xref: /csrg-svn/lib/libm/common_source/j1.c (revision 48402)

/*-
 * Copyright (c) 1985 The Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.proprietary.c%
 */

#ifndef lint
static char sccsid[] = "@(#)j1.c	5.4 (Berkeley) 04/20/91";
#endif /* not lint */

/*
	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, if on the VAX, error number EDOM is set and
	the reserved operand fault is generated;
	otherwise (an IEEE machine) an invalid operation is performed.

	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 "mathimpl.h"

#if defined(vax)||defined(tahoe)
#include <errno.h>
#else	/* defined(vax)||defined(tahoe) */
static const double zero = 0.e0;
#endif	/* defined(vax)||defined(tahoe) */

static double pzero, qzero;

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

static void asympt();

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

	x = arg;
	if(x < 0.) x = -x;
	if(x > 8.){
		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;
	int i;

	x = arg;
	if(x <= 0.){
#if defined(vax)||defined(tahoe)
		return(infnan(EDOM));		/* NaN */
#else	/* defined(vax)||defined(tahoe) */
		return(zero/zero);	/* IEEE machines: invalid operation */
#endif	/* defined(vax)||defined(tahoe) */
	}
	if(x > 8.){
		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 void
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);
}