From: Alan Stern <stern@xxxxxxxxxxxxxxxxxxx> 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@xxxxxxxxxxxxxxxxxxx> Reviewed-by: Andrea Parri <parri.andrea@xxxxxxxxx> Signed-off-by: Paul E. McKenney <paulmck@xxxxxxxxxxxxxxxxxx> --- tools/memory-model/Documentation/explanation.txt | 168 +++++++++++++++-------- tools/memory-model/linux-kernel.cat | 33 +++-- 2 files changed, 129 insertions(+), 72 deletions(-) diff --git a/tools/memory-model/Documentation/explanation.txt b/tools/memory-model/Documentation/explanation.txt index 1a387d703212..1b09f3175a1f 100644 --- a/tools/memory-model/Documentation/explanation.txt +++ b/tools/memory-model/Documentation/explanation.txt @@ -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. - -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. +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 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 -------------------- -------------------- -------------------- diff --git a/tools/memory-model/linux-kernel.cat b/tools/memory-model/linux-kernel.cat index cdf682859d4e..1e5c4653dd12 100644 --- a/tools/memory-model/linux-kernel.cat +++ b/tools/memory-model/linux-kernel.cat @@ -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 + *) -- 2.5.2
