///PHYSICAL CONSTANTS///

Pi = Math.PI;
c0 = 299792458;
mu0 = 4E-7*Pi;
epsilon0 = 1/mu0/Math.pow(c0,2);


//ELEMENTARY FUNCTIONS

function sign(y){
 return ((y < 0) ? -1 : 1);
}

function trunc(value,places) {
	dummy = value*Math.pow(10,places);
	dummy = Math.round(dummy);
	dummy = dummy*Math.pow(10,places);
	return dummy;
}


//TRIGONOMETRIC FUNCTIONS

Math.csc = function(x) {
	return 1 / Math.sin(x);
}

Math.sec = function(x) {
	return 1/Math.cos(x);
}

Math.cot = function(x) {
	return 1/Math.tan(x);
} 


//BESSEL FUNCTIONS
//from http://mhtlab.uwaterloo.ca/old/courses/me3532/js/bessel.html

function BesselJ0(x) {
	var ax,z,xx,y,ans,ans1,ans2;
	ax = Math.abs(x)
	if (ax < 8.0) {
		y = x * x;
		ans1 = 57568490574.0 + y * (-13362590354.0 + y * (651619640.7 + y * (-11214424.18 + y * (77392.33017 + y * (-184.9052456)))));
		ans2 = 57568490411.0 + y * (1029532985.0 + y * (9494680.718 + y * (59272.64853 + y * (267.8532712 + y * 1.0))));
		ans = ans1 / ans2;
	} else {
		z = 8.0 / ax;
		y = z * z;
		xx = ax - 0.785398164;
		ans1 = 1.0 + y * (-0.1098628627e-2 + y * (0.2734510407e-4 + y * (-0.2073370639e-5 + y * 0.2093887211e-6)));
		ans2 = -0.1562499995e-1 + y * (0.1430488765e-3 + y * (-0.6911147651e-5 + y * (0.7621095161e-6 - y * 0.934935152e-7)));
		ans = Math.sqrt(0.636619772 / ax) * (Math.cos(xx) * ans1 - z * Math.sin(xx) * ans2);
	}
	return ans;
}

function BesselJ1(x) {
	var ax,z,xx,y,ans,ans1,ans2;
	ax = Math.abs(x);
	if (ax < 8.0) {
		y=x*x;
		ans1 = x*(72362614232.0+y*(-7895059235.0+y*(242396853.1+y*(-2972611.439+y*(15704.48260+y*(-30.16036606))))));
		ans2 = 144725228442.0+y*(2300535178.0+y*(18583304.74+y*(99447.43394+y*(376.9991397+y*1.0))));
		ans = ans1/ans2;
	} else {
		z=8.0/ax;
		y=z*z;
		xx=ax-2.356194491;
		ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4+y*(0.2457520174e-5+y*(-0.240337019e-6))));
		ans2=0.04687499995+y*(-0.2002690873e-3+y*(0.8449199096e-5+y*(-0.88228987e-6+y*0.105787412e-6)));
		ans=Math.sqrt(0.636619772/ax)*(Math.cos(xx)*ans1-z*Math.sin(xx)*ans2);
		if (x < 0.0) ans = -ans;
	}
	return ans;	
}

function BesselY0(x) {
	var z, xx, y, ans, ans1, ans2;
	if (x < 8.0)  {
		y=x*x;
		ans1 = -2957821389.0+y*(7062834065.0+y*(-512359803.6+y*(10879881.29+y*(-86327.92757+y*228.4622733))));
		ans2 = 40076544269.0+y*(745249964.8+y*(7189466.438+y*(47447.26470+y*(226.1030244+y*1.0))));
		ans = (ans1/ans2)+0.636619772*BesselJ0(x)*Math.log(x);
	} else {
		z=8.0/x;
		y=z*z;
		xx=x-0.785398164;
		ans1 = 1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4+y*(-0.2073370639e-5+y*0.2093887211e-6)));
		ans2 = -0.1562499995e-1+y*(0.1430488765e-3+y*(-0.6911147651e-5+y*(0.7621095161e-6+y*(-0.934945152e-7))));
		ans = Math.sqrt(0.636619772/x)*(Math.sin(xx)+ans1+z*Math.cos(xx)*ans2);
	}
	return ans;
}

function BesselY1(x) {
	var z, xx, y, ans, ans1, ans2;
	if (x < 8.0) { 
		y=x*x
		ans1 = x*(-0.4900604943e13+y*(0.1275274390e13+y*(-0.5153438139e11+y*(0.7349264551e9+y*(-0.4237922726e7+y*0.8511937935e4)))));
		ans2 = 0.2499580570e14+y*(0.4244419664e12+y*(0.3733650367e10+y*(0.2245904002e8+y*(0.1020426050e6+y*(0.3549632885e3+y)))));
		ans = (ans1/ans2)+0.636619772*(BesselJ1(x)*Math.log(x)-1.0/x);
	} else {
		z=8.0/x;
		y=z*z;
		xx=x-2.356194491;
		ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4+y*(0.2457520174e-5+y*(-0.240337019e-6))));
		ans2=0.04687499995+y*(-0.202690873e-3+y*(0.8449199096e-5+y*(-0.88228987e-6+y*0.10578e-6)));
		ans=Math.sqrt(0.636619772/x)*(Math.sin(xx)*ans1+z*Math.cos(xx)*ans2);
	}
	return ans;
}

function BesselI0(x) {
	var ax,ans,y;
	ax=Math.abs(x);
	if (ax < 3.75) {
		y=x/3.75;
		y*=y;
		ans=1.0+y*(3.5156229+y*(3.0899424+y*(1.2067492+y*(0.2659732+y*(0.360768e-1+y*0.45813e-2)))));
	} else {
		y=3.75/ax;
		ans=(Math.exp(ax)/Math.sqrt(ax))*(0.39894228+y*(0.1328592e-1+y*(0.225319e-2+y*(-0.157565e-2+y*(0.916281e-2+y*(-0.2057706e-1+y*(0.2635537e-1+y*(-0.1647633e-1+y*0.392377e-2))))))));
	}
	return ans;
}

function BesselI1(x) {
	var ax,ans,y;
	ax=Math.abs(x);
	if (ax<3.75) {
		y=x/3.75;
		y*=y;
		ans=ax*(0.5+y*(0.87890594+y*(0.51498869+y*(0.15084934+y*(0.2658733e-1+y*(0.301532e-2+y*0.32411e-3))))));
	} else {
		y=3.75/ax;
		ans=0.2282967e-1+y*(-0.2895312e-1+y*(0.1787654e-1-y*0.420059e-2));
		ans=0.39894228+y*(-0.3988024e-1+y*(-0.362018e-2+y*(0.163801e-2+y*(-0.1031555e-1+y*ans))));
		ans*=(Math.exp(ax)/Math.sqrt(ax));
	}
	return x < 0.0 ? -ans : ans;
}
	
function BesselK0(x) {
	var y,ans;
	if (x <= 2.0) {
		y=x*x/4.0;
		ans=(-Math.log(x/2.0)*BesselI0(x))-0.57721566+0.42278420*y+0.23069756*y*y+0.03488590*y*y*y+0.00262698*y*y*y*y+0.00010750*y*y*y*y*y+0.00000740*y*y*y*y*y*y;
	} else {
		y=2.0/x;
		ans=(Math.exp(-x)/Math.sqrt(x))*(1.25331414+y*(-0.7832358e-1+y*(0.2189568e-1+y*(-0.1062446e-1+y*(0.587872e-2+y*(-0.251540e-2+y*0.53208e-3))))));
	}
	return ans;
}

function BesselK1(x) {
	var y,ans;
	if (x <= 2.0) {
		y=x*x/4.0;
		ans=(Math.log(x/2.0)*BesselI1(x))+(1.0/x)*(1.0+y*(0.15443144+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1+y*(-0.110404e-2+y*(-0.4686e-4)))))));
	} else {
		y=2.0/x
		ans=(Math.exp(-x)/Math.sqrt(x))*(1.25331414+y*(0.23498619+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2+y*(0.325614e-2+y*(-0.68245e-3)))))));
	}
	return ans;
}

function BesselJ(n,x) {
	if (n == null || n.length == 0) return "n not specified";
	if (Math.floor(n) != n) return "Error: n not integer";
	if (n < 2) return "Error: n < 2";
	var ACC = 40.0;		// Make larger to increase accuracy.
	var BIGNO = 1.0e10;
	var BIGNI = 1.0e-10;
	var j,jsum,m,ax,bj,bjm,bjp,sum,tox,ans;
	ax=Math.abs(x);
	if (ax == 0.0) return 0.0;
	else if (ax > n) {
		tox = 2.0/ax;
		bjm=BesselJ0(ax);
		bj=BesselJ1(ax);
		for (j=1;j<n;j++) {
			bjp=j*tox*bj-bjm;
			bjm=bj;
			bj=bjp;
		}
		ans=bj;
	} else {
		tox=2.0/ax;
		if (Math.sqrt(ACC*n) >= 0)
			m=2*((n + Math.floor(Math.sqrt(ACC*n))) / 2);
		else
			m=2*((n + Math.ceil(Math.sqrt(ACC*n))) / 2);
		jsum=0;
		bjp=ans=sum=0.0;
		bj=1.0;
		for (j=m;j>0;j--) {
			bjm=j*tox*bj-bjp;
			bjp=bj;
			bj=bjm;
			if (Math.abs(bj) > BIGNO) {
				bj *= BIGNI;
				bjp *= BIGNI;
				ans *= BIGNI;
				sum *= BIGNI;
			}
			if (jsum) sum += bj;
			jsum=!jsum;
			if (j == n) ans=bjp;
		}
		sum=2.0*sum-bj;
		ans /= sum;
	}
	return x < 0.0 && (n & 1) ? -ans : ans;
}

function BesselY(n,x) {
	if (n == null || n.length == 0) return "n not specified";
	if (Math.floor(n) != n) return "Error: n not integer";
	if (n < 2) return "Error: n < 2";
	var j,by,bym,byp,tox;
	tox=2.0/x;
	by=BesselY1(x);
	bym=BesselY0(x);
	for (j=1;j<n;j++) {
		byp=j*tox*by-bym;
		bym=by;
		by=byp;
	}
	return by;
}

function BesselI(n,x) {
	if (n == null || n.length == 0) return "n not specified";
	if (Math.floor(n) != n) return "Error: n not integer";
	if (n < 2) return "Error: n < 2";
	var ACC = 40.0;		// Make larger to increase accuracy.
	var BIGNO = 1.0e10;
	var BIGNI = 1.0e-10;
	var j,bi,bim,bip,tox,ans;
	if (x == 0.0) return 0.0;
	else {
		tox=2.0/Math.abs(x);
		bip=ans=0.0;
		bi=1.0;
                for (j=2*(n+Math.floor(Math.sqrt(ACC*n)));j>0;j--) {
			bim=bip+j*tox*bi;
			bip=bi;
			bi=bim;
			if (Math.abs(bi) > BIGNO) {
				ans *= BIGNI;
				bi *= BIGNI;
				bip *= BIGNI;
			}
			if (j == n) ans=bip;
		}
		ans *= BesselI0(x) / bi;
		return x < 0.0 && (n & 1) ? -ans : ans;
	}
}

function BesselK(n,x) {
	if (n == null || n.length == 0) return "n not specified";
	if (Math.floor(n) != n) return "Error: n not integer";
	if (n < 2) return "Error: n < 2";
	var j,bk,bkm,bkp,tox;
	tox=2.0/x;
	bkm=BesselK0(x);
	bk=BesselK1(x);
	for (j=1;j<n;j++) {
		bkp=bkm+j*tox*bk;
		bkm=bk;
		bk=bkp;
	0}
	return bk;
}