1/* @(#)e_atanh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
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
9 * is preserved.
10 * ====================================================
11 */
12
13#include <sys/cdefs.h>
14#if defined(LIBM_SCCS) && !defined(lint)
15__RCSID("$NetBSD: e_atanh.c,v 1.10 1999/07/02 15:37:38 simonb Exp $");
16#endif
17
18/* __ieee754_atanh(x)
19 * Method :
20 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
21 *    2.For x>=0.5
22 *                  1              2x                          x
23 *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
24 *                  2             1 - x                      1 - x
25 *
26 * 	For x<0.5
27 *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
28 *
29 * Special cases:
30 *	atanh(x) is NaN if |x| > 1 with signal;
31 *	atanh(NaN) is that NaN with no signal;
32 *	atanh(+-1) is +-INF with signal.
33 *
34 */
35
36#include "math.h"
37#include "math_private.h"
38
39static const double one = 1.0, huge = 1e300;
40
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