/**
 * evaluating generalized polynomials: x^a for a real a.
 * method: use Taylor Expansion:
 *	f(x) = f(1) + (x-1)f'(1) + (x-1)^2 f''(1)/2! + (x-1)^3 f'''(1)/3! +...
 *	x^a = 1 + (x-1).a + (x-1)^2.a.(a-1)/2 + (x-1)^3.a.(a-1).(a-2)/3! + ...
 */
import java.math.*;

public class genpoly extends series 
{
	protected int sign = 1;
	protected Rational base = 0;
	protected Rational expo = 0;
	protected long NoTerms = 1;
	protected Rational valpos = 0.0;
	protected Rational 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 genpoly Series
	 *
	 * @param e is the exponent of the monomial
	 * @param b is the base of the monomial, M=b^e.
	 */
	genpoly(double b, double e){
		base = b;
		expo = e;
		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;
	}
	
	/**
	 * Advances to the next term in the series.
	 */
	public void nextTerm(){
		n++;
		term = term*(base-1)*(expo-n+1)/n;
		if (term>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
	 * @return the mth term
	 */
	public double termAt(int m){
		first();
		for (int i=0; i<m; i++)
			nextTerm();
		return term;
	}
	
	/**
	 * 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){
		first();
		for (int i=0; i<m; i++)
			nextTerm();
		return (valpos-valneg);
	}
	
}