xref: /netbsd-src/lib/libm/src/s_tanh.c (revision 1ca5c1b28139779176bd5c13ad7c5f25c0bcd5f8)
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 
45 #ifdef __STDC__
46 static const double one=1.0, two=2.0, tiny = 1.0e-300;
47 #else
48 static double one=1.0, two=2.0, tiny = 1.0e-300;
49 #endif
50 
51 #ifdef __STDC__
52 	double tanh(double x)
53 #else
54 	double tanh(x)
55 	double x;
56 #endif
57 {
58 	double t,z;
59 	int32_t jx,ix;
60 
61     /* High word of |x|. */
62 	GET_HIGH_WORD(jx,x);
63 	ix = jx&0x7fffffff;
64 
65     /* x is INF or NaN */
66 	if(ix>=0x7ff00000) {
67 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
68 	    else       return one/x-one;    /* tanh(NaN) = NaN */
69 	}
70 
71     /* |x| < 22 */
72 	if (ix < 0x40360000) {		/* |x|<22 */
73 	    if (ix<0x3c800000) 		/* |x|<2**-55 */
74 		return x*(one+x);    	/* tanh(small) = small */
75 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
76 		t = expm1(two*fabs(x));
77 		z = one - two/(t+two);
78 	    } else {
79 	        t = expm1(-two*fabs(x));
80 	        z= -t/(t+two);
81 	    }
82     /* |x| > 22, return +-1 */
83 	} else {
84 	    z = one - tiny;		/* raised inexact flag */
85 	}
86 	return (jx>=0)? z: -z;
87 }
88