[compiler-rt] [compiler-rt] Use __atomic builtins whenever possible (PR #84439)

[Dmitry Vyukov via llvm-commits]

dvyukov wrote:

> Which architectures do you care about for these diffs? X86 should be easiest to generate

x86 is good.

> The reason I did not use std::atomic is that I was under the assumption that we can't rely on the C++ standard library here and have to roll our own.

Yes, this may be the case. I think I will withdraw this part of my comment, let's just ensure there are no codegen degradation for the most important functions.

https://github.com/llvm/llvm-project/pull/84439