> In this case, even though rax is needed to hold the full 64-bit long result, by writing to eax, we get a nice effect: Unlike other partial register writes, when writing to an e register like eax, the architecture zeros the top 32 bits for free. So xor eax, eax sets all 64 bits to zero.

Huh, news to me. Although the amount of x86-64 assembly programming I've personally done is extremely minimal. Frankly, this is exactly the sort of architecture-specific detail I'm happy to let an ASM-generating library know for me rather than know myself.