j1.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

/* @(#)j1.c	4.1	ULTRIX	7/17/90 */

/************************************************************************
 *									*
 *			Copyright (c) 1989 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
 *      --------------------
 *
 *	5-Jul-89		Tim N
 *		Added checking for ERANGE.  Added this header and SCCS
 *		keywords.  This file had header:
 *		"@(#)j1.c	4.1	12/25/82"
 ************************************************************************/


/*
	floating point Bessel's function
	of the first and second kinds
	of order one

	j1(x) returns the value of J1(x)
	for all real values of x.

	There are no error returns.
	Calls sin, cos, sqrt.

	There is a niggling bug in J1 which
	causes errors up to 2e-16 for x in the
	interval [-8,8].
	The bug is caused by an inappropriate order
	of summation of the series.  rhm will fix it
	someday.

	Coefficients are from Hart & Cheney.
	#6050 (20.98D)
	#6750 (19.19D)
	#7150 (19.35D)

	y1(x) returns the value of Y1(x)
	for positive real values of x.
	For x<=0, error number EDOM is set and a
	large negative value is returned.

	Calls sin, cos, sqrt, log, j1.

	The values of Y1 have not been checked
	to more than ten places.

	Coefficients are from Hart & Cheney.
	#6447 (22.18D)
	#6750 (19.19D)
	#7150 (19.35D)
*/

#include <math.h>
#include <errno.h>
#include <values.h>

int	errno;
static double pzero, qzero;
static double tpi	= .6366197723675813430755350535e0;
static double pio4	= .7853981633974483096156608458e0;
static double p1[] = {
	0.581199354001606143928050809e21,
	-.6672106568924916298020941484e20,
	0.2316433580634002297931815435e19,
	-.3588817569910106050743641413e17,
	0.2908795263834775409737601689e15,
	-.1322983480332126453125473247e13,
	0.3413234182301700539091292655e10,
	-.4695753530642995859767162166e7,
	0.2701122710892323414856790990e4,
};
static double q1[] = {
	0.1162398708003212287858529400e22,
	0.1185770712190320999837113348e20,
	0.6092061398917521746105196863e17,
	0.2081661221307607351240184229e15,
	0.5243710262167649715406728642e12,
	0.1013863514358673989967045588e10,
	0.1501793594998585505921097578e7,
	0.1606931573481487801970916749e4,
	1.0,
};
static double p2[] = {
	-.4435757816794127857114720794e7,
	-.9942246505077641195658377899e7,
	-.6603373248364939109255245434e7,
	-.1523529351181137383255105722e7,
	-.1098240554345934672737413139e6,
	-.1611616644324610116477412898e4,
	0.0,
};
static double q2[] = {
	-.4435757816794127856828016962e7,
	-.9934124389934585658967556309e7,
	-.6585339479723087072826915069e7,
	-.1511809506634160881644546358e7,
	-.1072638599110382011903063867e6,
	-.1455009440190496182453565068e4,
	1.0,
};
static double p3[] = {
	0.3322091340985722351859704442e5,
	0.8514516067533570196555001171e5,
	0.6617883658127083517939992166e5,
	0.1849426287322386679652009819e5,
	0.1706375429020768002061283546e4,
	0.3526513384663603218592175580e2,
	0.0,
};
static double q3[] = {
	0.7087128194102874357377502472e6,
	0.1819458042243997298924553839e7,
	0.1419460669603720892855755253e7,
	0.4002944358226697511708610813e6,
	0.3789022974577220264142952256e5,
	0.8638367769604990967475517183e3,
	1.0,
};
static double p4[] = {
	-.9963753424306922225996744354e23,
	0.2655473831434854326894248968e23,
	-.1212297555414509577913561535e22,
	0.2193107339917797592111427556e20,
	-.1965887462722140658820322248e18,
	0.9569930239921683481121552788e15,
	-.2580681702194450950541426399e13,
	0.3639488548124002058278999428e10,
	-.2108847540133123652824139923e7,
	0.0,
};
static double q4[] = {
	0.5082067366941243245314424152e24,
	0.5435310377188854170800653097e22,
	0.2954987935897148674290758119e20,
	0.1082258259408819552553850180e18,
	0.2976632125647276729292742282e15,
	0.6465340881265275571961681500e12,
	0.1128686837169442121732366891e10,
	0.1563282754899580604737366452e7,
	0.1612361029677000859332072312e4,
	1.0,
};

double
j1(arg) double arg;{
	double xsq, n, d, x;
	double sin(), cos(), sqrt();
	int i;

	x = arg;
	if(x < 0.) x = -x;
	if(x > 8.){
		if( x > X_TLOSS){
			errno = ERANGE;
			return( 0.0 );
		}
		asympt(x);
		n = x - 3.*pio4;
		n = sqrt(tpi/x)*(pzero*cos(n) - qzero*sin(n));
		if(arg <0.) n = -n;
		return(n);
	}
	xsq = x*x;
	for(n=0,d=0,i=8;i>=0;i--){
		n = n*xsq + p1[i];
		d = d*xsq + q1[i];
	}
	return(arg*n/d);
}

double
y1(arg) double arg;{
	double xsq, n, d, x;
	double sin(), cos(), sqrt(), log(), j1();
	int i;

	errno = 0;
	x = arg;
	if(x <= 0.){
		errno = EDOM;
		return(-HUGE_VAL);
	}
	if(x > 8.){
		if( x > X_TLOSS){
			errno = ERANGE;
			return( 0.0 );
		}
		asympt(x);
		n = x - 3*pio4;
		return(sqrt(tpi/x)*(pzero*sin(n) + qzero*cos(n)));
	}
	xsq = x*x;
	for(n=0,d=0,i=9;i>=0;i--){
		n = n*xsq + p4[i];
		d = d*xsq + q4[i];
	}
	return(x*n/d + tpi*(j1(x)*log(x)-1./x));
}

static
asympt(arg) double arg;{
	double zsq, n, d;
	int i;

	zsq = 64./(arg*arg);
	for(n=0,d=0,i=6;i>=0;i--){
		n = n*zsq + p2[i];
		d = d*zsq + q2[i];
	}
	pzero = n/d;
	for(n=0,d=0,i=6;i>=0;i--){
		n = n*zsq + p3[i];
		d = d*zsq + q3[i];
	}
	qzero = (8./arg)*(n/d);
}