Question

What is a good bit-twiddling routine to convert a number in the range [2^N,2^(N-1)-1] to N?

Some examples:

• f(1) -> 0
• f([2-3]) -> 1
• f([4-7]) -> 2
• f([8-15]) -> 3

Here is one implementation:

uint f(uint num)
{
    for (uint shifts = 0; num; shifts++) 
        num >>= 1;
    return (shifts - 1);
}

Answer 1

Depending on how wide your data-type is, and how much memory you have available, a lookup-table is one possibility. It’s almost certainly the fastest approach.

For other approaches, see http://www-graphics.stanford.edu/~seander/bithacks.html#IntegerLogObvious, and the subsequent sections.