atomic_compare_exchange with greater-than instead of equals?

As requested, here's my comment as an answer:

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I, too, wish this existed, but it does not, as far as I know (certainly not for x86/x64), apart from conceptually, of course, and workarounds that (potentially) use more than a single atomic instruction (which work but are not wait-free).

I think you misunderstand how compare and swap/exchange works: the basic idea is that having looked at the current value you can work out some corresponding new value - and you attempt that update. If it succeeds - great - continue with whatever you need to, but if it fails then start all over again: looking at the new value that some other thread's put in there and thinking about the value that you'd consequently now need.

I want it to be set when one is greater-than the other (assume we're talking about an ordered type).

So say you want to store 11 but only if the existing value's still atomically less than 11. You won't find an instruction to do that directly, but you can easily do it with the existing compare and swap:

int target_value = 11;
do {
    int snapped_x = x;
    if (snapped_x >= target_value)
        what do you want to do instead?
} while (!compare_and_swap(x, snapped_x, target_value));
         // ...or whatever your exact calling convention is...

You still get the behaviour you want, just with a potentially higher failure/spin rate....