xref: /freebsd/lib/msun/src/s_tanh.c (revision 6580f5c38dd5b01aeeaed16b370f1a12423437f0)
1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /* Tanh(x)
13  * Return the Hyperbolic Tangent of x
14  *
15  * Method :
16  *				       x    -x
17  *				      e  - e
18  *	0. tanh(x) is defined to be -----------
19  *				       x    -x
20  *				      e  + e
21  *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
22  *	2.  0      <= x <  2**-28 : tanh(x) := x with inexact if x != 0
23  *					        -t
24  *	    2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
25  *					       t + 2
26  *						     2
27  *	    1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
28  *						   t + 2
29  *	    22     <= x <= INF    : tanh(x) := 1.
30  *
31  * Special cases:
32  *	tanh(NaN) is NaN;
33  *	only tanh(0)=0 is exact for finite argument.
34  */
35 
36 #include <float.h>
37 
38 #include "math.h"
39 #include "math_private.h"
40 
41 static const volatile double tiny = 1.0e-300;
42 static const double one = 1.0, two = 2.0, huge = 1.0e300;
43 
44 double
45 tanh(double x)
46 {
47 	double t,z;
48 	int32_t jx,ix;
49 
50 	GET_HIGH_WORD(jx,x);
51 	ix = jx&0x7fffffff;
52 
53     /* x is INF or NaN */
54 	if(ix>=0x7ff00000) {
55 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
56 	    else       return one/x-one;    /* tanh(NaN) = NaN */
57 	}
58 
59     /* |x| < 22 */
60 	if (ix < 0x40360000) {		/* |x|<22 */
61 	    if (ix<0x3e300000) {	/* |x|<2**-28 */
62 		if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
63 	    }
64 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
65 		t = expm1(two*fabs(x));
66 		z = one - two/(t+two);
67 	    } else {
68 	        t = expm1(-two*fabs(x));
69 	        z= -t/(t+two);
70 	    }
71     /* |x| >= 22, return +-1 */
72 	} else {
73 	    z = one - tiny;		/* raise inexact flag */
74 	}
75 	return (jx>=0)? z: -z;
76 }
77 
78 #if (LDBL_MANT_DIG == 53)
79 __weak_reference(tanh, tanhl);
80 #endif
81