1 
2 /* @(#)s_tanh.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 /* Tanh(x)
15  * Return the Hyperbolic Tangent of x
16  *
17  * Method :
18  *				       x    -x
19  *				      e  - e
20  *	0. ieee_tanh(x) is defined to be -----------
21  *				       x    -x
22  *				      e  + e
23  *	1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x).
24  *	2.  0      <= x <= 2**-55 : ieee_tanh(x) := x*(one+x)
25  *					        -t
26  *	    2**-55 <  x <=  1     : ieee_tanh(x) := -----; t = ieee_expm1(-2x)
27  *					       t + 2
28  *						     2
29  *	    1      <= x <=  22.0  : ieee_tanh(x) := 1-  ----- ; t=ieee_expm1(2x)
30  *						   t + 2
31  *	    22.0   <  x <= INF    : ieee_tanh(x) := 1.
32  *
33  * Special cases:
34  *	tanh(NaN) is NaN;
35  *	only ieee_tanh(0)=0 is exact for finite argument.
36  */
37 
38 #include "fdlibm.h"
39 
40 #ifdef __STDC__
41 static const double one=1.0, two=2.0, tiny = 1.0e-300;
42 #else
43 static double one=1.0, two=2.0, tiny = 1.0e-300;
44 #endif
45 
46 #ifdef __STDC__
ieee_tanh(double x)47 	double ieee_tanh(double x)
48 #else
49 	double ieee_tanh(x)
50 	double x;
51 #endif
52 {
53 	double t,z;
54 	int jx,ix;
55 
56     /* High word of |x|. */
57 	jx = __HI(x);
58 	ix = jx&0x7fffffff;
59 
60     /* x is INF or NaN */
61 	if(ix>=0x7ff00000) {
62 	    if (jx>=0) return one/x+one;    /* ieee_tanh(+-inf)=+-1 */
63 	    else       return one/x-one;    /* ieee_tanh(NaN) = NaN */
64 	}
65 
66     /* |x| < 22 */
67 	if (ix < 0x40360000) {		/* |x|<22 */
68 	    if (ix<0x3c800000) 		/* |x|<2**-55 */
69 		return x*(one+x);    	/* ieee_tanh(small) = small */
70 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
71 		t = ieee_expm1(two*ieee_fabs(x));
72 		z = one - two/(t+two);
73 	    } else {
74 	        t = ieee_expm1(-two*ieee_fabs(x));
75 	        z= -t/(t+two);
76 	    }
77     /* |x| > 22, return +-1 */
78 	} else {
79 	    z = one - tiny;		/* raised inexact flag */
80 	}
81 	return (jx>=0)? z: -z;
82 }
83