fraction 1/3

[Brenda Bowers]

From the sample test of Bill Brogden's Exam Cram, I compiled and ran the following :
float A = 1.0F / 3.0F;
if ( (A * 3.0F) == 1.0F )
System.out.println("Equal");
else System.out.println("Not Equal");

and I got "Equal" printed.
But the answer is "Not Equal". The reason given is a floating-point number cannot exactly represent the fraction 1/3 -- multiplying by 3 does not recover the original number. I think the explanation makes sense. Could anybody help me understand why I got "Equal"?
Thanks.

[Jim Yingst]

Strange. I get the same result. I think the key is, you get roundoff error both ways - when you divide and when you multiply. It just so happens that the two cancel each other out in this case. Surprisingly, it seems to cancel out in most of the cases I tried. Try using 41.0F in place of 3.0F, and you may get "Not Equal" instead. At least, that's what I got on my machine.
The thing to remember is that whenever using floats or doubles, the == operator is unreliable either way. It may give false positives or false negatives. To get meaningful results from comparisons with floats, use > or < instead. E.g.:

  static boolean areNearlyEqual(double x, double y) {
  return ( Math.abs((x - y) / x) < 0.0000001 );
}

This returns true if x and y are within .00001 % of each other.

[Greg Torrance]

Brogden does make a slight mod to this in the errata for the book. He changes the second line from
if ( (A * 3.0F) == 1.0F )
to
if ( (A * 3.0) == 1.0F )
Hope that helps ...
Greg

[Brenda Bowers]

Thanks Jim & Greg.