// This code calculates effective index of materials  as decribed in
// the formula in 10.1364...
// power(x,n) returns the nth power of x (x^n)
// n is an integer
// x is a double
// return type is long long
long long power(double x, int n){//Compliant
	long long BN = 1;
	for(int i = 0; i<n;++i){
		BN*=x;
	}
	return BN;
}
// CalculateU(m) calculates the first intermediate variable
// required to calculate  polarization
// m is the relative refractive index
// return type is double;
double CalculateU(double m){//Compliant
	return (power(m,2) - 1)/(power(m,2)+2);
}
// CalculateV(m) calculates the second intermediate variable
// required to calculate  polarization
// m is the relative refractive index
// return type is double;
double CalculateV(double m){//Compliant
	return (power(m,4) + 27*power(m,2)+38)/(2*power(m,2)+3);
}
// CalculateMid(m,f) calculates the large term present in both numerator and denominator
// of the effective index calculation
// m is the relative refractive index
// f is the fillfactor 
// return type is double;
double CalculateMid(double m, double f){//Compliant
	double U = CalculateU(m);
	double V = CalculateU(m); 
	return 2*f*power(U,2)*(1+power(m,2)*U*V + power(m,3)/power(m,3)*(U-V));
}
//AppxIndex(m,f) calculates the approximate effective index
// m is the relative refractive index
// f is the fillfactor
//return type is double
double AppxIndex(double m, double f){//Compliant
	return (1+CalculateMid(m,f))/( (1-CalculateMid(m,f)));
}