Question

This method returns ‘true’. Why ?

public static boolean f() {
   double val = Double.MAX_VALUE/10;
   double save = val;
   for (int i = 1; i < 1000; i++) {
       val -= i;
   }
   return (val == save);
}

Answer 1

You’re subtracting quite a small value (less than 1000) from a huge value. The small value is so much smaller than the large value that the closest representable value to the theoretical result is still the original value.

Basically it’s a result of the way floating point numbers work.

Imagine we had some decimal floating point type (just for simplicity) which only stored 5 significant digits in the mantissa, and an exponent in the range 0 to 1000.

Your example is like writing 10⁹⁹⁹ – 1000… think about what the result of that would be, when rounded to 5 significant digits. Yes, the exact result is 99999…..9000 (with 999 digits) but if you can only represent values with 5 significant digits, the closest result is 10⁹⁹⁹ again.