e_atanh.c revision 141296 
1
2/* @(#)e_atanh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15#ifndef lint
16static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_atanh.c 141296 2005-02-04 18:26:06Z das $";
17#endif
18
19/* __ieee754_atanh(x)
20 * Method :
21 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
22 *    2.For x>=0.5
23 *                  1              2x                          x
24 *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
25 *                  2             1 - x                      1 - x
26 *
27 * 	For x<0.5
28 *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
29 *
30 * Special cases:
31 *	atanh(x) is NaN if |x| > 1 with signal;
32 *	atanh(NaN) is that NaN with no signal;
33 *	atanh(+-1) is +-INF with signal.
34 *
35 */
36
37#include "math.h"
38#include "math_private.h"
39
40static const double one = 1.0, huge = 1e300;
41static const double zero = 0.0;
42
43double
44__ieee754_atanh(double x)
45{
46	double t;
47	int32_t hx,ix;
48	u_int32_t lx;
49	EXTRACT_WORDS(hx,lx,x);
50	ix = hx&0x7fffffff;
51	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
52	    return (x-x)/(x-x);
53	if(ix==0x3ff00000)
54	    return x/zero;
55	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
56	SET_HIGH_WORD(x,ix);
57	if(ix<0x3fe00000) {		/* x < 0.5 */
58	    t = x+x;
59	    t = 0.5*log1p(t+t*x/(one-x));
60	} else
61	    t = 0.5*log1p((x+x)/(one-x));
62	if(hx>=0) return t; else return -t;
63}
64