Question in floating point operation

Question

Hi,
I have question in java floating point operation.
public class test
     public static void main(String args[])
          double d1 = 243.35 ;
          double d2 = 2.3 ;
          System.out.println(d1 * d2) ;
          System.out.println((float)d1 * (float)d2) ;
The result is,
java version "1.4.1_02"
Java(TM) 2 Runtime Environment, Standard Edition (build 1.4.1_02-b06)
Java HotSpot(TM) Client VM (build 1.4.1_02-b06, mixed mode)
5.597049999999999E8
5.5970502E8
Though the multiplication does not result irrational number like 1/3, the result of the first statement is not accurate enough. In our project, this multiplication involves with money and we cannot ignore this.
Can anyone suggest why this is happening? Do I need to convert all the numbers to float to avoid this...Or Is it a bug?
~ Sathiya Dhanapal.

Answer 1

The underlying problem is that not all numbers can be represented exactly in a floating point representation. But if you perform all calculations using doubles and then round to two fractional digits at the end you should get a "correct" result UNLESS you have used ill-conditioned formulas introducing other kinds of arithmetic errors.
There's another way around this when it comes to counting money and that's to use integers (long or int). You convert every number to the lowest monetary unit (like a cent or whatever). Every money-amount can now be represented exactly but you still have to be careful because the rounding problem is still there (What do you do with the last cent when you split 100 cents in 3).
In your example the "more correct" you've got from using floats instead of doubles is only an illusion. The result has been implictly rounded becasuse fewer bits have been used. If you round the double result to the same precision as the float result, they're the same.
The important lesson in all this is TO KNOW WHEN TO ROUND.