newlib/libm/mathfp/e_atanh.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
        @ifnottex
        |<[x]>|
        @end ifnottex
        @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
        @ifnottex
        |<[x]>|
        @end ifnottex
        @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) */