sinh.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

#ifndef lint
static char	*sccsid ="@(#)sinh.c	4.1	ULTRIX	7/17/90";
#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		14-Jan-86
*
* 001	Replaced old version with BSD 4.3 version as part of upgrade
*
* 002	Jon Reeves, 1990-Jan-19
*	Corrected overflow limits.
*
*	Based on:	sinh.c		4.3		8/21/85
*
*************************************************************************/

/* SINH(X)
 * RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85.
 *
 * Required system supported functions :
 *	copysign(x,y)
 *	scalb(x,N)
 *
 * Required kernel functions:
 *	expm1(x)	...return exp(x)-1
 *
 * Method :
 *	1. reduce x to non-negative by sinh(-x) = - sinh(x).
 *	2. 
 *
 *	                                      expm1(x) + expm1(x)/(expm1(x)+1)
 *	    0 <= x <= lnovfl     : sinh(x) := --------------------------------
 *			       		                      2
 *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
 * lnovfl+ln2 <  x <  INF        :  overflow to INF
 *	
 *
 * Special cases:
 *	sinh(x) is x if x is +INF, -INF, or NaN.
 *	only sinh(0)=0 is exact for finite argument.
 *
 * Accuracy:
 *	sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
 *	a test run with 1,024,000 random arguments on a VAX, the maximum
 *	observed error was 1.93 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 <errno.h>
#include <math.h>
#include <float.h>

#define LN_MAXDOUBLE (M_LN2 * DBL_MAX_EXP)

#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 sinh(x)
double x;
{
	static double  one=1.0, half=1.0/2.0 ;
	double expm1(), t, scalb(), copysign(), sign;
	double max_arg;

	max_arg = LN_MAXDOUBLE + M_LN2;

#ifndef vax
	if(x!=x) return(x);	/* x is NaN */
#endif
	if (x > max_arg)
		{ errno = ERANGE; return(HUGE_VAL); }
	if (x < (-max_arg))
		{ errno = ERANGE; return(-HUGE_VAL); }
	sign=copysign(one,x);
	x=copysign(x,one);
	if(x<lnovfl)
	    {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}

	else if(x <= lnovfl+0.7)
		/* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
	    		to avoid unnecessary overflow */
	    return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));

	else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
	    return( expm1(x)*sign );
}