acosh.c

VXWORKS源代码

/* acosh.c - ANSI math routines */

/* Copyright 1992 Wind River Systems, Inc. */

/*
modification history
--------------------
01d,14oct92,jdi  made acosh() nomanual.
01c,13oct92,jdi  mangen fixes
01b,20sep92,smb  documentation additions
01a,08jul92,smb  documentation
*/

/*
DESCRIPTION
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that the above copyright notice and this paragraph are
* duplicated in all such forms and that any documentation,
* advertising materials, and other materials related to such
* distribution and use acknowledge that the software was developed
* by the University of California, Berkeley.  The name of the
* University may not be used to endorse or promote products derived
* from this software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*
SEE ALSO: American National Standard X3.159-1989
NOMANUAL
*/

#include "vxWorks.h"
#include "math.h"


#if defined(vax)||defined(tahoe)	/* VAX D format */
#ifdef vax
#define _0x(A,B)	0x/**/A/**/B
#else	/* vax */
#define _0x(A,B)	0x/**/B/**/A
#endif	/* vax */
/* static double */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#else	/* defined(vax)||defined(tahoe) */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
#endif	/* defined(vax)||defined(tahoe) */

/*****************************************************************************
*
* acosh - compute the inverse hyperbolic cosine of <x>
*
* This routine returns the inverse hyperbolic cosine of <x>
* in double precision (VAX D Format 56 BITS, IEEE Double 53 BITS).
*
* Required system support function: sqrt()
*
* Required kernel function:
* .CS
*	log1p(x) 		...return log(1+x)
* .CE
*
* Based on acosh(x) = log [ x + sqrt(x*x-1) ] we have
* .CS
*     acosh(x) := log1p(x)+ln2,	if (x > 1.0E20); else
*     acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
* .CE
* These formulae avoid the over/underflow complication.
*
* Special cases are acosh(x) is NaN with signal if x<1 and acosh(NaN) 
* is NaN without signal.
*
* RETURNS: The inverse hyperbolic cosine of <x>.
* It 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.
*
* INTERNAL
* 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.
*
* NOMANUAL
*/

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

#if !defined(vax)&&!defined(tahoe)
	if(x!=x) return(x);	/* x is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */

    /* 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))));
}