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/* @(#)e_acosh.c 5.1 93/09/24 */

/*

FUNCTION

<<acosh>>, <<acoshf>>---inverse hyperbolic cosine

INDEX

acosh

INDEX

acoshf

ANSI_SYNOPSIS

        #include <math.h>

        double acosh(double <[x]>);

        float acoshf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double acosh(<[x]>)

        double <[x]>;

        float acoshf(<[x]>)

        float <[x]>;

DESCRIPTION

<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.

<<acosh>> is defined as

@ifnottex

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

@end ifnottex

@tex

$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$

@end tex

<[x]> must be a number greater than or equal to 1.

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

RETURNS

<<acosh>> and <<acoshf>> return the calculated value.  If <[x]>

less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.

You can change the error-handling behavior with the non-ANSI

<<matherr>> function.

PORTABILITY

Neither <<acosh>> nor <<acoshf>> are ANSI C.  They are not recommended

for portable programs.

QUICKREF ANSI SVID POSIX RENTRANT

 acos    n,n,n,m

 acosf   n,n,n,m

MATHREF

 acosh, NAN,   arg,DOMAIN,EDOM

 acosh, < 1.0, NAN,DOMAIN,EDOM

 acosh, >=1.0, acosh(arg),,,

MATHREF

 acoshf, NAN,   arg,DOMAIN,EDOM

 acoshf, < 1.0, NAN,DOMAIN,EDOM

 acoshf, >=1.0, acosh(arg),,,

*/

/*

 * ====================================================

 * 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.

 * ====================================================

 *

 */

/* acosh(x)

 * Method :

 *      Based on

 *              acosh(x) = log [ x + sqrt(x*x-1) ]

 *      we have

 *              acosh(x) := log(x)+ln2, if x is large; else

 *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else

 *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.

 *

 * Special cases:

 *      acosh(x) is NaN with signal if x<1.

 *      acosh(NaN) is NaN without signal.

 */

#include "fdlibm.h"

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

static const double

#else

static double

#endif

one     = 1.0,

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

#ifdef __STDC__

        double acosh(double x)

#else

        double acosh(x)

        double x;

#endif

{

        double t;

        __int32_t hx;

        __uint32_t lx;

        EXTRACT_WORDS(hx,lx,x);

        if(hx<0x3ff00000) {             /* x < 1 */

            return (x-x)/(x-x);

        } else if(hx >=0x41b00000) {    /* x > 2**28 */

            if(hx >=0x7ff00000) {       /* x is inf of NaN */

                return x+x;

            } else

                return log(x)+ln2;      /* acosh(huge)=log(2x) */

        } else if(((hx-0x3ff00000)|lx)==0) {

            return 0.0;                 /* acosh(1) = 0 */

        } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */

            t=x*x;

            return log(2.0*x-one/(x+sqrt(t-one)));

        } else {                        /* 1<x<2 */

            t = x-one;

            return log1p(t+sqrt(2.0*t+t*t));

        }

}

#endif /* defined(_DOUBLE_IS_32BITS) */