z;
50	int32_t jx,ix;
51
52    /* High word of |x|. */
53	GET_HIGH_WORD(jx,x);
54	ix = jx&0x7fffffff;
55
56    /* x is INF or NaN */
57	if(ix>=0x7ff00000) {
58	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
59	    else       return one/x-one;    /* tanh(NaN) = NaN */
60	}
61
62    /* |x| < 22 */
63	if (ix < 0x40360000) {		/* |x|<22 */
64	    if (ix<0x3c800000) 		/* |x|<2**-55 */
65		return x*(one+x);    	/* tanh(small) = small */
66	    if (ix>=0x3ff00000) {	/* |x|>=1  */
67		t = expm1(two*fabs(x));
68		z = one - two/(t+two);
69	    } else {
70	        t = expm1(-two*fabs(x));
71	        z= -t/(t+two);
72	    }
73    /* |x| > 22, return +-1 */
74	} else {
75	    z = one - tiny;		/* raised inexact flag */
76	}
77	return (jx>=0)? z: -z;
78}
79