With the advent of the FASTCALL/Vectorcall protocol, it is now much easier to drastically lower the overhead currently associated with __array_function__ without the need to subtly change the semantics, e.g. by in-lining the "not a NumPy array" check.

Here is a branch starting a big chunk of this: main...seberg:faster-array-function

However, it is not polished or finished, it requires still the following:

• Fixing like= for Python defined functions: They are broken, I have
  one possible approach, but it is just an "idea stage".
  (should not be hard, but needs a some thought)
• Make sure the C entry-point looks and feel right, such as printing
  (I am not sure what is left to do here, maybe we can find prior art?)
• Enable pickling (should be very easy)
• Ensure PyPy compatibility if necessary
• Change all warning stacklevel= to one lower (in wrapped functions).
  (simple, but a lot of churn)
• General code cleanup

This may be a nice and very worthwhile project for someone interested in decreasing overheads and familiar with the Python C-API. I do not expect any of these things to be particularly hard nuts to crack, but they may be very hard to approach without a good working knowledge of the Python C-API.