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/* @(#)s_asinh.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

        <<asinh>>, <<asinhf>>---inverse hyperbolic sine

INDEX

        asinh

INDEX

        asinhf

ANSI_SYNOPSIS

        #include <math.h>

        double asinh(double <[x]>);

        float asinhf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double asinh(<[x]>)

        double <[x]>;

        float asinhf(<[x]>)

        float <[x]>;

DESCRIPTION

<<asinh>> calculates the inverse hyperbolic sine of <[x]>.

<<asinh>> is defined as

@ifnottex

. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))

@end ifnottex

@tex

$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$

@end tex

<<asinhf>> is identical, other than taking and returning floats.

RETURNS

<<asinh>> and <<asinhf>> return the calculated value.

PORTABILITY

Neither <<asinh>> nor <<asinhf>> are ANSI C.

*/

/* asinh(x)

 * Method :

 *      Based on

 *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]

 *      we have

 *      asinh(x) := x  if  1+x*x=1,

 *               := sign(x)*(log(x)+ln2)) for large |x|, else

 *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else

 *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))

 */

#include "fdlibm.h"

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

static const double

#else

static double

#endif

one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */

ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */

huge=  1.00000000000000000000e+300;

#ifdef __STDC__

        double asinh(double x)

#else

        double asinh(x)

        double x;

#endif

{

        double t,w;

        __int32_t hx,ix;

        GET_HIGH_WORD(hx,x);

        ix = hx&0x7fffffff;

        if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */

        if(ix< 0x3e300000) {    /* |x|<2**-28 */

            if(huge+x>one) return x;    /* return x inexact except 0 */

        }

        if(ix>0x41b00000) {     /* |x| > 2**28 */

            w = __ieee754_log(fabs(x))+ln2;

        } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */

            t = fabs(x);

            w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));

        } else {                /* 2.0 > |x| > 2**-28 */

            t = x*x;

            w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));

        }

        if(hx>0) return w; else return -w;

}

#endif /* _DOUBLE_IS_32BITS */