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__FBSDID("$FreeBSD$");
15
16/* Tanh(x)
17 * Return the Hyperbolic Tangent of x
18 *
19 * Method :
20 *				       x    -x
21 *				      e  - e
22 *	0. tanh(x) is defined to be -----------
23 *				       x    -x
24 *				      e  + e
25 *	1. reduce x to non-negative by tanh(-x) = -tanh(x).
26 *	2.  0      <= x <  2**-28 : tanh(x) := x with inexact if x != 0
27 *					        -t
28 *	    2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
29 *					       t + 2
30 *						     2
31 *	    1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
32 *						   t + 2
33 *	    22     <= x <= INF    : tanh(x) := 1.
34 *
35 * Special cases:
36 *	tanh(NaN) is NaN;
37 *	only tanh(0)=0 is exact for finite argument.
38 */
39
40#include "math.h"
41#include "math_private.h"
42
43static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
44
45double
46tanh(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