xref: /freebsd/lib/msun/src/s_tanh.c (revision 2008043f386721d58158e37e0d7e50df8095942d)
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 /* Tanh(x)
15  * Return the Hyperbolic Tangent of x
16  *
17  * Method :
18  *				       x    -x
19  *				      e  - e
20  *	0. tanh(x) is defined to be -----------
21  *				       x    -x
22  *				      e  + e
23  *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
24  *	2.  0      <= x <  2**-28 : tanh(x) := x with inexact if x != 0
25  *					        -t
26  *	    2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
27  *					       t + 2
28  *						     2
29  *	    1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
30  *						   t + 2
31  *	    22     <= x <= INF    : tanh(x) := 1.
32  *
33  * Special cases:
34  *	tanh(NaN) is NaN;
35  *	only tanh(0)=0 is exact for finite argument.
36  */
37 
38 #include <float.h>
39 
40 #include "math.h"
41 #include "math_private.h"
42 
43 static const volatile double tiny = 1.0e-300;
44 static const double one = 1.0, two = 2.0, huge = 1.0e300;
45 
46 double
47 tanh(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 
80 #if (LDBL_MANT_DIG == 53)
81 __weak_reference(tanh, tanhl);
82 #endif
83