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Doesn't asm have the disadvantage that you end up spilling if you exceed 8 xmm registers even when running on x86_64 with 16 xmm registers available?

Or do you actually write separate asm for x86 and x86_64?

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You either write an entire separate asm function, or use macro utilities to ifdef portions of the function. See for example: https://git.ffmpeg.org/gitweb/ffmpeg.git/blob/HEAD:/libavcod...

I would imagine they write separate asm for x86, x86_64, and the various instruction set extensions that exist.

A project may even go so far as to write different asm for the same ISA for different architectures in order to optimize for specific pipeline behavior or whatnot

https://github.com/z-classic/libgmp/tree/master/mpn/x86_64

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