ref: 75c92428225428c8fde2d015f010e608a0b12f1d
dir: purgatorio/libmath/fdlibm/e_atanh.c
/* derived from /netlib/fdlibm */
/* @(#)e_atanh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
*
* Special cases:
* atanh(x) is NaN if |x| > 1 with signal;
* atanh(NaN) is that NaN with no signal;
* atanh(+-1) is +-INF with signal.
*
*/
#include "fdlibm.h"
static const double one = 1.0, Huge = 1e300;
static double zero = 0.0;
double __ieee754_atanh(double x)
{
double t;
int hx,ix;
unsigned lx;
hx = __HI(x); /* high word */
lx = __LO(x); /* low word */
ix = hx&0x7fffffff;
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3ff00000)
return x/zero;
if(ix<0x3e300000&&(Huge+x)>zero) return x; /* x<2**-28 */
__HI(x) = ix; /* x <- |x| */
if(ix<0x3fe00000) { /* x < 0.5 */
t = x+x;
t = 0.5*log1p(t+t*x/(one-x));
} else
t = 0.5*log1p((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}