Finding the total number of set-bits from 1 to n

Question

Write an algorithm to find F(n) the number of bits set to 1, in all numbers from 1 to n for any given value of n.

Complexity should be O(log n)

Answer 1

short and sweet!

 public static int countbits(int num){
    int count=0, n;
    while(num > 0){
        n=0;
        while(num >= 1<<(n+1))
            n++;
        num -= 1<