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

I know this post came in late to the party, please find logn solution below:

static int countSetBitWithinRange(int n)
{
    int x = n + 1, index = 0, count = 0;
    int numberOfOnesInAGroup = (int)Math.pow(2, index);
    while(x >= numberOfOnesInAGroup)
    {
        int countOfZeroOnePairs = (x / numberOfOnesInAGroup);
        int numberOfPairsOfZerosAndOnes = countOfZeroOnePairs / 2;
        int numberOfSetBits = numberOfPairsOfZerosAndOnes * numberOfOnesInAGroup;
        //If countOfZeroOnePairs is even then the pairs are complete else there will be ones that do not have a corresponding zeros pair
        int remainder = (countOfZeroOnePairs % 2 == 1) ? (x % numberOfOnesInAGroup) : 0;
        count = count + numberOfSetBits + remainder;
        numberOfOnesInAGroup = 1 << ++index;
    }
    return count;
}