1 /* origin: FreeBSD /usr/src/lib/msun/src/s_tanh.c */
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 * ====================================================
13 * Return the Hyperbolic Tangent of x
18 * 0. tanh(x) is defined to be -----------
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
24 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
27 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
29 * 22 <= x <= INF : tanh(x) := 1.
33 * only tanh(0)=0 is exact for finite argument.
38 static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
49 if (ix >= 0x7ff00000) {
51 return one/x + one; /* tanh(+-inf)=+-1 */
53 return one/x - one; /* tanh(NaN) = NaN */
56 if (ix < 0x40360000) { /* |x| < 22 */
57 if (ix < 0x3e300000) { /* |x| < 2**-28 */
58 /* tanh(tiny) = tiny with inexact */
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 } else { /* |x| >= 22, return +-1 */
70 z = one - tiny; /* raise inexact */
72 return jx >= 0 ? z : -z;