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 static char rcsid[] = "$FreeBSD$";
18 * Return the Hyperbolic Tangent of x
23 * 0. tanh(x) is defined to be -----------
26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
27 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
29 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
34 * 22.0 < x <= INF : tanh(x) := 1.
38 * only tanh(0)=0 is exact for finite argument.
42 #include "math_private.h"
44 static const double one=1.0, two=2.0, tiny = 1.0e-300;
52 /* High word of |x|. */
58 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
59 else return one/x-one; /* tanh(NaN) = NaN */
63 if (ix < 0x40360000) { /* |x|<22 */
64 if (ix<0x3c800000) /* |x|<2**-55 */
65 return x*(one+x); /* tanh(small) = small */
66 if (ix>=0x3ff00000) { /* |x|>=1 */
67 t = expm1(two*fabs(x));
68 z = one - two/(t+two);
70 t = expm1(-two*fabs(x));
73 /* |x| > 22, return +-1 */
75 z = one - tiny; /* raised inexact flag */
77 return (jx>=0)? z: -z;