/**
 * pi Series 
 *   -- this is based on pi/4 = 1 - (1/3) + (1/5) - (1/7) +...
 *   -- this is the straightforward version
 */
public class pi1 extends series 
{

	protected int sign = 1;
	protected double valpos = 0.0;
	protected double valneg = 0.0;
	
	/**
	 * Constructor for Pi Series
	 *
	 * @param x is the argument for the series
	 */
	pi1(double x){
		param = x;
		n = -1;
		term = 0.0;
		valpos = 0.0;  valneg = 0.0;
		val = valpos;
	}

	/**
	 * First initializes the first term of series
	 */
	public void first(){
		term=1.0;
		sign=1;
		n=0;
		valpos = term; valneg = 0.0;
		val = valpos - valneg;
	}
	
	/**
	 * Advances to the next term in the series.
	 */
	public void nextTerm(){
		n++;
		sign = -1*sign;
		term = 1.0/(2*n+1.0);
		if (sign>0) valpos = valpos + term;
		else valneg = valneg + term;
		val = val + sign*term;	// inaccurate way
	//	val = valpos - valneg;	// accurate   way
	//	System.out.println("n=" + n + ", sign=" + sign + ", term=" +term);
	}	
	
	/**
	 * Returns the value of the mth term in series
	 *
	 * @param m the index of a term
	 */
	public double valAt(int m){
		first();
		for (int i=0; i<m; i++)
			nextTerm();
		return 4*val;
	}
	
}