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 /* tanhl(x)
14  * Return the Hyperbolic Tangent of x
15  *
16  * Method :
17  *				        x    -x
18  *				       e  - e
19  *	0. tanhl(x) is defined to be -----------
20  *				        x    -x
21  *				       e  + e
22  *	1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
23  *	2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
24  *					         -t
25  *	    2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
26  *					        t + 2
27  *						      2
28  *	    1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
29  *						    t + 2
30  *	    23.0   <  x <= INF    : tanhl(x) := 1.
31  *
32  * Special cases:
33  *	tanhl(NaN) is NaN;
34  *	only tanhl(0)=0 is exact for finite argument.
35  */
36 
37 #include <math.h>
38 
39 #include "math_private.h"
40 
41 static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
42 
43 long double
44 tanhl(long double x)
45 {
46 	long double t,z;
47 	int32_t se;
48 	u_int32_t jj0,jj1,ix;
49 
50     /* High word of |x|. */
51 	GET_LDOUBLE_WORDS(se,jj0,jj1,x);
52 	ix = se&0x7fff;
53 
54     /* x is INF or NaN */
55 	if(ix==0x7fff) {
56 	    /* for NaN it's not important which branch: tanhl(NaN) = NaN */
57 	    if (se&0x8000) return one/x-one;	/* tanhl(-inf)= -1; */
58 	    else	   return one/x+one;	/* tanhl(+inf)=+1 */
59 	}
60 
61     /* |x| < 23 */
62 	if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */
63 	    if ((ix|jj0|jj1) == 0)
64 		return x;		/* x == +- 0 */
65 	    if (ix<0x3fc8)		/* |x|<2**-55 */
66 		return x*(one+tiny);	/* tanh(small) = small */
67 	    if (ix>=0x3fff) {	/* |x|>=1  */
68 		t = expm1l(two*fabsl(x));
69 		z = one - two/(t+two);
70 	    } else {
71 		t = expm1l(-two*fabsl(x));
72 		z= -t/(t+two);
73 	    }
74     /* |x| > 23, return +-1 */
75 	} else {
76 	    z = one - tiny;		/* raised inexact flag */
77 	}
78 	return (se&0x8000)? -z: z;
79 }
80