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 * ====================================================
13 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $");
19 * Return the Hyperbolic Tangent of x
24 * 0. tanh(x) is defined to be -----------
27 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
28 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
30 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
33 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
35 * 22.0 < x <= INF : tanh(x) := 1.
39 * only tanh(0)=0 is exact for finite argument.
43 #include "math_private.h"
45 static const double one
=1.0, two
=2.0, tiny
= 1.0e-300;
53 /* High word of |x|. */
59 if (jx
>=0) return one
/x
+one
; /* tanh(+-inf)=+-1 */
60 else return one
/x
-one
; /* tanh(NaN) = NaN */
64 if (ix
< 0x40360000) { /* |x|<22 */
65 if (ix
<0x3c800000) /* |x|<2**-55 */
66 return x
*(one
+x
); /* tanh(small) = small */
67 if (ix
>=0x3ff00000) { /* |x|>=1 */
68 t
= expm1(two
*fabs(x
));
69 z
= one
- two
/(t
+two
);
71 t
= expm1(-two
*fabs(x
));
74 /* |x| > 22, return +-1 */
76 z
= one
- tiny
; /* raised inexact flag */
78 return (jx
>=0)? z
: -z
;