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

Here is my solution to this. Time complexity : O (Log n)

public int countSetBits(int n){
    int count=0;
    while(n>0){
        int i= (int)(Math.log10(n)/Math.log10(2));
        count+= Math.pow(2, i-1)*i;
        count+= n-Math.pow(2, i)+1;
        n-= Math.pow(2, i);
    }
    return count;
}