import java.util.Scanner;

/* Java class with a method that performs exponentiation.
** The intent is for students to work with the Java's assert statement
** and the loop invariant concept.
*/
public class Exponentiate {

   /* Returns (an approximation of) x raised to the nth power.
   ** pre: n >= 0
   */
   public static double xToN(double x, int n) {
      final double X = x;  // Store original value of x in X
      final int N = n;     // Store original value of n in N

      double f = ??;  // missing initialization of f 

      System.out.printf("x:%f, n:%d, f:%f\n", x, n ,f);
      assert loopInvariant(X, N, x, n, f);
      // loop invariant: X^N = x^n * f
      while (n != 0) {

         // missing loop body

         System.out.printf("x:%f, n:%d, f:%f\n", x, n, f);
         assert loopInvariant(X, N, x, n, f);
      }
      // At this point, n = 0 and so x^n = 1, which makes x^n * f = f.
      return f;   
   }

   /* Returns true iff X^N and x^n * f are "almost equal", as judged
   ** by the almostEqual() method.
   */
   private static boolean loopInvariant(double X, int N, 
                                        double x, int n, double f) {
      return almostEqual(Math.pow(X,N), Math.pow(x,n)*f);
   }

   /* Returns true iff the two given real numbers are "almost equal",
   ** as measured by the "relative error" between them.
   */
   private static boolean almostEqual(double u, double v) {
      double larger = Math.max(u,v);
      return Math.abs(u-v) / larger <= 0.0001;
   }

   /* For testing the xToN() method.  The user is invited to enter a base x
   ** (which can be any real number) and an exponent n (necessarily a 
   ** nonnegative integer).  It uses both Math.pow() and xToN() to
   ** compute x^n and displays the results.
   */
   public static void main(String[] args) {
      System.out.println("Welcome to the Exponentiate program.\n");

      Scanner input = new Scanner(System.in);
      System.out.print("Enter x: ");
      double x = input.nextDouble();  input.nextLine();
      System.out.print("Enter (nonnegative) exponent n: ");
      int n = input.nextInt();  input.nextLine();
      System.out.println();
      System.out.printf("\nYour method says %f to the %dth power = %f\n", 
                        x, n, xToN(x,n)); 
      System.out.printf("Math.pow()  says %f to the %dth power = %f\n", 
                        x, n, Math.pow(x,n)); 

      System.out.println("\nGoodbye.");
   }

}