# atanh_freeBSD.c   [plain text]

```
/* @(#)e_atanh.c 1.3 95/01/18 */
/*
* ====================================================
*
* 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.
* ====================================================
*
*/

#ifndef lint
static char rcsid[] = "\$FreeBSD: src/lib/msun/src/e_atanh.c,v 1.7 2005/02/04 18:26:05 das Exp \$";
#endif

/* 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 "math.h"
#include "math_private.h"

static const double one = 1.0, huge = 1e300;
static const double zero = 0.0;

double
atanh(double x)
{
double t;
int32_t hx,ix;
u_int32_t lx;
EXTRACT_WORDS(hx,lx,x);
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 */
SET_HIGH_WORD(x,ix);
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;
}
```