we are given 4 integers, where a <= b , c <= d.

We have to find Sum of Xor of all the pairs (i,j) such that ( a <= i <= b , && c <= j <= d )

int sum = 0;

for(int i=a ; i <= b; i++) {
    for(int j = c; j <= d ; j++) {
         sum += (i ^ j)
    }
}
return sum;

How to find this sum optimally ?