If you asked for more accuracy than is possible in double precision variables, what might happen? For example, say that smallValue were 1.0E-21?

Answer:

The loop ends when it has achieved the goal. If the goal cannot be achieved, the loop might go on forever. Or, you might get lucky and accidentally reach the goal.

Improvement to the Program

Here is the familiar program fragment that asks the user to enter a floating point value:

    // get the number from the user
    Scanner scan = new Scanner( System.in );
    System.out.println("Enter the number:"); 
    N = scan.nextDouble();

Here is the program:

class  SquareRoot
{

  public static void main( String[] args ) 
  {
    final double smallValue = 1.0E-14 ;
    double N     = 3.00 ;
    double guess = 1.00 ;

    while ( Math.abs( N/(guess*guess) - 1.0 ) > smallValue )
    {      
       guess =  N/(2*guess) + guess/2 ; // calculate a new value for the guess
    }

    System.out.println("The square root of " + N + " is " + guess ) ;
  }
}

It would be nice if the user could enter number for which the square root is computed.

QUESTION 18:

(Mentally) copy the program fragment and paste it into the program so that the user can enter N.