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 * ====================================================
14 static char rcsid[] = "$FreeBSD$";
19 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
22 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
26 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
29 * atanh(x) is NaN if |x| > 1 with signal;
30 * atanh(NaN) is that NaN with no signal;
31 * atanh(+-1) is +-INF with signal.
36 #include "math_private.h"
38 static const double one = 1.0, huge = 1e300;
39 static const double zero = 0.0;
42 __ieee754_atanh(double x)
47 EXTRACT_WORDS(hx,lx,x);
49 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
53 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
55 if(ix<0x3fe00000) { /* x < 0.5 */
57 t = 0.5*log1p(t+t*x/(one-x));
59 t = 0.5*log1p((x+x)/(one-x));
60 if(hx>=0) return t; else return -t;