This is doable, but the risk is that looking at the numbers might take longer than just sorting them, even with a sub optimal algorithm.

I guess someone will just have to try this.

Here is what a human did:

It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold.

I think machines can do this too.

If you need to sort bit and very often, then I imagine profiling it with your load and optimizing automagically every night could bring benefits.