xref: /plan9/sys/src/ape/lib/ap/math/jn.c (revision 3e12c5d1bb89fc02707907988834ef147769ddaf)

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

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

	int n;
	double x;
	jn(n,x);

	returns the value of Jn(x) for all
	integer values of n and all real values
	of x.

	There are no error returns.
	Calls j0, j1.

	For n=0, j0(x) is called,
	for n=1, j1(x) is called,
	for n<x, forward recursion us used starting
	from values of j0(x) and j1(x).
	for n>x, a continued fraction approximation to
	j(n,x)/j(n-1,x) is evaluated and then backward
	recursion is used starting from a supposed value
	for j(n,x). The resulting value of j(0,x) is
	compared with the actual value to correct the
	supposed value of j(n,x).

	yn(n,x) is similar in all respects, except
	that forward recursion is used for all
	values of n>1.
*/

double	j0(double);
double	j1(double);
double	y0(double);
double	y1(double);

double
jn(int n, double x)
{
	int i;
	double a, b, temp;
	double xsq, t;

	if(n < 0) {
		n = -n;
		x = -x;
	}
	if(n == 0)
		return j0(x);
	if(n == 1)
		return j1(x);
	if(x == 0)
		return 0;
	if(n > x)
		goto recurs;

	a = j0(x);
	b = j1(x);
	for(i=1; i<n; i++) {
		temp = b;
		b = (2*i/x)*b - a;
		a = temp;
	}
	return b;

recurs:
	xsq = x*x;
	for(t=0,i=n+16; i>n; i--)
		t = xsq/(2*i - t);
	t = x/(2*n-t);

	a = t;
	b = 1;
	for(i=n-1; i>0; i--) {
		temp = b;
		b = (2*i/x)*b - a;
		a = temp;
	}
	return t*j0(x)/b;
}

double
yn(int n, double x)
{
	int i;
	int sign;
	double a, b, temp;

	if (x <= 0) {
		errno = EDOM;
		return -HUGE_VAL;
	}
	sign = 1;
	if(n < 0) {
		n = -n;
		if(n%2 == 1)
			sign = -1;
	}
	if(n == 0)
		return y0(x);
	if(n == 1)
		return sign*y1(x);

	a = y0(x);
	b = y1(x);
	for(i=1; i<n; i++) {
		temp = b;
		b = (2*i/x)*b - a;
		a = temp;
	}
	return sign*b;
}