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
41static const volatile double tiny = 1.0e-300;
42static const double one = 1.0, two = 2.0, huge = 1.0e300;
43
44double
45tanh(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