Re: [PATCH 2/2 v2 RFC] tools/memory-model: redefine rb in terms of rcu-fence

[Boqun Feng]

On Wed, Feb 28, 2018 at 03:13:54PM -0500, Alan Stern wrote:
> 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>
> 
> ---
> 
> v2: Rebase on top of the preceding patch which renames "link" to
> "rcu-link" and "rcu-path" to "rb".  Add back the missing "rec" keyword
> in the definition of rcu-fence.  Minor editing improvements in
> explanation.txt.
> 
> Index: usb-4.x/tools/memory-model/linux-kernel.cat
> ===================================================================
> --- usb-4.x.orig/tools/memory-model/linux-kernel.cat
> +++ usb-4.x/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

I wonder whether we can simplify things as:

	let rec rcu-fence =
	    (gp; rcu-link; rscs) |
	    (rscs; rcu-link; gp) |
	    (gp; rcu-link; rcu-fence; rcu-link; rscs) |
	    (rscs; rcu-link; rcu-fence; rcu-link; gp)
	
	(* gp and rcu-fence; rcu-link; rcu-fence removed *)
	
	let rb = prop; rcu-fence; hb*; pb*

	acycle rb as rcu

In this way, "rcu-fence" is defined as "any sequence containing as many
grace periods as RCU read-side critical sections (joined by rcu-link)."
Note that "rcu-link" contains "gp", so we don't miss the case where
there are more grace periods. And since we use "acycle" now, so we don't
need "rcu-fence; rcu-link; rcu-fence" to build "rcu-fence" recursively.

I prefer this because we already treat "gp" as "strong-fence", which
already is a "rcu-link". Also, recurisively extending rcu-fence with
itself is exactly calculating the transitive closure, which we can avoid
by using a "acycle" rule. Besides, it looks more consistent with hb and
pb.

Thoughts?

Regards,
Boqun


> +
> +(*
> + * 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
> + *)
> Index: usb-4.x/tools/memory-model/Documentation/explanation.txt
> ===================================================================
> --- usb-4.x.orig/tools/memory-model/Documentation/explanation.txt
> +++ usb-4.x/tools/memory-model/Documentation/explanation.txt
> @@ -27,7 +27,7 @@ Explanation of the Linux-Kernel Memory C
>    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 c
>  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 u
>  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:
> -
> -	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 ->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.
> +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 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 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
>  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
>  	}
>  
>  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
>  --------------------	--------------------	--------------------
> 
>

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