> It does look like gmpy2.mpz() is like 100 times faster than int() or something. Is this just because it's doing it all in assembly rather than in Python bytec

> It does look like gmpy2.mpz() is like 100 times faster than int() or something. Is this just because it's doing it all in assembly rather than in Python bytecodes, or are the Python data structures here also not so hot? It's not the data structures. The data structures are really more or less the same: you have some array of words, with a length and a sign. The only real differences are in the particular length of word that you choose, which is not a very interesting difference. Assembly language optimizations do tend to matter here, because you're working with the carry bit for lots of these operations, and each architecture also has some different way of multiplying numbers. Multiplying numbers is "funny" because it produces two words of output for one word of input. There are also sometimes some different algorithms in use, and GMP uses some different algorithms depending on the size. Here's a page describing the algorithms used by GMP: https://gmplib.org/manual/Multiplication-Algorithms https://gmplib.org/manual/Multiplication-Algorithms Here's a description of how carries are propagated: https://gmplib.org/manual/Assembly-Carry-Propagation https://gmplib.org/manual/Assembly-Carry-Propagation IMO, I wouldn't expect my language's built-in bigint type to use the best, most cutting-edge algorithms and lots of hand-tuned assembly. GMP is a specialized library for doing special things.