Mark Dickinson <dicki...@gmail.com> added the comment:

(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.

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<https://bugs.python.org/issue37295>
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