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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.
* ====================================================
*
*/
/*
FUNCTION
<<atanh>>, <<atanhf>>---inverse hyperbolic tangent
INDEX
atanh
INDEX
atanhf
ANSI_SYNOPSIS
#include <math.h>
double atanh(double <[x]>);
float atanhf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double atanh(<[x]>)
double <[x]>;
float atanhf(<[x]>)
float <[x]>;
DESCRIPTION
<<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
<<atanhf>> is identical, other than taking and returning
<<float>> values.
RETURNS
<<atanh>> and <<atanhf>> return the calculated value.
If
@ifinfo
|<[x]>|
@end ifinfo
@tex
$|x|$
@end tex
is greater than 1, the global <<errno>> is set to <<EDOM>> and
the result is a NaN. A <<DOMAIN error>> is reported.
If
@ifinfo
|<[x]>|
@end ifinfo
@tex
$|x|$
@end tex
is 1, the global <<errno>> is set to <<EDOM>>; and the result is
infinity with the same sign as <<x>>. A <<SING error>> is reported.
You can modify the error handling for these routines using
<<matherr>>.
PORTABILITY
Neither <<atanh>> nor <<atanhf>> are ANSI C.
QUICKREF
atanh - pure
atanhf - pure
*/
/* 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"
#ifndef _DOUBLE_IS_32BITS
#ifdef __STDC__
static const double one = 1.0, huge = 1e300;
#else
static double one = 1.0, huge = 1e300;
#endif
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
#ifdef __STDC__
double atanh(double x)
#else
double atanh(x)
double x;
#endif
{
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) 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;
}
#endif /* defined(_DOUBLE_IS_32BITS) */
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