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 * ====================================================
12 * $NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $
13 * $DragonFly: src/lib/libm/src/s_tanh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
17 * Return the Hyperbolic Tangent of x
22 * 0. tanh(x) is defined to be -----------
25 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
26 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
28 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
31 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
33 * 22.0 < x <= INF : tanh(x) := 1.
37 * only tanh(0)=0 is exact for finite argument.
41 #include "math_private.h"
43 static const double one
=1.0, two
=2.0, tiny
= 1.0e-300;
51 /* High word of |x|. */
57 if (jx
>=0) return one
/x
+one
; /* tanh(+-inf)=+-1 */
58 else return one
/x
-one
; /* tanh(NaN) = NaN */
62 if (ix
< 0x40360000) { /* |x|<22 */
63 if (ix
<0x3c800000) /* |x|<2**-55 */
64 return x
*(one
+x
); /* tanh(small) = small */
65 if (ix
>=0x3ff00000) { /* |x|>=1 */
66 t
= expm1(two
*fabs(x
));
67 z
= one
- two
/(t
+two
);
69 t
= expm1(-two
*fabs(x
));
72 /* |x| > 22, return +-1 */
74 z
= one
- tiny
; /* raised inexact flag */
76 return (jx
>=0)? z
: -z
;