3. Equality of floating-point numbers

• You should be careful when comparing floating-point numbers for equality:

  • One way to check whether two floating-point numbers are equal is to check whether the absolute value of their difference is less than a certain tolerance.

  • For example, suppose the tolerance is .000001.

  • Then double x and y are equal if the absolute value of difference

    
        (x – y)
    
    

    is less than 0.000001.

  • To find the absolute value, you can use the function Math.abs of the Math class:

    
        Math.abs(x – y) < 0.000001
    
    

    The above expression determines whether the absolute value of (x – y) is less than 0.000001.