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/* origin: FreeBSD /usr/src/lib/msun/src/e_atanh.c */
/*
* ====================================================
* 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.
* ====================================================
*
*/
/* 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 "libm.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;
uint32_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) /* x < 2**-28 */
return x;
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;
return -t;
}
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