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tools/memory-model: Redefine rb in terms of rcu-fence

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This patch reorganizes the definition of rb in the Linux Kernel Memory
Consistency Model.  The relation is now expressed in terms of
rcu-fence, which consists of a sequence of gp and rscs links separated
by rcu-link links, in which the number of occurrences of gp is >= the
number of occurrences of rscs.

Arguments similar to those published in
http://diy.inria.fr/linux/long.pdf show that rcu-fence behaves like an
inter-CPU strong fence.  Furthermore, the definition of rb in terms of
rcu-fence is highly analogous to the definition of pb in terms of
strong-fence, which can help explain why rcu-path expresses a form of
temporal ordering.

This change should not affect the semantics of the memory model, just
its internal organization.

Signed-off-by: Alan Stern <stern@rowland.harvard.edu>
Signed-off-by: Paul E. McKenney <paulmck@linux.vnet.ibm.com>
Reviewed-by: Boqun Feng <boqun.feng@gmail.com>
Reviewed-by: Andrea Parri <parri.andrea@gmail.com>
Cc: Andrew Morton <akpm@linux-foundation.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: Will Deacon <will.deacon@arm.com>
Cc: akiyks@gmail.com
Cc: dhowells@redhat.com
Cc: j.alglave@ucl.ac.uk
Cc: linux-arch@vger.kernel.org
Cc: luc.maranget@inria.fr
Cc: npiggin@gmail.com
Link: http://lkml.kernel.org/r/1526340837-12222-2-git-send-email-paulmck@linux.vnet.ibm.com
Signed-off-by: Ingo Molnar <mingo@kernel.org>
This commit is contained in:
Alan Stern 2018-05-14 16:33:40 -07:00 committed by Ingo Molnar
parent 1ee2da5f9b
commit 9d036883a1
2 changed files with 128 additions and 71 deletions
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166
tools/memory-model/Documentation/explanation.txt
View File

@ -27,7 +27,7 @@ Explanation of the Linux-Kernel Memory Consistency Model
19. AND THEN THERE WAS ALPHA
20. THE HAPPENS-BEFORE RELATION: hb
21. THE PROPAGATES-BEFORE RELATION: pb
22. RCU RELATIONS: rcu-link, gp-link, rscs-link, and rb
22. RCU RELATIONS: rcu-link, gp, rscs, rcu-fence, and rb
23. ODDS AND ENDS
@ -1451,8 +1451,8 @@ they execute means that it cannot have cycles. This requirement is
the content of the LKMM's "propagation" axiom.
RCU RELATIONS: rcu-link, gp-link, rscs-link, and rb
---------------------------------------------------
RCU RELATIONS: rcu-link, gp, rscs, rcu-fence, and rb
----------------------------------------------------
RCU (Read-Copy-Update) is a powerful synchronization mechanism. It
rests on two concepts: grace periods and read-side critical sections.
@ -1537,49 +1537,100 @@ relation, and the details don't matter unless you want to comb through
a somewhat lengthy formal proof. Pretty much all you need to know
about rcu-link is the information in the preceding paragraph.
The LKMM goes on to define the gp-link and rscs-link relations. They
bring grace periods and read-side critical sections into the picture,
in the following way:
The LKMM also defines the gp and rscs relations. They bring grace
periods and read-side critical sections into the picture, in the
following way:
E ->gp-link F means there is a synchronize_rcu() fence event S
and an event X such that E ->po S, either S ->po X or S = X,
and X ->rcu-link F. In other words, E and F are linked by a
grace period followed by an instance of rcu-link.
E ->gp F means there is a synchronize_rcu() fence event S such
that E ->po S and either S ->po F or S = F. In simple terms,
there is a grace period po-between E and F.
E ->rscs-link F means there is a critical section delimited by
an rcu_read_lock() fence L and an rcu_read_unlock() fence U,
and an event X such that E ->po U, either L ->po X or L = X,
and X ->rcu-link F. Roughly speaking, this says that some
event in the same critical section as E is linked by rcu-link
to F.
E ->rscs F means there is a critical section delimited by an
rcu_read_lock() fence L and an rcu_read_unlock() fence U, such
that E ->po U and either L ->po F or L = F. You can think of
this as saying that E and F are in the same critical section
(in fact, it also allows E to be po-before the start of the
critical section and F to be po-after the end).
If we think of the rcu-link relation as standing for an extended
"before", then E ->gp-link F says that E executes before a grace
period which ends before F executes. (In fact it covers more than
this, because it also includes cases where E executes before a grace
period and some store propagates to F's CPU before F executes and
doesn't propagate to some other CPU until after the grace period
ends.) Similarly, E ->rscs-link F says that E is part of (or before
the start of) a critical section which starts before F executes.
"before", then X ->gp Y ->rcu-link Z says that X executes before a
grace period which ends before Z executes. (In fact it covers more
than this, because it also includes cases where X executes before a
grace period and some store propagates to Z's CPU before Z executes
but doesn't propagate to some other CPU until after the grace period
ends.) Similarly, X ->rscs Y ->rcu-link Z says that X is part of (or
before the start of) a critical section which starts before Z
executes.
The LKMM goes on to define the rcu-fence relation as a sequence of gp
and rscs links separated by rcu-link links, in which the number of gp
links is >= the number of rscs links. For example:
X ->gp Y ->rcu-link Z ->rscs T ->rcu-link U ->gp V
would imply that X ->rcu-fence V, because this sequence contains two
gp links and only one rscs link. (It also implies that X ->rcu-fence T
and Z ->rcu-fence V.) On the other hand:
X ->rscs Y ->rcu-link Z ->rscs T ->rcu-link U ->gp V
does not imply X ->rcu-fence V, because the sequence contains only
one gp link but two rscs links.
The rcu-fence relation is important because the Grace Period Guarantee
means that rcu-fence acts kind of like a strong fence. In particular,
if W is a write and we have W ->rcu-fence Z, the Guarantee says that W
will propagate to every CPU before Z executes.
To prove this in full generality requires some intellectual effort.
We'll consider just a very simple case:
W ->gp X ->rcu-link Y ->rscs Z.
This formula means that there is a grace period G and a critical
section C such that:
1. W is po-before G;
2. X is equal to or po-after G;
3. X comes "before" Y in some sense;
4. Y is po-before the end of C;
5. Z is equal to or po-after the start of C.
From 2 - 4 we deduce that the grace period G ends before the critical
section C. Then the second part of the Grace Period Guarantee says
not only that G starts before C does, but also that W (which executes
on G's CPU before G starts) must propagate to every CPU before C
starts. In particular, W propagates to every CPU before Z executes
(or finishes executing, in the case where Z is equal to the
rcu_read_lock() fence event which starts C.) This sort of reasoning
can be expanded to handle all the situations covered by rcu-fence.
Finally, the LKMM defines the RCU-before (rb) relation in terms of
rcu-fence. This is done in essentially the same way as the pb
relation was defined in terms of strong-fence. We will omit the
details; the end result is that E ->rb F implies E must execute before
F, just as E ->pb F does (and for much the same reasons).
Putting this all together, the LKMM expresses the Grace Period
Guarantee by requiring that there are no cycles consisting of gp-link
and rscs-link links in which the number of gp-link instances is >= the
number of rscs-link instances. It does this by defining the rb
relation to link events E and F whenever it is possible to pass from E
to F by a sequence of gp-link and rscs-link links with at least as
many of the former as the latter. The LKMM's "rcu" axiom then says
that there are no events E with E ->rb E.
Guarantee by requiring that the rb relation does not contain a cycle.
Equivalently, this "rcu" axiom requires that there are no events E and
F with E ->rcu-link F ->rcu-fence E. Or to put it a third way, the
axiom requires that there are no cycles consisting of gp and rscs
alternating with rcu-link, where the number of gp links is >= the
number of rscs links.
Justifying this axiom takes some intellectual effort, but it is in
fact a valid formalization of the Grace Period Guarantee. We won't
attempt to go through the detailed argument, but the following
analysis gives a taste of what is involved. Suppose we have a
violation of the first part of the Guarantee: A critical section
starts before a grace period, and some store propagates to the
critical section's CPU before the end of the critical section but
doesn't propagate to some other CPU until after the end of the grace
period.
Justifying the axiom isn't easy, but it is in fact a valid
formalization of the Grace Period Guarantee. We won't attempt to go
through the detailed argument, but the following analysis gives a
taste of what is involved. Suppose we have a violation of the first
part of the Guarantee: A critical section starts before a grace
period, and some store propagates to the critical section's CPU before
the end of the critical section but doesn't propagate to some other
CPU until after the end of the grace period.
Putting symbols to these ideas, let L and U be the rcu_read_lock() and
rcu_read_unlock() fence events delimiting the critical section in
@ -1606,11 +1657,14 @@ by rcu-link, yielding:
S ->po X ->rcu-link Z ->po U.
The formulas say that S is po-between F and X, hence F ->gp-link Z
via X. They also say that Z comes before the end of the critical
section and E comes after its start, hence Z ->rscs-link F via E. But
now we have a forbidden cycle: F ->gp-link Z ->rscs-link F. Thus the
"rcu" axiom rules out this violation of the Grace Period Guarantee.
The formulas say that S is po-between F and X, hence F ->gp X. They
also say that Z comes before the end of the critical section and E
comes after its start, hence Z ->rscs E. From all this we obtain:
F ->gp X ->rcu-link Z ->rscs E ->rcu-link F,
a forbidden cycle. Thus the "rcu" axiom rules out this violation of
the Grace Period Guarantee.
For something a little more down-to-earth, let's see how the axiom
works out in practice. Consider the RCU code example from above, this
@ -1639,15 +1693,15 @@ time with statement labels added to the memory access instructions:
If r2 = 0 at the end then P0's store at X overwrites the value that
P1's load at Z reads from, so we have Z ->fre X and thus Z ->rcu-link X.
In addition, there is a synchronize_rcu() between Y and Z, so therefore
we have Y ->gp-link X.
we have Y ->gp Z.
If r1 = 1 at the end then P1's load at Y reads from P0's store at W,
so we have W ->rcu-link Y. In addition, W and X are in the same critical
section, so therefore we have X ->rscs-link Y.
section, so therefore we have X ->rscs W.
This gives us a cycle, Y ->gp-link X ->rscs-link Y, with one gp-link
and one rscs-link, violating the "rcu" axiom. Hence the outcome is
not allowed by the LKMM, as we would expect.
Then X ->rscs W ->rcu-link Y ->gp Z ->rcu-link X is a forbidden cycle,
violating the "rcu" axiom. Hence the outcome is not allowed by the
LKMM, as we would expect.
For contrast, let's see what can happen in a more complicated example:
@ -1683,15 +1737,11 @@ For contrast, let's see what can happen in a more complicated example:
}
If r0 = r1 = r2 = 1 at the end, then similar reasoning to before shows
that W ->rscs-link Y via X, Y ->gp-link U via Z, and U ->rscs-link W
via V. And just as before, this gives a cycle:
W ->rscs-link Y ->gp-link U ->rscs-link W.
However, this cycle has fewer gp-link instances than rscs-link
instances, and consequently the outcome is not forbidden by the LKMM.
The following instruction timing diagram shows how it might actually
occur:
that W ->rscs X ->rcu-link Y ->gp Z ->rcu-link U ->rscs V ->rcu-link W.
However this cycle is not forbidden, because the sequence of relations
contains fewer instances of gp (one) than of rscs (two). Consequently
the outcome is allowed by the LKMM. The following instruction timing
diagram shows how it might actually occur:
P0 P1 P2
-------------------- -------------------- --------------------

33
tools/memory-model/linux-kernel.cat
View File

@ -102,20 +102,27 @@ let rscs = po ; crit^-1 ; po?
*)
let rcu-link = hb* ; pb* ; prop
(* Chains that affect the RCU grace-period guarantee *)
let gp-link = gp ; rcu-link
let rscs-link = rscs ; rcu-link
(*
* A cycle containing at least as many grace periods as RCU read-side
* critical sections is forbidden.
* Any sequence containing at least as many grace periods as RCU read-side
* critical sections (joined by rcu-link) acts as a generalized strong fence.
*)
let rec rb =
gp-link |
(gp-link ; rscs-link) |
(rscs-link ; gp-link) |
(rb ; rb) |
(gp-link ; rb ; rscs-link) |
(rscs-link ; rb ; gp-link)
let rec rcu-fence = gp |
(gp ; rcu-link ; rscs) |
(rscs ; rcu-link ; gp) |
(gp ; rcu-link ; rcu-fence ; rcu-link ; rscs) |
(rscs ; rcu-link ; rcu-fence ; rcu-link ; gp) |
(rcu-fence ; rcu-link ; rcu-fence)
(* rb orders instructions just as pb does *)
let rb = prop ; rcu-fence ; hb* ; pb*
irreflexive rb as rcu
(*
* The happens-before, propagation, and rcu constraints are all
* expressions of temporal ordering. They could be replaced by
* a single constraint on an "executes-before" relation, xb:
*
* let xb = hb | pb | rb
* acyclic xb as executes-before
*)