xref: /freebsd/lib/msun/src/s_tanh.c (revision f5463265955b829775bbb32e1fd0bc11dafc36ce)
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 #include <sys/cdefs.h>
13 /* Tanh(x)
14  * Return the Hyperbolic Tangent of x
15  *
16  * Method :
17  *				       x    -x
18  *				      e  - e
19  *	0. tanh(x) is defined to be -----------
20  *				       x    -x
21  *				      e  + e
22  *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
23  *	2.  0      <= x <  2**-28 : tanh(x) := x with inexact if x != 0
24  *					        -t
25  *	    2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
26  *					       t + 2
27  *						     2
28  *	    1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
29  *						   t + 2
30  *	    22     <= x <= INF    : tanh(x) := 1.
31  *
32  * Special cases:
33  *	tanh(NaN) is NaN;
34  *	only tanh(0)=0 is exact for finite argument.
35  */
36 
37 #include <float.h>
38 
39 #include "math.h"
40 #include "math_private.h"
41 
42 static const volatile double tiny = 1.0e-300;
43 static const double one = 1.0, two = 2.0, huge = 1.0e300;
44 
45 double
46 tanh(double x)
47 {
48 	double t,z;
49 	int32_t jx,ix;
50 
51 	GET_HIGH_WORD(jx,x);
52 	ix = jx&0x7fffffff;
53 
54     /* x is INF or NaN */
55 	if(ix>=0x7ff00000) {
56 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
57 	    else       return one/x-one;    /* tanh(NaN) = NaN */
58 	}
59 
60     /* |x| < 22 */
61 	if (ix < 0x40360000) {		/* |x|<22 */
62 	    if (ix<0x3e300000) {	/* |x|<2**-28 */
63 		if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
64 	    }
65 	    if (ix>=0x3ff00000) {	/* |x|>=1  */
66 		t = expm1(two*fabs(x));
67 		z = one - two/(t+two);
68 	    } else {
69 	        t = expm1(-two*fabs(x));
70 	        z= -t/(t+two);
71 	    }
72     /* |x| >= 22, return +-1 */
73 	} else {
74 	    z = one - tiny;		/* raise inexact flag */
75 	}
76 	return (jx>=0)? z: -z;
77 }
78 
79 #if (LDBL_MANT_DIG == 53)
80 __weak_reference(tanh, tanhl);
81 #endif
82