1 /* @(#)s_tanh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
14 * Return the Hyperbolic Tangent of x
19 * 0. tanh(x) is defined to be -----------
22 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
23 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
25 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
28 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
30 * 22.0 < x <= INF : tanh(x) := 1.
34 * only tanh(0)=0 is exact for finite argument.
38 #include "math_private.h"
40 static const double one=1.0, two=2.0, tiny = 1.0e-300;
48 /* High word of |x|. */
54 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
55 else return one/x-one; /* tanh(NaN) = NaN */
59 if (ix < 0x40360000) { /* |x|<22 */
60 if (ix<0x3c800000) /* |x|<2**-55 */
61 return x*(one+x); /* tanh(small) = small */
62 if (ix>=0x3ff00000) { /* |x|>=1 */
63 t = expm1(two*fabs(x));
64 z = one - two/(t+two);
66 t = expm1(-two*fabs(x));
69 /* |x| > 22, return +-1 */
71 z = one - tiny; /* raised inexact flag */
73 return (jx>=0)? z: -z;