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/* @(#)e_atanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, 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 <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>
static const long double one = 1.0L, huge = 1e300L;
static const long double zero = 0.0L;
long double
__ieee754_atanhl(long double x)
{
long double t;
int64_t hx,ix;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
ix = hx&0x7fffffffffffffffLL;
if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */
if (ix > 0x3ff0000000000000LL)
return (x-x)/(x-x);
t = fabsl (x);
if (t > one)
return (x-x)/(x-x);
if (t == one)
return x/zero;
}
if(ix<0x3c70000000000000LL&&(huge+x)>zero) /* x<2**-56 */
{
math_check_force_underflow (x);
return x;
}
x = fabsl (x);
if(ix<0x3fe0000000000000LL) { /* x < 0.5 */
t = x+x;
t = 0.5*__log1pl(t+t*x/(one-x));
} else
t = 0.5*__log1pl((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}
libm_alias_finite (__ieee754_atanhl, __atanhl)
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