2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
14 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
17 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
21 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
24 * atanh(x) is NaN if |x| > 1 with signal;
25 * atanh(NaN) is that NaN with no signal;
26 * atanh(+-1) is +-INF with signal.
31 #include "math_private.h"
33 static const double one = 1.0, huge = 1e300;
35 static const double zero = 0.0;
37 double attribute_hidden __ieee754_atanh(double x)
42 EXTRACT_WORDS(hx,lx,x);
44 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
48 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
50 if(ix<0x3fe00000) { /* x < 0.5 */
52 t = 0.5*log1p(t+t*x/(one-x));
54 t = 0.5*log1p((x+x)/(one-x));
55 if(hx>=0) return t; else return -t;
62 double atanh(double x)
65 z = __ieee754_atanh(x);
66 if (_LIB_VERSION == _IEEE_ || isnan(x))
71 return __kernel_standard(x, x, 30); /* atanh(|x|>1) */
72 return __kernel_standard(x, x, 31); /* atanh(|x|==1) */
77 strong_alias(__ieee754_atanh, atanh)
79 libm_hidden_def(atanh)