Detect if a number is power of 2

Daniele Esposti's Blog
, in 15 August 2013

Easy post today: simple method to detect if a number is a power of 2 in O(1) complexity.

Yes, O(1), no naive loops involved :-).

The code is very simple:

bool powerof2(unsigned int n) {
    return n > 0 & !(n & (n - 1));
}

The code looks cryptic, the core of the algorithm is the n & (n - 1) part. To understand why and how it’s working lets see what’s happen at binary level. Suppose the easy case where we want to test if 4 is a power of 2:

n    4  00000100  &
n-1  3  00000011
---  -  --------
     0  00000000

Subtracting 1 from a power of 2’s number equals to inverting all the bits below the only set bit, applying a bitwise AND with the original number returns a 0. What’s happen in case of a number which is NOT a power of 2, for example 6:

n    6  00000110  &
n-1  5  00000101
---  -  --------
     0  00000100

Subtracting 1 from the original number changes only the less significant bits but the most significant bit set to 1 is unchanged, the result is different than 0 so the given number is not a power of 2.

Now that we know how the core of the algorithm works the other parts of the boolean expression are easy to understand: the NOT invert the result of the n & (n - 1) operation to be true when the result is zero and the block n > 0 ensures the given number is not zero (zero is not a power of 2).