cosh.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

#ifndef lint
static char	*sccsid = " @(#)cosh.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:	cosh.c		1.2		8/21/85
*
*************************************************************************/

/* COSH(X)
 * RETURN THE HYPERBOLIC COSINE OF X
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 1/8/85; 
 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
 *
 * Required system supported functions :
 *	copysign(x,y)
 *	scalb(x,N)
 *
 * Required kernel function:
 *	exp(x) 
 *	exp__E(x,c)	...return exp(x+c)-1-x for |x|<0.3465
 *
 * Method :
 *	1. Replace x by |x|. 
 *	2. 
 *		                                        [ exp(x) - 1 ]^2 
 *	    0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
 *			       			           2*exp(x)
 *
 *		                                   exp(x) +  1/exp(x)
 *	    0.3465   <= x <= 22      :  cosh(x) := -------------------
 *			       			           2
 *	    22       <= x <= lnovfl  :  cosh(x) := exp(x)/2 
 *	    lnovfl   <= x <= lnovfl+log(2)
 *				     :  cosh(x) := exp(x)/2 (avoid overflow)
 *	    log(2)+lnovfl <  x <  INF:  overflow to INF
 *
 *	Note: .3465 is a number near one half of ln2.
 *
 * Special cases:
 *	cosh(x) is x if x is +INF, -INF, or NaN.
 *	only cosh(0)=1 is exact for finite x.
 *
 * Accuracy:
 *	cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
 *	In a test run with 768,000 random arguments on a VAX, the maximum
 *	observed error was 1.23 ulps (units in the last place).
 *
 * 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.
 */
#include <math.h>

#ifdef VAX
/* double static  */
/* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
/* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
/* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
static long    mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2};
static long    mln2lox[] = { 0x1b60a70f, 0x582a279e};
static long    lnovflx[] = { 0x0f3343b0, 0x2bdac7e2};
#define   mln2hi    (*(double*)mln2hix)
#define   mln2lo    (*(double*)mln2lox)
#define   lnovfl    (*(double*)lnovflx)
#else	/* IEEE double */
double static 
mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
#endif

#ifdef VAX
static max = 126                      ;
#else	/* IEEE double */
static max = 1023                     ;
#endif

double cosh(x)
double x;
{	
	static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
	double scalb(),copysign(),exp(),exp__E(),t;

#ifndef vax
	if(x!=x) return(x);	/* x is NaN */
#endif
	if((x=copysign(x,one)) <= 22)
	    if(x<0.3465) 
		if(x<small) return(one+x);
		else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }

	    else /* for x lies in [0.3465,22] */
	        { t=exp(x); return((t+one/t)*half); }

	if( lnovfl <= x && x <= (lnovfl+0.7)) 
        /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 
         * and return 2^max*exp(x) to avoid unnecessary overflow 
         */
	    return(scalb(exp((x-mln2hi)-mln2lo), max)); 

	else
	    t = exp(x);
	    if( t == HUGE_VAL )
		return (HUGE_VAL);
	    else
		return( t * half );
#ifdef 0
	    return(exp(x)*half);	/* for large x,  cosh(x)=exp(x)/2 */
#endif
}