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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) */