newlib-cygwin/newlib/libm/mathfp/e_acosh.c

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

/*
FUNCTION
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine

INDEX
acosh
INDEX
acoshf

SYNOPSIS
        #include <math.h>
        double acosh(double <[x]>);
        float acoshf(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>>.

PORTABILITY
Neither <<acosh>> nor <<acoshf>> are ANSI C.  They are not recommended
for portable programs.


QUICKREF
 ansi posix rentrant
 acos    n,n,m
 acosf   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) */