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 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid
[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
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|. */
53 EXTRACT_WORDS (jx
, lx
, x
);
60 return one
/ x
+ one
; /* tanh(+-inf)=+-1 */
62 return one
/ x
- one
; /* tanh(NaN) = NaN */
66 if (ix
< 0x40360000) /* |x|<22 */
69 return x
; /* x == +-0 */
70 if (ix
< 0x3c800000) /* |x|<2**-55 */
71 return x
* (one
+ x
); /* tanh(small) = small */
72 if (ix
>= 0x3ff00000) /* |x|>=1 */
74 t
= __expm1 (two
* fabs (x
));
75 z
= one
- two
/ (t
+ two
);
79 t
= __expm1 (-two
* fabs (x
));
82 /* |x| > 22, return +-1 */
86 z
= one
- tiny
; /* raised inexact flag */
88 return (jx
>= 0) ? z
: -z
;
90 weak_alias (__tanh
, tanh
)
92 strong_alias (__tanh
, __tanhl
)
93 weak_alias (__tanh
, tanhl
)