2 /* @(#)e_atanh.c 1.3 95/01/18 */
3 /* $FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das $ */
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
18 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
21 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
25 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
28 * atanh(x) is NaN if |x| > 1 with signal;
29 * atanh(NaN) is that NaN with no signal;
30 * atanh(+-1) is +-INF with signal.
35 #include "math_private.h"
37 static const double one = 1.0, huge = 1e300;
38 static const double zero = 0.0;
41 __ieee754_atanh(double x)
46 EXTRACT_WORDS(hx,lx,x);
48 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
52 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
54 if(ix<0x3fe00000) { /* x < 0.5 */
56 t = 0.5*log1p(t+t*x/(one-x));
58 t = 0.5*log1p((x+x)/(one-x));
59 if(hx>=0) return t; else return -t;