Fastest way to count number of bit transitions in an unsigned int

Question

I\'m looking for the fastest way of counting the number of bit transitions in an unsigned int.

If the int contains: 0b0000000000000000000000000000101

Answer 1

Here's the code using arithmetic shift + xor and Kernighan's method for bit counting:

int count_transitions(int x)
{
    assert((-1 >> 1) < 0); // check for arithmetic shift
    int count = 0;
    for(x ^= (x >> 1); x; x &= x - 1)
        ++count;
    return count;
}