76 lines
1.7 KiB
C
76 lines
1.7 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.
|
||
|
|
* ====================================================
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
|
||
|
|
/* __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 "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 __ieee754_atanh(double x)
|
||
|
|
#else
|
||
|
|
double __ieee754_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) */
|