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SubjectRe: Adding plain accesses and detecting data races in the LKMM
On Tue, 2 Apr 2019, Andrea Parri wrote:

> On Tue, Mar 19, 2019 at 03:38:19PM -0400, Alan Stern wrote:
> > LKMM maintainers and other interested parties:
> >
> > Here is my latest proposal for extending the Linux Kernel Memory Model
> > to handle plain accesses and data races. The document below explains
> > the rationale behind the proposal, and a patch (based on the dev
> > branch of Paul's linux-rcu tree) is attached.
> Thank you for this! Unfortunately, I didn't have enough time to give it
> justice yet... Below are some first thoughts/questions.

Thanks for the feedback.

> > This extension is not a complete treatment of plain accesses, because
> > it pretty much ignores any ordering that plain accesses can provide.
> > For example, given:
> >
> > r0 = rcu_dereference(ptr);
> > r1 = r0->branch;
> > r2 = READ_ONCE(&r1->data);
> >
> > the memory model will not realize that the READ_ONCE must execute after
> > the rcu_dereference, because it doesn't take into account the address
> > dependency from the intermediate plain read. Hopefully we will add
> > such things to the memory model later on. Concentrating on data races
> > seems like enough for now.
> >
> > Some of the ideas below were originally proposed for the LKMM by Andrea
> > Parri.
> >
> > Alan
> >
> > -----------------------------------------------------------------------
> >
> > A Plan For Modeling Plain Accesses In The Linux Kernel Memory Model
> >
> > Definition: A "plain" access is one which is not "marked". Marked
> > accesses include all those annotated with READ_ONCE or WRITE_ONCE,
> > plus acquire and release accesses, Read-Modify-Write (RMW) atomic
> > and bitop accesses, and locking accesses.
> >
> > Plain accesses are those the compiler is free to mess around with.
> > Marked accesses are implemented in the kernel by means of inline
> > assembly or as volatile accesses, which greatly restricts what the
> > compiler can do.
> >
> > Definition: A "region" of code is a program-order source segment
> > contained in a single thread that is maximal with respect to not
> > containing any compiler barriers (i.e., it is bounded at each end by
> > either a compiler barrier or the start or end of its thread).
> >
> > Assumption: All memory barriers are also compiler barriers. This
> > includes acquire loads and release stores, which are not considered to
> > be compiler barriers in the C++11 Standard, as well as non-relaxed RMW
> > atomic operations. (Question: should this include situation-specific
> > memory barriers such as smp_mb__after_unlock_lock? Probably not.)
> I'd have:
> *x = 1; /* A */
> smp_mb__before_atomic();
> r0 = xchg_relaxed(x, 2); /* B (read or write part) */
> => (A ->barrier B)

Perhaps so. It wasn't clear initially how these should be treated, so
I just ignored them. For example, what should happen here if there
were other statements between the smp_mb__before_atomic and the

> smp_mb__after_unlock_lock() seems more tricky, given that it generates
> inter-threads links.

The inter-thread part is completely irrelevant as far as compiler
barriers are concerned.

> Intuitively, we would have a "barrier" that is a superset of "mb" (I'm
> not saying that this is feasible, but this seems worth considering...)

I don't understand that comment.

> ---
> I don't get the motivations for the component:
> (po ; [Acquire | Release]) |
> ([Acquire | Release] ; po)
> in "barrier". Why did you write it?

I was thinking that in situations like:

A: z = 1;
B: smp_store_release(z, 2);
C: r = z;

in addition to there being a compiler barrier between A and C, there
effectively has to be a barrier between A and B (that is, the object
code has to store first 1 and then 2 to z) and between B and C (that
is, the object code can't skip doing the load from z and just set r to

The basic principle was the idea that load-acquire and store-release
are special because each of them is both a memory access and a memory
barrier at the same time. Now, I didn't give this a tremendous amount
of thought and it's quite possible that the Cat code should be changed.
For example, maybe there should be a compiler barrier immediately
before a store-release but not immediately after, and vice versa for

> Also, consider the snippets:
> WRITE_ONCE(*x, 1);
> *x = 2;
> and
> smp_store_release(x, 1);
> *x = 2;
> The first snippet would be flagged "mixed-accesses" by the patch while
> the second snippet would not (thanks to the above component); was this
> intentional? (Notice that some implementations map the latter to:
> barrier();
> WRITE_ONCE(*x, 1);
> *x = 2;
> )

That last observation is a good reason for changing the Cat code.

> > To avoid complications, the LKMM will consider only code in which
> > plain writes are separated by a compiler barrier from any marked
> > accesses of the same location. (Question: Can this restriction be
> > removed?) As a consequence, if a region contains any marked accesses
> > to a particular location then it cannot contain any plain writes to
> > that location.
> I don't know if it can be removed... Said this, maybe we should go back
> to the (simpler?) question: "What can go wrong without the restriction?",
> ;-) IOW, what are those "complications", can you provide some examples?

Here's an example I sent to Will a little while ago. Suppose we

r = rcu_dereference(ptr);
*r = 1;

Imagine if the compiler transformed this to:

r = rcu_dereference(ptr);
if (r != &x)
*r = 1;

This is bad because it destroys the address dependency when ptr
contains &x.

> > This analysis is guided by the intuition that one can set up a limited
> > correspondence between an execution of the source code and an
> > execution of the generated object code. Such a correspondence is
> > based on some limitations on what compilers can do when translating a
> > program:
> >
> > Each marked access in the source-level execution must
> > correspond to a unique instruction in the object-level
> > execution. The corresponding events must access the same
> > location, have the same values, and be of the same type (read
> > or write).
> >
> > If a marked access is address-dependent on a marked read then
> > the corresponding object-level instructions must have the same
> > dependency (i.e., the compiler does not break address
> > dependencies for marked accesses).
> We known that this "limitation" does not hold, in this generality. Your
> proposal goes even further than that (by adding address dep. from marked
> reads to marked accesses): A warning, maybe also a pointer to doc. such
> as Documentation/RCU/rcu_dereference.txt wouldn't have hurt! ;-)


> > If a source region contains no plain accesses to a location
> > then the corresponding object-level region contains no
> > accesses to that location other than those corresponding to
> > marked accesses.
> >
> > If a source region contains no plain writes to a location then
> > the corresponding object-level region contains no stores to
> > that location other than those corresponding to marked writes.
> >
> > If a source region contains a plain write then the object code
> > corresponding to that region must contain at least one access
> > (it could be a load instead of a store) to the same location.
> >
> > If all the accesses to a particular location in some source
> > region are address-dependent on one of the marked reads in
> > some set S then every object-level access of that location
> > must be dependent (not necessarily address-dependent, when the
> > access is a store) on one of the instructions corresponding to
> > the members of S.
> >
> > The object code for a region must ensure that the final value
> > stored in a location is the same as the value of the po-final
> > source write in the region.
> >
> > The positions of the load and store instructions in the object code
> > for a region do not have to bear any particular relation to the plain
> > accesses in the source code. Subject to the restrictions above, a
> > sequence of m plain writes in the source could be implemented by a
> > sequence of n store instructions at runtime where n is <, =, or > m,
> > and likewise for plain reads.
> >
> > Similarly, the rf, co, and fr relations for plain accesses in
> > source-level executions have very limited meaning.
> >
> > Given an object-level execution, let A1 and B1 be accesses in region
> > R1 and let A2 and B2 be accesses in region R2, all of the same
> > location, not all reads, and not all corresponding to marked accesses.
> > (We explicitly allow A1 and B1 to be the same access, and the same for
> > A2 and B2.) The execution has a data race if the coherence ordering
> > from A1 to A2 is opposite to the ordering from B1 to B2.
> >
> > Definition: Two accesses of the same location "conflict" if they are
> > in different threads, they are not both marked, and they are not both
> > reads.
> >
> > The notions "executes before" and "is visible to" have already been
> > defined for marked accesses in the LKMM or in earlier proposals for
> > handling plain accesses (the xb -- or more properly, xb* -- and vis
> > relations). I trust the ideas are familiar to everyone. Note that
> > vis is contained in xb. Also note that the vis relation is not
> > transitive, because smp_wmb is not A-cumulative. That is, it's
> > possible for W1 to be visible to W2 and W2 to be visible to W3,
> > without W1 being visible to W3. (However, on systems that are other
> > multicopy-atomic, vis is indeed transitive.)
> >
> > We want to define data races for source programs in such a way that a
> > race-free source program has no data races in any of its object-level
> > executions. To that end, we could begin with some requirements:
> >
> > For any two conflicting writes, one must be visible to the
> > other.
> >
> > For a write conflicting with a read, either the write must be
> > visible to the read or the read must execute before the write.
> I'm missing the link with the notion of "data race of an object-level
> execution" given above (it is possible that I did not understand that
> description): could you elaborate? (maybe by providing some examples)

The argument here is based on an unstated principle (I didn't state it
explicitly because I don't know if it is really true): Given a
candidate execution in which write W is not visible to write X even
though W is co-before X, there is another, very similar (whatever
that means!) execution in which X is co-before W.

So consider as an example the case where W is a marked write which
conflicts with a plain write X. Since X is plain, the compiler is
allowed to generate object code which carries out the X write twice;
let's call these object-level writes X1 and X2. If W is not visible to
X1 and X2 and yet W ->co X2, the principle states that there is
an execution in which X1 ->co W ->co X2. This fits the object-level
definition of a data race above.

> > However, this isn't strong enough. A source-level write can give rise
> > to object-level loads as well as stores. Therefore whenever we
> > require that a plain write W be visible to some other access A, we
> > must also require that if W were a read then it would execute before
> > A. And similarly, if A is required to be visible to W, we must also
> > require that if W were a read then A would still be visible to it.
> >
> > At the same time, it is too strong. If W1 is required to be visible
> > to W2 and W2 is required to be visible to A, then W1 doesn't
> > necessarily have to be visible to A. Visibility is required only in
> > cases where W2 need not correspond to any object-level stores.
> >
> > Since vis and xb aren't defined for plain accesses, we have to extend
> > the definitions. We begin by saying that a plain access is pre- or
> > post-bounded by a marked access if the execution order can be
> > guaranteed, as follows.
> >
> > Definition:
> >
> > A write W is "w-post-bounded" by a po-later marked access A if
> > they are separated by an appropriate memory barrier (including
> > the case where A is a release write).
> >
> > A read R is "r-post-bounded" by a po-later marked access A if
> > they are separated by an appropriate memory barrier.
> >
> > Oddly, a plain write W is "r-post-bounded" by a po-later
> > marked access A whenever W would be considered to be
> > r-post-bounded by A if W were a read (for example, when A is a
> > read and the two are separated by smp_rmb).
> Looking at the patch, I see that a plain read can be "w-post-bounded":
> should/can we prevent this from happening?

It doesn't matter. w-post-bounded gets used only in situations where
the left-hand access is a write. (Unless I made a mistake somewhere.)

> > In addition, a marked write is w-post-bounded by itself and a
> > marked read is r-post-bounded by itself.
> >
> > An access being "w-pre-bounded" and "r-pre-bounded" by a
> > po-earlier marked access are defined analogously, except that
> > we also include cases where the later plain access is
> > address-dependent on the marked access.
> >
> > Note that as a result of these definitions, if one plain write is
> > w-post-bounded by a marked access than all the writes in the same
> > region are (this is because the memory barrier which enforces the
> > bounding is also a region delimiter). And if one plain access is
> > r-post-bounded by a marked access then all the plain accesses in the
> > same region are. The same cannot be said of w-pre-bounded and
> > r-pre-bounded, though, because of possible address dependencies.
> >
> > Definition: ww-vis, ww-xb, wr-vis, wr-xb, and rw-xb are given by the
> > following scheme. Let i and j each be either w or r, and let rel be
> > either vis or xb. Then access A is related to access D by ij-rel if
> > there are marked accesses B and C such that:
> >
> > A ->i-post-bounded B ->rel C ->j-pre-bounded D.
> >
> > For example, A is related by wr-vis to D if there are marked accesses
> > B and C such that A is w-post-bounded by B, B ->vis C, and C
> > r-pre-bounds D. In cases where A or D is marked, B could be equal to
> > A or C could be equal to D.
> >
> > As mentioned earlier, ww-vis is contained in ww-xb and wr-vis is
> > contained in wr-xb. It turns out that the LKMM can almost prove that
> > the ij-xb relations are transitive, in the following sense. If W is a
> > write and R is a read, then:
> >
> > (A ->iw-xb W ->wj-xb C) implies (A ->ij-xb C), and
> >
> > (A ->ir-xb R ->rj-xb C) implies (A ->ij-xb C).
> >
> > To fully prove this requires adding one new term to the ppo relation:
> >
> > [Marked & R] ; addr ; [Plain & W] ; wmb ; [Marked & W]
> ... or removing any of these links, right?

I don't understand. Remove any of which links? Remove it from the
candidate execution or from the memory model?

> > For example, given the code:
> >
> > r = READ_ONCE(ptr);
> > *r = 27;
> > smp_wmb();
> > WRITE_ONCE(x, 1);
> >
> > the new term says that the READ_ONCE must execute before the
> > WRITE_ONCE. To justify this, note that the object code is obliged to
> > ensure that *r contains 27 (or some co-later value) before the smp_wmb
> > executes. It can do so in one of three ways:
> >
> > (1) Actually store a 27 through the *r pointer;
> >
> > (2) Load through the *r pointer and check that the location already
> > holds 27; or
> >
> > (3) Check that r aliases a pointer to a location known to hold 27
> > already.
> >
> > In case (1), the ordering is enforced by the address dependency and
> > the smp_wmb. In case (2) there is an address dependency to the *r
> > load and a conditional depending on that load. Control dependencies
> > in object-code executions extend to all po-later stores; hence the
> > WRITE_ONCE must be ordered after the *r load. In case (3) there is a
> > conditional depending on the READ_ONCE and po-before the WRITE_ONCE.
> The proposed model is unsound w.r.t. (2); c.f., LB1 vs. LB2 from:

Again, I don't understand. What's unsound about the proposed model?

For LB1 it says that the WRITE_ONCE must execute after the
rcu_dereference, which is correct. For LB2 it doesn't say anything,
because in LB2 there is no plain write event between the
rcu_dereference and the smp_wmb events.

> Mmh..., no particular suggestions at the moment (just blaming "addr"
> and "wmb", I guess ;-) ); the fact is that "soundness" looks like a
> very desirable property...
> >
> > With this new term added, the LKMM can show that a cycle in the ij-xb
> > relations would give rise to a cycle in xb of marked accesses. It
> > follows that in an allowed execution, the regions containing accesses
> > to a particular location x can be totally ordered in a way compatible
> > with the ij-xb relations, and this ordering must agree with the co and
> > rf orderings for x.
> >
> > Therefore we can try defining a race-free execution to be one which
> > obeys the following requirements:
> >
> > ww-race: If W1 ->co W2 and the two writes conflict then we must have
> > W1 ->ww-vis W2. If W1 is a plain write then we must also have
> > W1 ->rw-xb W2, and if W2 is a plain write then we must also
> > have W1 ->wr-vis W2.
> >
> > wr-race: If W ->(co?;rf) R and the two accesses conflict then we must
> > have W ->wr-vis R.
> >
> > rw-race: If R ->fr W and the two accesses conflict then we must have
> > R ->rw-xb W.
> >
> > However, as described earlier, this is stronger than we really need.
> > In ww-race, we don't need to have W1 ->ww-vis W2 or W1 ->wr-vis W2 if
> > there is a third write W3 in between such that W3 must give rise to a
> > store in the object code. In this case it doesn't matter whether W1
> > is visible to W2 or not; they can't race because W3 will be visible to
> > W2 and being co-later than W1, it will prevent W1 from interfering
> > with W2. Much the same is true for wr-race.
> >
> > If W3 is a marked write, it certainly corresponds to a write in the
> > object code. But what if it is a plain write?
> >
> > Definition: A write is "major" if it is not overwritten by any
> > po-later writes in its region. A major write is "super" if it has a
> > different value from the co-preceding major write. In addition, all
> > marked writes are considered to be super.
> >
> > If a region contains a super write then the object code for the region
> > must contain a store to the write's location. Otherwise, when
> > execution reached the end of the region at runtime, the value
> > contained in that location would still be the value from the end of
> > the preceding region -- that is, the value would be wrong.
> >
> > Thus, ww-race need not apply if there is a super write co-between W1
> > and W2. Likewise, wr-race need not apply if there is a super write
> > co-after W and co?-before the write which R reads from. Note that
> > these weakenings do not apply in situations where W2 is the co-next
> > write after W1 or when R reads from W; in such cases ww-race and
> > wr-race retain their full force.
> I don't know yet... Frankly, this idea of "semantics depending on the
> _values_ of plain accesses" simply scares me. ;-)

Unfortunately, that's how computer programs work in the real world:
Their behavior depends on the values that reads obtain.

> Let's look at your "non-transitive-wmb" test: I tend to read the write
> "*x = 2" as nothing more than "write 2 to the 1st byte, write 0 to the
> 2nd byte, write 0 to the next byte, ..."; and similarly for "*x = 1";

That's already a mistake. The compiler can do extraordinary things to
the code. It doesn't have to end up being anything as simple as "write
2 to the 1st byte, ...".

> maybe some of these writes aren't performed at all (the compiler knows
> that the most significant byte, say, is never touched/modified); maybe
> they intersect (overwrite) one another... what else?

That's the thing. According to one of the assumptions listed earlier
in this document, it's not possible that the "write 2 to the 1st byte"
access isn't performed at all. The higher-order bytes, yes, they might
not be touched. But if no writes are performed at all then at the end
of the region *x will contain 1, not 2 -- and that would be a bug in
the compiler.

> So, for example,
> if we "slice" the most significant parts of the plain writes in P0 and
> P1 then they have the "same value" in a certain sense.
> Mmh, I still don't feel comfortable with these concepts sorry, maybe I
> just need more time to process them...
> >
> > The LKMM also has to detect forbidden executions involving plain
> > accesses. There are three obvious coherence-related checks:
> >
> > If W ->rf R then we must not have R ->rw-xb W.
> >
> > If R ->fr W then we must not have W ->wr-vis R.
> >
> > If W1 ->co W2 then we must not have W2 ->ww-vis W1.
> >
> > (Question: Are these checks actually correct? I'm not certain; they
> > are hard to reason about because co, rf, and fr don't have clear
> > meanings for plain accesses in racy executions.)
> So maybe they were not that "obvious". ;-)

Well, they were pretty obvious to me -- they are just restatements of
the coherence-related rules in the operational model. Of course,
"obvious" doesn't always mean "correct".

> This all deserves a careful review and testing; unfortunately, I doubt
> that I'll be able to do much more in the next couple of weeks. bbl,

Good luck on all the more pressing engagements!


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