s_tanh.c revision 160122 
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: head/lib/msun/src/s_tanh.c 160122 2006-07-05 22:59:33Z bde $";
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**-28 : tanh(x) := x with inexact if x != 0
28 *					        -t
29 *	    2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
30 *					       t + 2
31 *						     2
32 *	    1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
33 *						   t + 2
34 *	    22     <= 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, huge = 1.0e300;
45
46double
47tanh(double x)
48{
49	double t,z;
50	int32_t jx,ix;
51
52	GET_HIGH_WORD(jx,x);
53	ix = jx&0x7fffffff;
54
55    /* x is INF or NaN */
56	if(ix>=0x7ff00000) {
57	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
58	    else       return one/x-one;    /* tanh(NaN) = NaN */
59	}
60
61    /* |x| < 22 */
62	if (ix < 0x40360000) {		/* |x|<22 */
63	    if (ix<0x3e300000) {	/* |x|<2**-28 */
64		if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
65	    }
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;		/* raise inexact flag */
76	}
77	return (jx>=0)? z: -z;
78}
79