package rebelsky.sqrt;

import java.math.BigDecimal;
import java.io.PrintWriter;

public class MyMath2 {
       
	public static BigDecimal sqrt(BigDecimal num, BigDecimal epsilon)
	throws Exception
	{
		PrintWriter pencil = new PrintWriter(System.out, true);
		BigDecimal approx = new BigDecimal(1);
		return sqrt(num, approx, epsilon, pencil);
	}

	public static BigDecimal sqrt(BigDecimal num, BigDecimal approx, BigDecimal epsilon, PrintWriter pencil)
	throws Exception
	{
		int scale;
		scale = epsilon.scale()+1;
		approx = approx.add(num.divide(approx, scale, BigDecimal.ROUND_HALF_UP));
		approx = approx.divide(new BigDecimal(2));
	    
		// Compute the difference between a and n/a
		BigDecimal diff;
		diff = approx.subtract(num.divide(approx, scale, BigDecimal.ROUND_HALF_UP));
		diff = diff.abs();
	       
		if (diff.compareTo(epsilon) <= 0) {
			return approx;
		}
		else {
			pencil.println(approx);
			return sqrt(num, approx, epsilon, pencil);
		}
	       
	}
}

/*
 * Problems?
 *   * Might give too good an approximation b/c it improves the approximation
 *     before checking.
 *   * Do we need a scale?
 *     YES
 *   * Could we just type "epsilon.scale()+1" instead?
 *     YES, but this is clearer.
 *   * The primary sqrt procedure should not create a pencil, it should
 *     take it as a parameter.
 *   * Why use new BigDecimal(1) instead of BigDecimal.ONE?
 *   * Computing the quality of an approximation by dividing is inefficient.
 */