I see no use of 128-bit ints in the CPython core. Advice: forget it. 

int64_t and uint64_t are required by C99, and are used many places in the core. Advice: use freely.

Note that if tables of "odd part mod 2**64" and "number of trailing zeroes" are used up through 67, then factorials up through 25! are trivially computed via

Fodd[i] << Fntz[i]


(at 26, the odd part no longer fits in 64 bits)