cast from double to int is not always just dropping decimal part

Question

I'm experimenting with the code I found here The Java Specialists' Newsletter.

public class MeaningOfLife {
  public static String findOutWhatLifeIsAllAbout() {
  int meaning = 0;
  for (int i = 0; i < 10; i++) {
    for (int j = 0; j < 20; j++) {
      for (int k = 0; k < 300; k++) {
        for (int m = 0; m < 7000; m++) {
          meaning += Math.random() + 1;
        }
      }
    }
  }
  return String.valueOf(meaning).replaceAll("0*$", "");
  }

public static void main(String[] args) {
  System.out.println(findOutWhatLifeIsAllAbout());
}
}

The answer to the question "what does it print" seemed obvious once I realized that there is an implicit cast with the compound assignment operator +=.

But it printed something like: 420000006 or 420000007, instead of (the expected) 420000000 (or "42", after removing trailing zeros).

So that was showing that casting from double to int is not always just dropping the decimal part of the double as stated here: How to cast a double to an int in Java?

So I made some trials and here is an example of what I found:

System.out.println((int)  (131070.99999999999)); // -> 131070
System.out.println((int)  (131071.99999999999)); // -> 131071
System.out.println((int)  (131072.99999999999)); // -> 131073 !!!
System.out.println((int)  (131073.99999999999)); // -> 131074 !!!


System.out.println((int)  (16382.999999999999)); // -> 16382
System.out.println((int)  (16383.999999999999)); // -> 16383
System.out.println((int)  (16384.999999999999)); // -> 16385 !!!
System.out.println((int)  (16385.999999999999)); // -> 16386 !!!

...So now I'm looking for an explanation for that behavior ???

Answer 1

Many decimal values are not possible double values. Before they can be used they first have to be squeezed to whatever double value is closest.

Example: 16384.999999999999 has no exact double representation. The two closest values are 16384.99999999999636202119290828704833984375 and 16385.0. Squeezing down results in a difference of about 0.000000000003, while squeezing up results in a difference of 0.000000000001 - going up results in a closer value, so that's what it's interpreted as.