What formally guarantees that non-atomic variables can't see out-of-thin-air values and create a data race like atomic relaxed theoretically can?

When a race condition potentially exists, what guarantees that a read of a shared variable (normal, non atomic) cannot see a write

There is no such guarantee.

When race condition exists, the behaviour of the program is undefined:

[intro.races]

Two actions are potentially concurrent if

• they are performed by different threads, or
• they are unsequenced, at least one is performed by a signal handler, and they are not both performed by the same signal handler invocation.

The execution of a program contains a data race if it contains two potentially concurrent conflicting actions, at least one of which is not atomic, and neither happens before the other, except for the special case for signal handlers described below. Any such data race results in undefined behavior. ...

The special case is not very relevant to the question, but I'll include it for completeness:

Two accesses to the same object of type volatile std::sig_­atomic_­t do not result in a data race if both occur in the same thread, even if one or more occurs in a signal handler. ...

The text of your question seems to be missing the point of the example and out-of-thin-air values. Your example does not contain data-race UB. (It might if x or y were set to 42 before those threads ran, in which case all bets are off and the other answers citing data-race UB apply.)

There is no protection against real data races, only against out-of-thin-air values.

I think you're really asking how to reconcile that mo_relaxed example with sane and well-defined behaviour for non-atomic variables. That's what this answer covers.

The note is pointing out a hole in the atomic mo_relaxed formalism, not warning you of a real possible effect on some implementations.

This gap does not (I think) apply to non-atomic objects, only to mo_relaxed.

They say However, implementations should not allow such behavior. – end note]. Apparently the standards committee couldn't find a way to formalize that requirement so for now it's just a note, but is not intended to be optional.

It's clear that even though this isn't strictly normative, the C++ standard intends to disallow out-of-thin-air values for relaxed atomic (and in general I assume). Later standards discussion, e.g. 2018's p0668r5: Revising the C++ memory model (which doesn't "fix" this, it's an unrelated change) includes juicy side-nodes like:

We still do not have an acceptable way to make our informal (since C++14) prohibition of out-of-thin-air results precise. The primary practical effect of that is that formal verification of C++ programs using relaxed atomics remains unfeasible. The above paper suggests a solution similar to http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3710.html . We continue to ignore the problem here ...

So yes, the normative parts of the standard are apparently weaker for relaxed_atomic than they are for non-atomic. This seems to be an unfortunately side effect of how they define the rules.

AFAIK no implementations can produce out-of-thin-air values in real life.

Later versions of the standard phrase the informal recommendation more clearly, e.g. in the current draft: https://timsong-cpp.github.io/cppwp/atomics.order#8

8. Implementations should ensure that no “out-of-thin-air” values are computed that circularly depend on their own computation.
   ...

9. [ Note: The recommendation [of 8.] similarly disallows r1 == r2 == 42 in the following example, with x and y again initially zero:

      // Thread 1:   r1 = x.load(memory_order::relaxed);   if (r1 == 42) y.store(42, memory_order::relaxed);   // Thread 2:   r2 = y.load(memory_order::relaxed);   if (r2 == 42) x.store(42, memory_order::relaxed);

   — end note ]

(This rest of the answer was written before I was sure that the standard intended to disallow this for mo_relaxed, too.)

I'm pretty sure the C++ abstract machine does not allow r1 == r2 == 42.
Every possible ordering of operations in the C++ abstract machine operations leads to r1=r2=0 without UB, even without synchronization. Therefore the program has no UB and any non-zero result would violate the "as-if" rule.

Formally, ISO C++ allows an implementation to implement functions / programs in any way that gives the same result as the C++ abstract machine would. For multi-threaded code, an implementation can pick one possible abstract-machine ordering and decide that's the ordering that always happens. (e.g. when reordering relaxed atomic stores when compiling to asm for a strongly-ordered ISA. The standard as written even allows coalescing atomic stores but compilers choose not to). But the result of the program always has to be something the abstract machine could have produced. (Only the Atomics chapter introduces the possibility of one thread observing the actions of another thread without mutexes. Otherwise that's not possible without data-race UB).

I think the other answers didn't look carefully enough at this. (And neither did I when it was first posted). Code that doesn't execute doesn't cause UB (including data-race UB), and compilers aren't allowed to invent writes to objects. (Except in code paths that already unconditionally write them, like y = (x==42) ? 42 : y; which would obviously create data-race UB.)

For any non-atomic object, if don't actually write it then other threads might also be reading it, regardless of code inside not-executed if blocks. The standard allows this and doesn't allow a variable to suddenly read as a different value when the abstract machine hasn't written it. (And for objects we don't even read, like neighbouring array elements, another thread might even be writing them.)

Therefore we can't do anything that would let another thread temporarily see a different value for the object, or step on its write. Inventing writes to non-atomic objects is basically always a compiler bug; this is well known and universally agreed upon because it can break code that doesn't contain UB (and has done so in practice for a few cases of compiler bugs that created it, e.g. IA-64 GCC I think had such a bug at one point that broke the Linux kernel). IIRC, Herb Sutter mentioned such bugs in part 1 or 2 of his talk, atomic<> Weapons: The C++ Memory Model and Modern Hardware", saying that it was already usually considered a compiler bug before C++11, but C++11 codified that and made it easier to be sure.

Or another recent example with ICC for x86:Crash with icc: can the compiler invent writes where none existed in the abstract machine?

In the C++ abstract machine, there's no way for execution to reach either y = r1; or x = r2;, regardless of sequencing or simultaneity of the loads for the branch conditions. x and y both read as 0 and neither thread ever writes them.

No synchronization is required to avoid UB because no order of abstract-machine operations leads to a data-race. The ISO C++ standard doesn't have anything to say about speculative execution or what happens when mis-speculation reaches code. That's because speculation is a feature of real implementations, not of the abstract machine. It's up to implementations (HW vendors and compiler writers) to ensure the "as-if" rule is respected.

It's legal in C++ to write code like if (global_id == mine) shared_var = 123; and have all threads execute it, as long as at most one thread actually runs the shared_var = 123; statement. (And as long as synchronization exists to avoid a data race on non-atomic int global_id). If things like this broke down, it would be chaos. For example, you could apparently draw wrong conclusions like reordering atomic operations in C++

Observing that a non-write didn't happen isn't data-race UB.

It's also not UB to run if(i<SIZE) return arr[i]; because the array access only happens if i is in bounds.

I think the "out of the blue" value-invention note only applies to relaxed-atomics, apparently as a special caveat for them in the Atomics chapter. (And even then, AFAIK it can't actually happen on any real C++ implementations, certainly not mainstream ones. At this point implementations don't have to take any special measures to make sure it can't happen for non-atomic variables.)

I'm not aware of any similar language outside the atomics chapter of the standard that allows an implementation to allow values to appear out of the blue like this.

I don't see any sane way to argue that the C++ abstract machine causes UB at any point when executing this, but seeing r1 == r2 == 42 would imply that unsynchronized read+write had happened, but that's data-race UB. If that can happen, can an implementation invent UB because of speculative execution (or some other reason)? The answer has to be "no" for the C++ standard to be usable at all.

For relaxed atomics, inventing the 42 out of nowhere wouldn't imply that UB had happened; perhaps that's why the standard says it's allowed by the rules? As far as I know, nothing outside the Atomics chapter of the standard allows it.

A hypothetical asm / hardware mechanism that could cause this

(Nobody wants this, hopefully everyone agrees that it would be a bad idea to build hardware like this. It seems unlikely that coupling speculation across logical cores would ever be worth the downside of having to roll back all cores when one detects a mispredict or other mis-speculation.)

For 42 to be possible, thread 1 has to see thread 2's speculative store and the store from thread 1 has to be seen by thread 2's load. (Confirming that branch speculation as good, allowing this path of execution to become the real path that was actually taken.)

i.e. speculation across threads: Possible on current HW if they ran on the same core with only a lightweight context switch, e.g. coroutines or green threads.

But on current HW, memory reordering between threads is impossible in that case. Out-of-order execution of code on the same core gives the illusion of everything happening in program order. To get memory reordering between threads, they need to be running on different cores.

So we'd need a design that coupled together speculation between two logical cores. Nobody does that because it means more state needs to rollback if a mispredict is detected. But it is hypothetically possible. For example an OoO SMT core that allows store-forwarding between its logical cores even before they've retired from the out-of-order core (i.e. become non-speculative).

PowerPC allows store-forwarding between logical cores for retired stores, meaning that threads can disagree about the global order of stores. But waiting until they "graduate" (i.e. retire) and become non-speculative means it doesn't tie together speculation on separate logical cores. So when one is recovering from a branch miss, the others can keep the back-end busy. If they all had to rollback on a mispredict on any logical core, that would defeat a significant part of the benefit of SMT.

I thought for a while I'd found an ordering that lead to this on single core of a real weakly-ordered CPUs (with user-space context switching between the threads), but the final step store can't forward to the first step load because this is program order and OoO exec preserves that.

• T2: r2 = y; stalls (e.g. cache miss)

• T2: branch prediction predicts that r2 == 42 will be true. ( x = 42 should run.

• T2: x = 42 runs. (Still speculative; r2 = yhasn't obtained a value yet so ther2 == 42` compare/branch is still waiting to confirm that speculation).

• a context switch to Thread 1 happens without rolling back the CPU to retirement state or otherwise waiting for speculation to be confirmed as good or detected as mis-speculation.

  This part won't happen on real C++ implementations unless they use an M:N thread model, not the more common 1:1 C++ thread to OS thread. Real CPUs don't rename the privilege level: they don't take interrupts or otherwise enter the kernel with speculative instructions in flight that might need to rollback and redo entering kernel mode from a different architectural state.

• T1: r1 = x; takes its value from the speculative x = 42 store

• T1: r1 == 42 is found to be true. (Branch speculation happens here, too, not actually waiting for store-forwarding to complete. But along this path of execution, where the x = 42 did happen, this branch condition will execute and confirm the prediction).

• T1: y = 42 runs.

• this was all on the same CPU core so this y=42 store is after the r2=y load in program-order; it can't give that load a 42 to let the r2==42 speculation be confirmed. So this possible ordering doesn't demonstrate this in action after all. This is why threads have to be running on separate cores with inter-thread speculation for effects like this to be possible.

Note that x = 42 doesn't have a data dependency on r2 so value-prediction isn't required to make this happen. And the y=r1 is inside an if(r1 == 42) anyway so the compiler can optimize to y=42 if it wants, breaking the data dependency in the other thread and making things symmetric.

Note that the arguments about Green Threads or other context switch on a single core isn't actually relevant: we need separate cores for the memory reordering.

I commented earlier that I thought this might involve value-prediction. The ISO C++ standard's memory model is certainly weak enough to allow the kinds of crazy "reordering" that value-prediction can create to use, but it's not necessary for this reordering. y=r1 can be optimized to y=42, and the original code includes x=42 anyway so there's no data dependency of that store on the r2=y load. Speculative stores of 42 are easily possible without value prediction. (The problem is getting the other thread to see them!)

Speculating because of branch prediction instead of value prediction has the same effect here. And in both cases the loads need to eventually see 42 to confirm the speculation as correct.

Value-prediction doesn't even help make this reordering more plausible. We still need inter-thread speculation and memory reordering for the two speculative stores to confirm each other and bootstrap themselves into existence.

ISO C++ chooses to allow this for relaxed atomics, but AFAICT is disallows this non-atomic variables. I'm not sure I see exactly what in the standard does allow the relaxed-atomic case in ISO C++ beyond the note saying it's not explicitly disallowed. If there was any other code that did anything with x or y then maybe, but I think my argument does apply to the relaxed atomic case as well. No path through the source in the C++ abstract machine can produce it.

As I said, it's not possible in practice AFAIK on any real hardware (in asm), or in C++ on any real C++ implementation. It's more of an interesting thought-experiment into crazy consequences of very weak ordering rules, like C++'s relaxed-atomic. (Those ordering rules don't disallow it, but I think the as-if rule and the rest of the standard does, unless there's some provision that allows relaxed atomics to read a value that was never actually written by any thread.)

If there is such a rule, it would only be for relaxed atomics, not for non-atomic variables. Data-race UB is pretty much all the standard needs to say about non-atomic vars and memory ordering, but we don't have that.

What part of the so called "memory model" protects non atomic objects from these interactions caused by reads that see the interaction?

None. In fact, you get the opposite and the standard explicitly calls this out as undefined behavior. In [intro.races]\21 we have

The execution of a program contains a data race if it contains two potentially concurrent conflicting actions, at least one of which is not atomic, and neither happens before the other, except for the special case for signal handlers described below. Any such data race results in undefined behavior.

which covers your second example.

The rule is that if you have shared data in multiple threads, and at least one of those threads write to that shared data, then you need synchronization. Without that you have a data race and undefined behavior. Do note that volatile is not a valid synchronization mechanism. You need atomics/mutexs/condition variables to protect shared access.