[empath-nirvana]

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.

[jameshart]

Right. O(f(n)) is literally only defined for situations where n 1: varies between different runs of the algorithm, and 2: can grow arbitrarily large. Even though in practice ‘arbitrarily large’ is always limited by memory, storage, etc.

Talking about algorithms being O(n) in the number of bits in a value is only reasonable if the number of bits in the value actually varies between runs.