Why does misusing 1 instead of 1.0 from an int exceeding limits effect the value we get when we convert it to a double

Question

This is the code I will be using...

public class foo {
    
    public static void main(String [] args){
        int a = (int) Math.pow(2, 30);

        double d = (a + a - 1.0);
        double f = (a + a - 1);

        System.out.println(d);
        System.out.println(f);
    }


}

The outputs are -2.147483649E9 and 2.147483647E9.

I do not understand why these values are printed out. It is my understanding that a + a will exceed the limits of int and therefore will switch to being negative, however, f is positive. I would expect both to be negative but f would be fractional whilst d would be an double with a point 0 due to integer division.

Answer 1

In the first case a + a overflows to Integer.MIN_VALUE, then you switch to a double context with -1.0 which gives a negative number (Integer.MIN_VALUE - 1), since a double can hold a number smaller than Integer.MIN_VALUE.

In the second example you stay in an int context, which means that a + a overflows to Integer.MIN_VALUE, then subtracting 1 from that underflows and takes you back to Integer.MAX_VALUE.