In a practical sense, how you define big O depends on what you consider to be the inputs to the function. If the runtime doesn't change depending on the size of the inputs that you care about, it's O(1).
Like, you might have a function with 2 inputs, N and M, and the run time is like O(m2^n), but n is fixed at a low number every time you'll run it in practice, so it's really just O(m) for your purposes.
