/**
 * Pi Series 
 * -- this version tries to evaluate from the tail end!
 */
public class pi extends series 
{

	protected int sign = 1;
	protected long NoTerms = 1;
	protected double valpos = 0.0;
	protected double valneg = 0.0;
	
	/**
	 * Parity of int number
	 *
	 * @param N input integer
	 * @return 0 if even, 1 if odd
	 */
	public static int parity(int N){
		return parity((long)N);
	}

	/**
	 * Parity of long number
	 *
	 * @param N input integer
	 * @return 0 if even, 1 if odd
	 */
	public static int parity(long N){
		long m;
		m = N/2;
		if (N != 2*m) return 1;
		return 0;
	}

	/**
	 * Constructor for Pi Series
	 *
	 * @param x is the argument for the series
	 */
	pi(double x){
		param = x;
		n = -1;
		sign = -1;
	}

	/**
	 * 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;
	}
	
	/**
	 * First initializes the mth term of series
	 *
	 * @param m the last term of the series to sum
	 */
	public void last(long m){
                NoTerms = m;
                n = (int)m;
                sign = -1;
                if (parity(m)==0) sign = 1;
                term = 1.0/(2*m+1);
                if (sign>0) {valpos = term; valneg = 0.0;}
                else {valneg = term;  valpos = 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);
	}	
	
	/**
	 * Backs up to the previous term in the series.
	 */
	public void prevTerm(){
		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
	}	
	
	/**
	 * Returns the value of the mth term in series
	 *
	 * @param m the index of a term
	 * @return the mth term
	 */
	public double termAt(int m){
		first();
		for (int i=0; i<m; i++)
			nextTerm();
		return 4*val;
	}
	
	/**
	 * Returns the sum of the first m term in series
	 *
	 * @param m the number of terms to sum
	 * @return the sum of first m terms
	 */
	public double valAt(int m){
		last((long)m);
		for (int i=0; i<m; i++)
			prevTerm();
	/** debug **/
		double xx = 4*(valpos-valneg);
		System.out.println("valpos-valneg = " + xx );
	/** end debug **/
		return 4*val;
	}
	
}