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 the java function

private static int[] findx(int i) {
    //find the biggest power of two number that is smaller than i
    int c = 0;
    int pow2 = 1;
    while((pow2<< 1) <= i) {
        c++;
        pow2 = pow2 << 1;
    }
    return new int[] {c, pow2};
}

public static int TotalBits2(int number) {
    if(number == 0) {
        return 0;
    }
    int[] xAndPow = findx(number);
    int x = xAndPow[0];
    return x*(xAndPow[1] >> 1) + TotalBits2(number - xAndPow[1]) + number - xAndPow[1] + 1;
}