package Fibonacci1;

/**
 * Fibonacci Number Calculator.
 *
 * @author Wayne Eberly
 * @version 2
 */

public class Fibonacci {

  /**
  * Computes a specified Fibonacci number as a long integer
  * iteratively, using a set of three variables to store and reuse values
  * as needed.
  * 
  * <p>
  *  <strong>Precondition:</strong>
  *       <code>i</code> is a nonnegative integer.<br />
  *  <strong>Postcondition:</strong>
  *       Value returned is the <code>i</code><sup>th</sup>
  *       Fibonacci number.
  * </p>
  * 
  * @param i Index of the Fibonacci number to be calculated
  * @return The ith Fibonacci number
  * @throws IllegalArgumentException If the input integer is negative
  * 
  */
  public static long fib(int i) {
    if (i<0) {
      throw new IllegalArgumentException("Negative Input: " + i);
    } else {                          // i >= 0
      if (i==0){
        return 0;
      } else {                        // i >= 1
        if (i==1){
	  return 1;
	} else {                      // i >= 2
	  long previous = 0;
	  long current = 1;
	  long next;
	  for (int j=1; j < i; j++) {
	  /*
	  * Loop Invariant:
	  *  a) j is an integer such that 1 <= j <= i-1
	  *  b) previous is equal to the j-1'st Fibonacci
	  *     number
	  *  c) current is equal to the j'th Fibonacci number
	  * Loop Variant: i-j
	  */
	    next = previous + current;
	    previous = current;
	    current = next;
	    assert (previous == SFibonacci.fib(j))
                    && (current == SFibonacci.fib(j+1));
	  };
	  return current;
        }
      }
    }
  } 

}