acosh.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

#ifndef lint
static char	*sccsid ="@(#)acosh.c	1.2	(ULTRIX)	4/17/86";
#endif lint

/************************************************************************
 *									*
 *			Copyright (c) 1986 by				*
 *		Digital Equipment Corporation, Maynard, MA		*
 *			All rights reserved.				*
 *									*
 *   This software is furnished under a license and may be used and	*
 *   copied  only  in accordance with the terms of such license and	*
 *   with the  inclusion  of  the  above  copyright  notice.   This	*
 *   software  or  any  other copies thereof may not be provided or	*
 *   otherwise made available to any other person.  No title to and	*
 *   ownership of the software is hereby transferred.			*
 *									*
 *   This software is  derived  from  software  received  from  the	*
 *   University    of   California,   Berkeley,   and   from   Bell	*
 *   Laboratories.  Use, duplication, or disclosure is  subject  to	*
 *   restrictions  under  license  agreements  with  University  of	*
 *   California and with AT&T.						*
 *									*
 *   The information in this software is subject to change  without	*
 *   notice  and should not be construed as a commitment by Digital	*
 *   Equipment Corporation.						*
 *									*
 *   Digital assumes no responsibility for the use  or  reliability	*
 *   of its software on equipment which is not supplied by Digital.	*
 *									*
 ************************************************************************/

/************************************************************************
*
*			Modification History
*
*		David Metsky		13-Jan-86
*
* 001	Added from BSD 4.3 version as part of upgrade
*
*	Based on:	acosh.c		1.2		8/21/85
*
*************************************************************************/

/* ACOSH(X)
 * RETURN THE INVERSE HYPERBOLIC COSINE OF X
 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 2/16/85;
 * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
 *
 * Required system supported functions :
 *	sqrt(x)
 *
 * Required kernel function:
 *	log1p(x) 		...return log(1+x)
 *
 * Method :
 *	Based on 
 *		acosh(x) = log [ x + sqrt(x*x-1) ]
 *	we have
 *		acosh(x) := log1p(x)+ln2,	if (x > 1.0E20); else		
 *		acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
 *	These formulae avoid the over/underflow complication.
 *
 * Special cases:
 *	acosh(x) is NaN with signal if x<1.
 *	acosh(NaN) is NaN without signal.
 *
 * Accuracy:
 *	acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
 *	rounded. In a test run with 512,000 random arguments on a VAX, the
 *	maximum observed error was 3.30 ulps (units of the last place) at
 *	x=1.0070493753568216 .
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#ifdef VAX	/* VAX D format */
/* static double */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#else	/* IEEE double */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
#endif

double acosh(x)
double x;
{	
	double log1p(),sqrt(),t,big=1.E20; /* big+1==big */

#ifndef vax
	if(x!=x) return(x);	/* x is NaN */
#endif

    /* return log1p(x) + log(2) if x is large */
	if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 

	t=sqrt(x-1.0);
	return(log1p(t*(t+sqrt(x+1.0))));
}