Java's '==' operator on doubles

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.

Answer 2

When you set val to Double.MAX_VALUE/10, it is set to a value approximately equal to 1.7976931348623158 * 10^307. substracting values like 1000 from that would required a precision on the double representation that is not possible, so it basically leaves val unchanged.

Depending on your needs, you may use BigDecimal instead of double.