What is the time complexity of the right to left method in modular exponentiation?

Question

http://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method

What is the time complexity of the right to left method in modular exponentiation?

is it O(1) because we are going through the binary representation of e which is constant time? assuming e is a 32-bit integer

int mod(int b, int e, int m) {
    b = b % m;
    int result = 1;

    while (e) {
        if (e % 2 == 1) {
            result = (result * b) % m;
        }
        b = (b * b) % m;
        e >>= 1;
    }
    return result;
}