xref: /freebsd/lib/msun/src/s_tanh.c (revision 70fe064ad7cab6c0444b91622f60ec6a462f308a)
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
14 static char rcsid[] = "$FreeBSD$";
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__
45 static const double one=1.0, two=2.0, tiny = 1.0e-300;
46 #else
47 static 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