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/* __ieee754_atanh(x)
16 * Method :
17 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
18 *    2.For x>=0.5
19 *                  1              2x                          x
20 *	atanh(x) = --- * ieee_log(1 + -------) = 0.5 * ieee_log1p(2 * --------)
21 *                  2             1 - x                      1 - x
22 *
23 * 	For x<0.5
24 *	atanh(x) = 0.5*ieee_log1p(2x+2x*x/(1-x))
25 *
26 * Special cases:
27 *	atanh(x) is NaN if |x| > 1 with signal;
28 *	atanh(NaN) is that NaN with no signal;
29 *	atanh(+-1) is +-INF with signal.
30 *
31 */
32
33#include "fdlibm.h"
34
35#ifdef __STDC__
36static const double one = 1.0, huge = 1e300;
37#else
38static double one = 1.0, huge = 1e300;
39#endif
40
41static double zero = 0.0;
42
43#ifdef __STDC__
44	double __ieee754_atanh(double x)
45#else
46	double __ieee754_atanh(x)
47	double x;
48#endif
49{
50	double t;
51	int hx,ix;
52	unsigned lx;
53	hx = __HI(x);		/* high word */
54	lx = __LO(x);		/* low word */
55	ix = hx&0x7fffffff;
56	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
57	    return (x-x)/(x-x);
58	if(ix==0x3ff00000)
59	    return x/zero;
60	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
61	__HI(x) = ix;		/* x <- |x| */
62	if(ix<0x3fe00000) {		/* x < 0.5 */
63	    t = x+x;
64	    t = 0.5*ieee_log1p(t+t*x/(one-x));
65	} else
66	    t = 0.5*ieee_log1p((x+x)/(one-x));
67	if(hx>=0) return t; else return -t;
68}
69