140 lines
3.0 KiB
C
140 lines
3.0 KiB
C
|
|
/* @(#)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) */
|