C++: Black Scholes Put Option Theta

// Calculate the Black Scholes European put option Theta
double BS_Put_Option_Theta(double S, double K, double r, double v, double T) 
// Parameters: (S = Current Stock Price, K = Strike Price, r = Risk-Free Rate, v = Volatility of Stock Price, T = Time to Maturity)
{  return -(S*Normal_PDF(d_j(1, S, K, r, v, T))*v)/(2*sqrt(T))   + r*K*exp(-r*T)*Normal_CDF(-d_j(2, S, K, r, v, T)); }

const double Pi = 3.14159265359;

// Standard Normal cumulative distribution function
double Normal_CDF(const double & x) 
{  
	double k = 1.0/(1.0 + 0.2316419 * x);
	double k_sum = k * (0.319381530 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + 1.330274429 * k))));

	if (x >= 0.0) 
	{  return (1.0 - (1.0/(pow(2*Pi,0.5)))*exp(-0.5*x*x) * k_sum); } 
	else 
	{  return 1.0 - Normal_CDF(-x); } 
}