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**-55 : tanh(x) := x*(one+x)
23 * -t
24 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
25 * t + 2
26 * 2
27 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
28 * t + 2
29 * 22.0 < 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 "math.h"
37 #include "math_private.h"
38
39 static const double one=1.0, two=2.0, tiny = 1.0e-300;
40
tanh(double x)41 double tanh(double x)
42 {
43 double t,z;
44 int32_t jx,ix;
45
46 /* High word of |x|. */
47 GET_HIGH_WORD(jx,x);
48 ix = jx&0x7fffffff;
49
50 /* x is INF or NaN */
51 if(ix>=0x7ff00000) {
52 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
53 else return one/x-one; /* tanh(NaN) = NaN */
54 }
55
56 /* |x| < 22 */
57 if (ix < 0x40360000) { /* |x|<22 */
58 if (ix<0x3c800000) /* |x|<2**-55 */
59 return x*(one+x); /* tanh(small) = small */
60 if (ix>=0x3ff00000) { /* |x|>=1 */
61 t = expm1(two*fabs(x));
62 z = one - two/(t+two);
63 } else {
64 t = expm1(-two*fabs(x));
65 z= -t/(t+two);
66 }
67 /* |x| > 22, return +-1 */
68 } else {
69 z = one - tiny; /* raised inexact flag */
70 }
71 return (jx>=0)? z: -z;
72 }
73 libm_hidden_def(tanh)
74