(1), (4) and (5) sound good to me.

For (1), it might make sense to ignore the 32-bit vs. 64-bit distinction and use `uint64_t` for the internal computations. Then we can do up to n = 62 regardless of platform.

(2) feels like too much extra complication to me, but that would become clearer with an implementation.

For (3), I somewhat agree that the factorial method should be avoided.

For (4), I don't see how/when the GIL could be released: doesn't the algorithm involve lots of memory allocations/deallocations and reference count adjustments?

Can the suggested performance improvements go into 3.8, or should they wait for 3.9? It's not clear to me whether a performance improvement after feature freeze is okay or not.