[dathinab]

how is turning (a+b)/2 into a/2 + b/2 + a&b&1 even patentable?

Turning (a+b)/2 into a/2 + b/2 is basic obvious math.

If you do it and to any basic testing you will realize you are getting of by one errors, locking at them can then make it obvious that when they appear and hence how to fix them.

Sure a proof is more complex, but then you can just trivially test it for all smaller-bit numbers over all possible inputs, hence making proofs unnecessary (for that numbers).

This is a solution a not yet graduated bachelor student can find in less then a day.

Having granted a patent for this should lead to disciplinary measurements against the person granting the patent tbh.