1 /* @(#)e_atanh.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 * ====================================================
12 * $FreeBSD: src/lib/msun/src/e_atanh.c,v 1.5 1999/08/28 00:06:29 peter Exp $
13 * $DragonFly: src/lib/msun/src/Attic/e_atanh.c,v 1.2 2003/06/17 04:26:52 dillon Exp $
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"
38 static const double one = 1.0, huge = 1e300;
40 static double one = 1.0, huge = 1e300;
44 static const double zero = 0.0;
46 static double zero = 0.0;
50 double __ieee754_atanh(double x)
52 double __ieee754_atanh(x)
59 EXTRACT_WORDS(hx,lx,x);
61 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
65 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
67 if(ix<0x3fe00000) { /* x < 0.5 */
69 t = 0.5*log1p(t+t*x/(one-x));
71 t = 0.5*log1p((x+x)/(one-x));
72 if(hx>=0) return t; else return -t;