Determining Powers of 2?

Question

I am creating a simple bracket system and I need a way to check if there are a correct number of teams, OR if my program needs to compensate for bye rounds.

Right now, I am checking for "powers of two" with this function:

function validBracket(data) {
    var x = data.teams.length;
    return ((x != 0) && !(x & (x - 1)));
}

This works pretty well, but I am needing to know how many Bye rounds to add. For instance, if I had 16 teams, I would not need to add anymore teams. However, if I had 12 teams, I would need the first 4 teams to get a bye round.

How can I calculate number of bye rounds to add to my bracket? And would hard-coding an array of powers of two be better?

In pseudo code, something like this is what i was thinking of:

if(validateBracket(data)) {
    // Valid number of teams (power of two). Keep going.
} else {
    var byeRounds = calculateByeRounds();
}

NOTE: I would rather not use an array of powers of two like below:

var powersOfTwo = [2,4,8,16,32,...];

The reasoning behind this is that I would be limiting the number of teams that could be put in the system (however, I don't think a person would have over 256 teams).

Answer 1

var needed = (1 << Math.ceil(Math.log2(n))) - n;

More generalized solution for extreme cases:

var needed = Math.pow(2, Math.ceil(Math.log2(n))) - n;