Automate memory-barriers.txt; provide Linux-kernel memory model

There is some reason to believe that Documentation/memory-barriers.txt
could use some help, and a major purpose of this patch is to provide
that help in the form of a design-time tool that can produce all valid
executions of a small fragment of concurrent Linux-kernel code, which is
called a "litmus test". This tool's functionality is roughly similar to
a full state-space search. Please note that this is a design-time tool,
not useful for regression testing. However, we hope that the underlying
Linux-kernel memory model will be incorporated into other tools capable
of analyzing large bodies of code for regression-testing purposes.

The main tool is herd7, together with the linux-kernel.bell,
linux-kernel.cat, linux-kernel.cfg, linux-kernel.def, and lock.cat files
added by this patch. The herd7 executable takes the other files as input,
and all of these files collectively define the Linux-kernel memory memory
model. A brief description of each of these other files is provided
in the README file. Although this tool does have its limitations,
which are documented in the README file, it does improve on the version
reported on in the LWN series (https://lwn.net/Articles/718628/ and
https://lwn.net/Articles/720550/) by supporting locking and arithmetic,
including a much wider variety of read-modify-write atomic operations.
Please note that herd7 is not part of this submission, but is freely
available from http://diy.inria.fr/sources/index.html (and via "git"
at https://github.com/herd/herdtools7).

A second tool is klitmus7, which converts litmus tests to loadable
kernel modules for direct testing. As with herd7, the klitmus7
code is freely available from http://diy.inria.fr/sources/index.html
(and via "git" at https://github.com/herd/herdtools7).

Of course, litmus tests are not always the best way to fully understand a
memory model, so this patch also includes Documentation/explanation.txt,
which describes the memory model in detail. In addition,
Documentation/recipes.txt provides example known-good and known-bad use
cases for those who prefer working by example.

This patch also includes a few sample litmus tests, and a great many
more litmus tests are available at https://github.com/paulmckrcu/litmus.

This patch was the result of a most excellent collaboration founded
by Jade Alglave and also including Alan Stern, Andrea Parri, and Luc
Maranget. For more details on the history of this collaboration, please
refer to the Linux-kernel memory model presentations at 2016 LinuxCon EU,
2016 Kernel Summit, 2016 Linux Plumbers Conference, 2017 linux.conf.au,
or 2017 Linux Plumbers Conference microconference. However, one aspect
of the history does bear repeating due to weak copyright tracking earlier
in this project, which extends back to early 2015. This weakness came
to light in late 2017 after an LKMM presentation by Paul in which an
audience member noted the similarity of some LKMM code to code in early
published papers. This prompted a copyright review.

From Alan Stern:

To say that the model was mine is not entirely accurate.
Pieces of it (especially the Scpv and Atomic axioms) were taken
directly from Jade's models. And of course the Happens-before
and Propagation relations and axioms were heavily based on
Jade and Luc's work, even though they weren't identical to the
earlier versions. Only the RCU portion was completely original.

. . .

One can make a much better case that I wrote the bulk of lock.cat.
However, it was inspired by Luc's earlier version (and still
shares some elements in common), and of course it benefited from
feedback and testing from all members of our group.

The model prior to Alan's was Luc Maranget's. From Luc:

I totally agree on Alan Stern's account of the linux kernel model
genesis. I thank him for his acknowledgments of my participation
to previous model drafts. I'd like to complete Alan Stern's
statement: any bell cat code I have written has its roots in
discussions with Jade Alglave and Paul McKenney. Moreover I
have borrowed cat and bell code written by Jade Alglave freely.

This copyright review therefore resulted in late adds to the copyright
statements of several files.

Discussion of v1 has raised several issues, which we do not believe should
block acceptance given that this level of change will be ongoing, just
as it has been with memory-barriers.txt:

o Under what conditions should ordering provided by pure locking
be seen by CPUs not holding the relevant lock(s)? In particular,
should the message-passing pattern be forbidden?

o Should examples involving C11 release sequences be forbidden?
Note that this C11 is still a moving target for this issue:
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0735r0.html

o Some details of the handling of internal dependencies for atomic
read-modify-write atomic operations are still subject to debate.

o Changes recently accepted into mainline greatly reduce the need
to handle DEC Alpha as a special case. These changes add an
smp_read_barrier_depends() to READ_ONCE(), thus causing Alpha
to respect ordering of dependent reads. If these changes stick,
the memory model can be simplified accordingly.

o Will changes be required to accommodate RISC-V?

Differences from v1:
(http://lkml.kernel.org/r/[e-mail])

o Add SPDX notations to .bell and .cat files, replacing
textual license statements.

o Add reference to upcoming ASPLOS paper to .bell and .cat files.

o Updated identifier names in .bell and .cat files to match those
used in the ASPLOS paper.

o Updates to READMEs and other documentation based on review
feedback.

o Added a memory-ordering cheatsheet.

o Update sigs to new Co-Developed-by and add acks and
reviewed-bys.

o Simplify rules detecting nested RCU read-side critical sections.

o Update copyright statements as noted above.

Co-Developed-by: Alan Stern <[e-mail]>
Co-Developed-by: Andrea Parri <[e-mail]>
Co-Developed-by: Jade Alglave <[e-mail]>
Co-Developed-by: Luc Maranget <[e-mail]>
Co-Developed-by: "Paul E. McKenney" <[e-mail]>
Signed-off-by: Alan Stern <[e-mail]>
Signed-off-by: Andrea Parri <[e-mail]>
Signed-off-by: Jade Alglave <[e-mail]>
Signed-off-by: Luc Maranget <[e-mail]>
Signed-off-by: "Paul E. McKenney" <[e-mail]>
Reviewed-by: Boqun Feng <[e-mail]>
Acked-by: Will Deacon <[e-mail]>
Acked-by: Peter Zijlstra <[e-mail]>
Acked-by: Nicholas Piggin <[e-mail]>
Acked-by: David Howells <[e-mail]>
Acked-by: "Reshetova, Elena" <[e-mail]>
Acked-by: Michal Hocko <[e-mail]>
Acked-by: Akira Yokosawa <[e-mail]>
Cc: <[e-mail]>

tools/memory-model/Documentation/cheatsheet.txt

···
+                                  Prior Operation     Subsequent Operation
+                                  ---------------  ---------------------------
+                               C  Self  R  W  RWM  Self  R  W  DR  DW  RMW  SV
+                              __  ----  -  -  ---  ----  -  -  --  --  ---  --
+
+Store, e.g., WRITE_ONCE()            Y                                       Y
+Load, e.g., READ_ONCE()              Y                              Y        Y
+Unsuccessful RMW operation           Y                              Y        Y
+smp_read_barrier_depends()              Y                       Y   Y
+*_dereference()                      Y                          Y   Y        Y
+Successful *_acquire()               R                   Y  Y   Y   Y    Y   Y
+Successful *_release()         C        Y  Y    Y     W                      Y
+smp_rmb()                               Y       R        Y      Y        R
+smp_wmb()                                  Y    W           Y       Y    W
+smp_mb() & synchronize_rcu()  CP        Y  Y    Y        Y  Y   Y   Y    Y
+Successful full non-void RMW  CP     Y  Y  Y    Y     Y  Y  Y   Y   Y    Y   Y
+smp_mb__before_atomic()       CP        Y  Y    Y        a  a   a   a    Y
+smp_mb__after_atomic()        CP        a  a    Y        Y  Y   Y   Y
+
+
+Key:	C:	Ordering is cumulative
+	P:	Ordering propagates
+	R:	Read, for example, READ_ONCE(), or read portion of RMW
+	W:	Write, for example, WRITE_ONCE(), or write portion of RMW
+	Y:	Provides ordering
+	a:	Provides ordering given intervening RMW atomic operation
+	DR:	Dependent read (address dependency)
+	DW:	Dependent write (address, data, or control dependency)
+	RMW:	Atomic read-modify-write operation
+	SV	Same-variable access

tools/memory-model/Documentation/explanation.txt

···
+Explanation of the Linux-Kernel Memory Model
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+:Author: Alan Stern <[e-mail]>
+:Created: October 2017
+
+.. Contents
+
+  1. INTRODUCTION
+  2. BACKGROUND
+  3. A SIMPLE EXAMPLE
+  4. A SELECTION OF MEMORY MODELS
+  5. ORDERING AND CYCLES
+  6. EVENTS
+  7. THE PROGRAM ORDER RELATION: po AND po-loc
+  8. A WARNING
+  9. DEPENDENCY RELATIONS: data, addr, and ctrl
+  10. THE READS-FROM RELATION: rf, rfi, and rfe
+  11. CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe
+  12. THE FROM-READS RELATION: fr, fri, and fre
+  13. AN OPERATIONAL MODEL
+  14. PROPAGATION ORDER RELATION: cumul-fence
+  15. DERIVATION OF THE LKMM FROM THE OPERATIONAL MODEL
+  16. SEQUENTIAL CONSISTENCY PER VARIABLE
+  17. ATOMIC UPDATES: rmw
+  18. THE PRESERVED PROGRAM ORDER RELATION: ppo
+  19. AND THEN THERE WAS ALPHA
+  20. THE HAPPENS-BEFORE RELATION: hb
+  21. THE PROPAGATES-BEFORE RELATION: pb
+  22. RCU RELATIONS: link, gp-link, rscs-link, and rcu-path
+  23. ODDS AND ENDS
+
+
+
+INTRODUCTION
+------------
+
+The Linux-kernel memory model (LKMM) is rather complex and obscure.
+This is particularly evident if you read through the linux-kernel.bell
+and linux-kernel.cat files that make up the formal version of the
+memory model; they are extremely terse and their meanings are far from
+clear.
+
+This document describes the ideas underlying the LKMM.  It is meant
+for people who want to understand how the memory model was designed.
+It does not go into the details of the code in the .bell and .cat
+files; rather, it explains in English what the code expresses
+symbolically.
+
+Sections 2 (BACKGROUND) through 5 (ORDERING AND CYCLES) are aimed
+toward beginners; they explain what memory models are and the basic
+notions shared by all such models.  People already familiar with these
+concepts can skim or skip over them.  Sections 6 (EVENTS) through 12
+(THE FROM_READS RELATION) describe the fundamental relations used in
+many memory models.  Starting in Section 13 (AN OPERATIONAL MODEL),
+the workings of the LKMM itself are covered.
+
+Warning: The code examples in this document are not written in the
+proper format for litmus tests.  They don't include a header line, the
+initializations are not enclosed in braces, the global variables are
+not passed by pointers, and they don't have an "exists" clause at the
+end.  Converting them to the right format is left as an exercise for
+the reader.
+
+
+BACKGROUND
+----------
+
+A memory consistency model (or just memory model, for short) is
+something which predicts, given a piece of computer code running on a
+particular kind of system, what values may be obtained by the code's
+load instructions.  The LKMM makes these predictions for code running
+as part of the Linux kernel.
+
+In practice, people tend to use memory models the other way around.
+That is, given a piece of code and a collection of values specified
+for the loads, the model will predict whether it is possible for the
+code to run in such a way that the loads will indeed obtain the
+specified values.  Of course, this is just another way of expressing
+the same idea.
+
+For code running on a uniprocessor system, the predictions are easy:
+Each load instruction must obtain the value written by the most recent
+store instruction accessing the same location (we ignore complicating
+factors such as DMA and mixed-size accesses.)  But on multiprocessor
+systems, with multiple CPUs making concurrent accesses to shared
+memory locations, things aren't so simple.
+
+Different architectures have differing memory models, and the Linux
+kernel supports a variety of architectures.  The LKMM has to be fairly
+permissive, in the sense that any behavior allowed by one of these
+architectures also has to be allowed by the LKMM.
+
+
+A SIMPLE EXAMPLE
+----------------
+
+Here is a simple example to illustrate the basic concepts.  Consider
+some code running as part of a device driver for an input device.  The
+driver might contain an interrupt handler which collects data from the
+device, stores it in a buffer, and sets a flag to indicate the buffer
+is full.  Running concurrently on a different CPU might be a part of
+the driver code being executed by a process in the midst of a read(2)
+system call.  This code tests the flag to see whether the buffer is
+ready, and if it is, copies the data back to userspace.  The buffer
+and the flag are memory locations shared between the two CPUs.
+
+We can abstract out the important pieces of the driver code as follows
+(the reason for using WRITE_ONCE() and READ_ONCE() instead of simple
+assignment statements is discussed later):
+
+	int buf = 0, flag = 0;
+
+	P0()
+	{
+		WRITE_ONCE(buf, 1);
+		WRITE_ONCE(flag, 1);
+	}
+
+	P1()
+	{
+		int r1;
+		int r2 = 0;
+
+		r1 = READ_ONCE(flag);
+		if (r1)
+			r2 = READ_ONCE(buf);
+	}
+
+Here the P0() function represents the interrupt handler running on one
+CPU and P1() represents the read() routine running on another.  The
+value 1 stored in buf represents input data collected from the device.
+Thus, P0 stores the data in buf and then sets flag.  Meanwhile, P1
+reads flag into the private variable r1, and if it is set, reads the
+data from buf into a second private variable r2 for copying to
+userspace.  (Presumably if flag is not set then the driver will wait a
+while and try again.)
+
+This pattern of memory accesses, where one CPU stores values to two
+shared memory locations and another CPU loads from those locations in
+the opposite order, is widely known as the "Message Passing" or MP
+pattern.  It is typical of memory access patterns in the kernel.
+
+Please note that this example code is a simplified abstraction.  Real
+buffers are usually larger than a single integer, real device drivers
+usually use sleep and wakeup mechanisms rather than polling for I/O
+completion, and real code generally doesn't bother to copy values into
+private variables before using them.  All that is beside the point;
+the idea here is simply to illustrate the overall pattern of memory
+accesses by the CPUs.
+
+A memory model will predict what values P1 might obtain for its loads
+from flag and buf, or equivalently, what values r1 and r2 might end up
+with after the code has finished running.
+
+Some predictions are trivial.  For instance, no sane memory model would
+predict that r1 = 42 or r2 = -7, because neither of those values ever
+gets stored in flag or buf.
+
+Some nontrivial predictions are nonetheless quite simple.  For
+instance, P1 might run entirely before P0 begins, in which case r1 and
+r2 will both be 0 at the end.  Or P0 might run entirely before P1
+begins, in which case r1 and r2 will both be 1.
+
+The interesting predictions concern what might happen when the two
+routines run concurrently.  One possibility is that P1 runs after P0's
+store to buf but before the store to flag.  In this case, r1 and r2
+will again both be 0.  (If P1 had been designed to read buf
+unconditionally then we would instead have r1 = 0 and r2 = 1.)
+
+However, the most interesting possibility is where r1 = 1 and r2 = 0.
+If this were to occur it would mean the driver contains a bug, because
+incorrect data would get sent to the user: 0 instead of 1.  As it
+happens, the LKMM does predict this outcome can occur, and the example
+driver code shown above is indeed buggy.
+
+
+A SELECTION OF MEMORY MODELS
+----------------------------
+
+The first widely cited memory model, and the simplest to understand,
+is Sequential Consistency.  According to this model, systems behave as
+if each CPU executed its instructions in order but with unspecified
+timing.  In other words, the instructions from the various CPUs get
+interleaved in a nondeterministic way, always according to some single
+global order that agrees with the order of the instructions in the
+program source for each CPU.  The model says that the value obtained
+by each load is simply the value written by the most recently executed
+store to the same memory location, from any CPU.
+
+For the MP example code shown above, Sequential Consistency predicts
+that the undesired result r1 = 1, r2 = 0 cannot occur.  The reasoning
+goes like this:
+
+	Since r1 = 1, P0 must store 1 to flag before P1 loads 1 from
+	it, as loads can obtain values only from earlier stores.
+
+	P1 loads from flag before loading from buf, since CPUs execute
+	their instructions in order.
+
+	P1 must load 0 from buf before P0 stores 1 to it; otherwise r2
+	would be 1 since a load obtains its value from the most recent
+	store to the same address.
+
+	P0 stores 1 to buf before storing 1 to flag, since it executes
+	its instructions in order.
+
+	Since an instruction (in this case, P1's store to flag) cannot
+	execute before itself, the specified outcome is impossible.
+
+However, real computer hardware almost never follows the Sequential
+Consistency memory model; doing so would rule out too many valuable
+performance optimizations.  On ARM and PowerPC architectures, for
+instance, the MP example code really does sometimes yield r1 = 1 and
+r2 = 0.
+
+x86 and SPARC follow yet a different memory model: TSO (Total Store
+Ordering).  This model predicts that the undesired outcome for the MP
+pattern cannot occur, but in other respects it differs from Sequential
+Consistency.  One example is the Store Buffer (SB) pattern, in which
+each CPU stores to its own shared location and then loads from the
+other CPU's location:
+
+	int x = 0, y = 0;
+
+	P0()
+	{
+		int r0;
+
+		WRITE_ONCE(x, 1);
+		r0 = READ_ONCE(y);
+	}
+
+	P1()
+	{
+		int r1;
+
+		WRITE_ONCE(y, 1);
+		r1 = READ_ONCE(x);
+	}
+
+Sequential Consistency predicts that the outcome r0 = 0, r1 = 0 is
+impossible.  (Exercise: Figure out the reasoning.)  But TSO allows
+this outcome to occur, and in fact it does sometimes occur on x86 and
+SPARC systems.
+
+The LKMM was inspired by the memory models followed by PowerPC, ARM,
+x86, Alpha, and other architectures.  However, it is different in
+detail from each of them.
+
+
+ORDERING AND CYCLES
+-------------------
+
+Memory models are all about ordering.  Often this is temporal ordering
+(i.e., the order in which certain events occur) but it doesn't have to
+be; consider for example the order of instructions in a program's
+source code.  We saw above that Sequential Consistency makes an
+important assumption that CPUs execute instructions in the same order
+as those instructions occur in the code, and there are many other
+instances of ordering playing central roles in memory models.
+
+The counterpart to ordering is a cycle.  Ordering rules out cycles:
+It's not possible to have X ordered before Y, Y ordered before Z, and
+Z ordered before X, because this would mean that X is ordered before
+itself.  The analysis of the MP example under Sequential Consistency
+involved just such an impossible cycle:
+
+	W: P0 stores 1 to flag   executes before
+	X: P1 loads 1 from flag  executes before
+	Y: P1 loads 0 from buf   executes before
+	Z: P0 stores 1 to buf    executes before
+	W: P0 stores 1 to flag.
+
+In short, if a memory model requires certain accesses to be ordered,
+and a certain outcome for the loads in a piece of code can happen only
+if those accesses would form a cycle, then the memory model predicts
+that outcome cannot occur.
+
+The LKMM is defined largely in terms of cycles, as we will see.
+
+
+EVENTS
+------
+
+The LKMM does not work directly with the C statements that make up
+kernel source code.  Instead it considers the effects of those
+statements in a more abstract form, namely, events.  The model
+includes three types of events:
+
+	Read events correspond to loads from shared memory, such as
+	calls to READ_ONCE(), smp_load_acquire(), or
+	rcu_dereference().
+
+	Write events correspond to stores to shared memory, such as
+	calls to WRITE_ONCE(), smp_store_release(), or atomic_set().
+
+	Fence events correspond to memory barriers (also known as
+	fences), such as calls to smp_rmb() or rcu_read_lock().
+
+These categories are not exclusive; a read or write event can also be
+a fence.  This happens with functions like smp_load_acquire() or
+spin_lock().  However, no single event can be both a read and a write.
+Atomic read-modify-write accesses, such as atomic_inc() or xchg(),
+correspond to a pair of events: a read followed by a write.  (The
+write event is omitted for executions where it doesn't occur, such as
+a cmpxchg() where the comparison fails.)
+
+Other parts of the code, those which do not involve interaction with
+shared memory, do not give rise to events.  Thus, arithmetic and
+logical computations, control-flow instructions, or accesses to
+private memory or CPU registers are not of central interest to the
+memory model.  They only affect the model's predictions indirectly.
+For example, an arithmetic computation might determine the value that
+gets stored to a shared memory location (or in the case of an array
+index, the address where the value gets stored), but the memory model
+is concerned only with the store itself -- its value and its address
+-- not the computation leading up to it.
+
+Events in the LKMM can be linked by various relations, which we will
+describe in the following sections.  The memory model requires certain
+of these relations to be orderings, that is, it requires them not to
+have any cycles.
+
+
+THE PROGRAM ORDER RELATION: po AND po-loc
+-----------------------------------------
+
+The most important relation between events is program order (po).  You
+can think of it as the order in which statements occur in the source
+code after branches are taken into account and loops have been
+unrolled.  A better description might be the order in which
+instructions are presented to a CPU's execution unit.  Thus, we say
+that X is po-before Y (written as "X ->po Y" in formulas) if X occurs
+before Y in the instruction stream.
+
+This is inherently a single-CPU relation; two instructions executing
+on different CPUs are never linked by po.  Also, it is by definition
+an ordering so it cannot have any cycles.
+
+po-loc is a sub-relation of po.  It links two memory accesses when the
+first comes before the second in program order and they access the
+same memory location (the "-loc" suffix).
+
+Although this may seem straightforward, there is one subtle aspect to
+program order we need to explain.  The LKMM was inspired by low-level
+architectural memory models which describe the behavior of machine
+code, and it retains their outlook to a considerable extent.  The
+read, write, and fence events used by the model are close in spirit to
+individual machine instructions.  Nevertheless, the LKMM describes
+kernel code written in C, and the mapping from C to machine code can
+be extremely complex.
+
+Optimizing compilers have great freedom in the way they translate
+source code to object code.  They are allowed to apply transformations
+that add memory accesses, eliminate accesses, combine them, split them
+into pieces, or move them around.  Faced with all these possibilities,
+the LKMM basically gives up.  It insists that the code it analyzes
+must contain no ordinary accesses to shared memory; all accesses must
+be performed using READ_ONCE(), WRITE_ONCE(), or one of the other
+atomic or synchronization primitives.  These primitives prevent a
+large number of compiler optimizations.  In particular, it is
+guaranteed that the compiler will not remove such accesses from the
+generated code (unless it can prove the accesses will never be
+executed), it will not change the order in which they occur in the
+code (within limits imposed by the C standard), and it will not
+introduce extraneous accesses.
+
+This explains why the MP and SB examples above used READ_ONCE() and
+WRITE_ONCE() rather than ordinary memory accesses.  Thanks to this
+usage, we can be certain that in the MP example, P0's write event to
+buf really is po-before its write event to flag, and similarly for the
+other shared memory accesses in the examples.
+
+Private variables are not subject to this restriction.  Since they are
+not shared between CPUs, they can be accessed normally without
+READ_ONCE() or WRITE_ONCE(), and there will be no ill effects.  In
+fact, they need not even be stored in normal memory at all -- in
+principle a private variable could be stored in a CPU register (hence
+the convention that these variables have names starting with the
+letter 'r').
+
+
+A WARNING
+---------
+
+The protections provided by READ_ONCE(), WRITE_ONCE(), and others are
+not perfect; and under some circumstances it is possible for the
+compiler to undermine the memory model.  Here is an example.  Suppose
+both branches of an "if" statement store the same value to the same
+location:
+
+	r1 = READ_ONCE(x);
+	if (r1) {
+		WRITE_ONCE(y, 2);
+		...  /* do something */
+	} else {
+		WRITE_ONCE(y, 2);
+		...  /* do something else */
+	}
+
+For this code, the LKMM predicts that the load from x will always be
+executed before either of the stores to y.  However, a compiler could
+lift the stores out of the conditional, transforming the code into
+something resembling:
+
+	r1 = READ_ONCE(x);
+	WRITE_ONCE(y, 2);
+	if (r1) {
+		...  /* do something */
+	} else {
+		...  /* do something else */
+	}
+
+Given this version of the code, the LKMM would predict that the load
+from x could be executed after the store to y.  Thus, the memory
+model's original prediction could be invalidated by the compiler.
+
+Another issue arises from the fact that in C, arguments to many
+operators and function calls can be evaluated in any order.  For
+example:
+
+	r1 = f(5) + g(6);
+
+The object code might call f(5) either before or after g(6); the
+memory model cannot assume there is a fixed program order relation
+between them.  (In fact, if the functions are inlined then the
+compiler might even interleave their object code.)
+
+
+DEPENDENCY RELATIONS: data, addr, and ctrl
+------------------------------------------
+
+We say that two events are linked by a dependency relation when the
+execution of the second event depends in some way on a value obtained
+from memory by the first.  The first event must be a read, and the
+value it obtains must somehow affect what the second event does.
+There are three kinds of dependencies: data, address (addr), and
+control (ctrl).
+
+A read and a write event are linked by a data dependency if the value
+obtained by the read affects the value stored by the write.  As a very
+simple example:
+
+	int x, y;
+
+	r1 = READ_ONCE(x);
+	WRITE_ONCE(y, r1 + 5);
+
+The value stored by the WRITE_ONCE obviously depends on the value
+loaded by the READ_ONCE.  Such dependencies can wind through
+arbitrarily complicated computations, and a write can depend on the
+values of multiple reads.
+
+A read event and another memory access event are linked by an address
+dependency if the value obtained by the read affects the location
+accessed by the other event.  The second event can be either a read or
+a write.  Here's another simple example:
+
+	int a[20];
+	int i;
+
+	r1 = READ_ONCE(i);
+	r2 = READ_ONCE(a[r1]);
+
+Here the location accessed by the second READ_ONCE() depends on the
+index value loaded by the first.  Pointer indirection also gives rise
+to address dependencies, since the address of a location accessed
+through a pointer will depend on the value read earlier from that
+pointer.
+
+Finally, a read event and another memory access event are linked by a
+control dependency if the value obtained by the read affects whether
+the second event is executed at all.  Simple example:
+
+	int x, y;
+
+	r1 = READ_ONCE(x);
+	if (r1)
+		WRITE_ONCE(y, 1984);
+
+Execution of the WRITE_ONCE() is controlled by a conditional expression
+which depends on the value obtained by the READ_ONCE(); hence there is
+a control dependency from the load to the store.
+
+It should be pretty obvious that events can only depend on reads that
+come earlier in program order.  Symbolically, if we have R ->data X,
+R ->addr X, or R ->ctrl X (where R is a read event), then we must also
+have R ->po X.  It wouldn't make sense for a computation to depend
+somehow on a value that doesn't get loaded from shared memory until
+later in the code!
+
+
+THE READS-FROM RELATION: rf, rfi, and rfe
+-----------------------------------------
+
+The reads-from relation (rf) links a write event to a read event when
+the value loaded by the read is the value that was stored by the
+write.  In colloquial terms, the load "reads from" the store.  We
+write W ->rf R to indicate that the load R reads from the store W.  We
+further distinguish the cases where the load and the store occur on
+the same CPU (internal reads-from, or rfi) and where they occur on
+different CPUs (external reads-from, or rfe).
+
+For our purposes, a memory location's initial value is treated as
+though it had been written there by an imaginary initial store that
+executes on a separate CPU before the program runs.
+
+Usage of the rf relation implicitly assumes that loads will always
+read from a single store.  It doesn't apply properly in the presence
+of load-tearing, where a load obtains some of its bits from one store
+and some of them from another store.  Fortunately, use of READ_ONCE()
+and WRITE_ONCE() will prevent load-tearing; it's not possible to have:
+
+	int x = 0;
+
+	P0()
+	{
+		WRITE_ONCE(x, 0x1234);
+	}
+
+	P1()
+	{
+		int r1;
+
+		r1 = READ_ONCE(x);
+	}
+
+and end up with r1 = 0x1200 (partly from x's initial value and partly
+from the value stored by P0).
+
+On the other hand, load-tearing is unavoidable when mixed-size
+accesses are used.  Consider this example:
+
+	union {
+		u32	w;
+		u16	h[2];
+	} x;
+
+	P0()
+	{
+		WRITE_ONCE(x.h[0], 0x1234);
+		WRITE_ONCE(x.h[1], 0x5678);
+	}
+
+	P1()
+	{
+		int r1;
+
+		r1 = READ_ONCE(x.w);
+	}
+
+If r1 = 0x56781234 (little-endian!) at the end, then P1 must have read
+from both of P0's stores.  It is possible to handle mixed-size and
+unaligned accesses in a memory model, but the LKMM currently does not
+attempt to do so.  It requires all accesses to be properly aligned and
+of the location's actual size.
+
+
+CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe
+------------------------------------------------------------------
+
+Cache coherence is a general principle requiring that in a
+multi-processor system, the CPUs must share a consistent view of the
+memory contents.  Specifically, it requires that for each location in
+shared memory, the stores to that location must form a single global
+ordering which all the CPUs agree on (the coherence order), and this
+ordering must be consistent with the program order for accesses to
+that location.
+
+To put it another way, for any variable x, the coherence order (co) of
+the stores to x is simply the order in which the stores overwrite one
+another.  The imaginary store which establishes x's initial value
+comes first in the coherence order; the store which directly
+overwrites the initial value comes second; the store which overwrites
+that value comes third, and so on.
+
+You can think of the coherence order as being the order in which the
+stores reach x's location in memory (or if you prefer a more
+hardware-centric view, the order in which the stores get written to
+x's cache line).  We write W ->co W' if W comes before W' in the
+coherence order, that is, if the value stored by W gets overwritten,
+directly or indirectly, by the value stored by W'.
+
+Coherence order is required to be consistent with program order.  This
+requirement takes the form of four coherency rules:
+
+	Write-write coherence: If W ->po-loc W' (i.e., W comes before
+	W' in program order and they access the same location), where W
+	and W' are two stores, then W ->co W'.
+
+	Write-read coherence: If W ->po-loc R, where W is a store and R
+	is a load, then R must read from W or from some other store
+	which comes after W in the coherence order.
+
+	Read-write coherence: If R ->po-loc W, where R is a load and W
+	is a store, then the store which R reads from must come before
+	W in the coherence order.
+
+	Read-read coherence: If R ->po-loc R', where R and R' are two
+	loads, then either they read from the same store or else the
+	store read by R comes before the store read by R' in the
+	coherence order.
+
+This is sometimes referred to as sequential consistency per variable,
+because it means that the accesses to any single memory location obey
+the rules of the Sequential Consistency memory model.  (According to
+Wikipedia, sequential consistency per variable and cache coherence
+mean the same thing except that cache coherence includes an extra
+requirement that every store eventually becomes visible to every CPU.)
+
+Any reasonable memory model will include cache coherence.  Indeed, our
+expectation of cache coherence is so deeply ingrained that violations
+of its requirements look more like hardware bugs than programming
+errors:
+
+	int x;
+
+	P0()
+	{
+		WRITE_ONCE(x, 17);
+		WRITE_ONCE(x, 23);
+	}
+
+If the final value stored in x after this code ran was 17, you would
+think your computer was broken.  It would be a violation of the
+write-write coherence rule: Since the store of 23 comes later in
+program order, it must also come later in x's coherence order and
+thus must overwrite the store of 17.
+
+	int x = 0;
+
+	P0()
+	{
+		int r1;
+
+		r1 = READ_ONCE(x);
+		WRITE_ONCE(x, 666);
+	}
+
+If r1 = 666 at the end, this would violate the read-write coherence
+rule: The READ_ONCE() load comes before the WRITE_ONCE() store in
+program order, so it must not read from that store but rather from one
+coming earlier in the coherence order (in this case, x's initial
+value).
+
+	int x = 0;
+
+	P0()
+	{
+		WRITE_ONCE(x, 5);
+	}
+
+	P1()
+	{
+		int r1, r2;
+
+		r1 = READ_ONCE(x);
+		r2 = READ_ONCE(x);
+	}
+
+If r1 = 5 (reading from P0's store) and r2 = 0 (reading from the
+imaginary store which establishes x's initial value) at the end, this
+would violate the read-read coherence rule: The r1 load comes before
+the r2 load in program order, so it must not read from a store that
+comes later in the coherence order.
+
+(As a minor curiosity, if this code had used normal loads instead of
+READ_ONCE() in P1, on Itanium it sometimes could end up with r1 = 5
+and r2 = 0!  This results from parallel execution of the operations
+encoded in Itanium's Very-Long-Instruction-Word format, and it is yet
+another motivation for using READ_ONCE() when accessing shared memory
+locations.)
+
+Just like the po relation, co is inherently an ordering -- it is not
+possible for a store to directly or indirectly overwrite itself!  And
+just like with the rf relation, we distinguish between stores that
+occur on the same CPU (internal coherence order, or coi) and stores
+that occur on different CPUs (external coherence order, or coe).
+
+On the other hand, stores to different memory locations are never
+related by co, just as instructions on different CPUs are never
+related by po.  Coherence order is strictly per-location, or if you
+prefer, each location has its own independent coherence order.
+
+
+THE FROM-READS RELATION: fr, fri, and fre
+-----------------------------------------
+
+The from-reads relation (fr) can be a little difficult for people to
+grok.  It describes the situation where a load reads a value that gets
+overwritten by a store.  In other words, we have R ->fr W when the
+value that R reads is overwritten (directly or indirectly) by W, or
+equivalently, when R reads from a store which comes earlier than W in
+the coherence order.
+
+For example:
+
+	int x = 0;
+
+	P0()
+	{
+		int r1;
+
+		r1 = READ_ONCE(x);
+		WRITE_ONCE(x, 2);
+	}
+
+The value loaded from x will be 0 (assuming cache coherence!), and it
+gets overwritten by the value 2.  Thus there is an fr link from the
+READ_ONCE() to the WRITE_ONCE().  If the code contained any later
+stores to x, there would also be fr links from the READ_ONCE() to
+them.
+
+As with rf, rfi, and rfe, we subdivide the fr relation into fri (when
+the load and the store are on the same CPU) and fre (when they are on
+different CPUs).
+
+Note that the fr relation is determined entirely by the rf and co
+relations; it is not independent.  Given a read event R and a write
+event W for the same location, we will have R ->fr W if and only if
+the write which R reads from is co-before W.  In symbols,
+
+	(R ->fr W) := (there exists W' with W' ->rf R and W' ->co W).
+
+
+AN OPERATIONAL MODEL
+--------------------
+
+The LKMM is based on various operational memory models, meaning that
+the models arise from an abstract view of how a computer system
+operates.  Here are the main ideas, as incorporated into the LKMM.
+
+The system as a whole is divided into the CPUs and a memory subsystem.
+The CPUs are responsible for executing instructions (not necessarily
+in program order), and they communicate with the memory subsystem.
+For the most part, executing an instruction requires a CPU to perform
+only internal operations.  However, loads, stores, and fences involve
+more.
+
+When CPU C executes a store instruction, it tells the memory subsystem
+to store a certain value at a certain location.  The memory subsystem
+propagates the store to all the other CPUs as well as to RAM.  (As a
+special case, we say that the store propagates to its own CPU at the
+time it is executed.)  The memory subsystem also determines where the
+store falls in the location's coherence order.  In particular, it must
+arrange for the store to be co-later than (i.e., to overwrite) any
+other store to the same location which has already propagated to CPU C.
+
+When a CPU executes a load instruction R, it first checks to see
+whether there are any as-yet unexecuted store instructions, for the
+same location, that come before R in program order.  If there are, it
+uses the value of the po-latest such store as the value obtained by R,
+and we say that the store's value is forwarded to R.  Otherwise, the
+CPU asks the memory subsystem for the value to load and we say that R
+is satisfied from memory.  The memory subsystem hands back the value
+of the co-latest store to the location in question which has already
+propagated to that CPU.
+
+(In fact, the picture needs to be a little more complicated than this.
+CPUs have local caches, and propagating a store to a CPU really means
+propagating it to the CPU's local cache.  A local cache can take some
+time to process the stores that it receives, and a store can't be used
+to satisfy one of the CPU's loads until it has been processed.  On
+most architectures, the local caches process stores in
+First-In-First-Out order, and consequently the processing delay
+doesn't matter for the memory model.  But on Alpha, the local caches
+have a partitioned design that results in non-FIFO behavior.  We will
+discuss this in more detail later.)
+
+Note that load instructions may be executed speculatively and may be
+restarted under certain circumstances.  The memory model ignores these
+premature executions; we simply say that the load executes at the
+final time it is forwarded or satisfied.
+
+Executing a fence (or memory barrier) instruction doesn't require a
+CPU to do anything special other than informing the memory subsystem
+about the fence.  However, fences do constrain the way CPUs and the
+memory subsystem handle other instructions, in two respects.
+
+First, a fence forces the CPU to execute various instructions in
+program order.  Exactly which instructions are ordered depends on the
+type of fence:
+
+	Strong fences, including smp_mb() and synchronize_rcu(), force
+	the CPU to execute all po-earlier instructions before any
+	po-later instructions;
+
+	smp_rmb() forces the CPU to execute all po-earlier loads
+	before any po-later loads;
+
+	smp_wmb() forces the CPU to execute all po-earlier stores
+	before any po-later stores;
+
+	Acquire fences, such as smp_load_acquire(), force the CPU to
+	execute the load associated with the fence (e.g., the load
+	part of an smp_load_acquire()) before any po-later
+	instructions;
+
+	Release fences, such as smp_store_release(), force the CPU to
+	execute all po-earlier instructions before the store
+	associated with the fence (e.g., the store part of an
+	smp_store_release()).
+
+Second, some types of fence affect the way the memory subsystem
+propagates stores.  When a fence instruction is executed on CPU C:
+
+	For each other CPU C', smb_wmb() forces all po-earlier stores
+	on C to propagate to C' before any po-later stores do.
+
+	For each other CPU C', any store which propagates to C before
+	a release fence is executed (including all po-earlier
+	stores executed on C) is forced to propagate to C' before the
+	store associated with the release fence does.
+
+	Any store which propagates to C before a strong fence is
+	executed (including all po-earlier stores on C) is forced to
+	propagate to all other CPUs before any instructions po-after
+	the strong fence are executed on C.
+
+The propagation ordering enforced by release fences and strong fences
+affects stores from other CPUs that propagate to CPU C before the
+fence is executed, as well as stores that are executed on C before the
+fence.  We describe this property by saying that release fences and
+strong fences are A-cumulative.  By contrast, smp_wmb() fences are not
+A-cumulative; they only affect the propagation of stores that are
+executed on C before the fence (i.e., those which precede the fence in
+program order).
+
+smp_read_barrier_depends(), rcu_read_lock(), rcu_read_unlock(), and
+synchronize_rcu() fences have other properties which we discuss later.
+
+
+PROPAGATION ORDER RELATION: cumul-fence
+---------------------------------------
+
+The fences which affect propagation order (i.e., strong, release, and
+smp_wmb() fences) are collectively referred to as cumul-fences, even
+though smp_wmb() isn't A-cumulative.  The cumul-fence relation is
+defined to link memory access events E and F whenever:
+
+	E and F are both stores on the same CPU and an smp_wmb() fence
+	event occurs between them in program order; or
+
+	F is a release fence and some X comes before F in program order,
+	where either X = E or else E ->rf X; or
+
+	A strong fence event occurs between some X and F in program
+	order, where either X = E or else E ->rf X.
+
+The operational model requires that whenever W and W' are both stores
+and W ->cumul-fence W', then W must propagate to any given CPU
+before W' does.  However, for different CPUs C and C', it does not
+require W to propagate to C before W' propagates to C'.
+
+
+DERIVATION OF THE LKMM FROM THE OPERATIONAL MODEL
+-------------------------------------------------
+
+The LKMM is derived from the restrictions imposed by the design
+outlined above.  These restrictions involve the necessity of
+maintaining cache coherence and the fact that a CPU can't operate on a
+value before it knows what that value is, among other things.
+
+The formal version of the LKMM is defined by five requirements, or
+axioms:
+
+	Sequential consistency per variable: This requires that the
+	system obey the four coherency rules.
+
+	Atomicity: This requires that atomic read-modify-write
+	operations really are atomic, that is, no other stores can
+	sneak into the middle of such an update.
+
+	Happens-before: This requires that certain instructions are
+	executed in a specific order.
+
+	Propagation: This requires that certain stores propagate to
+	CPUs and to RAM in a specific order.
+
+	Rcu: This requires that RCU read-side critical sections and
+	grace periods obey the rules of RCU, in particular, the
+	Grace-Period Guarantee.
+
+The first and second are quite common; they can be found in many
+memory models (such as those for C11/C++11).  The "happens-before" and
+"propagation" axioms have analogs in other memory models as well.  The
+"rcu" axiom is specific to the LKMM.
+
+Each of these axioms is discussed below.
+
+
+SEQUENTIAL CONSISTENCY PER VARIABLE
+-----------------------------------
+
+According to the principle of cache coherence, the stores to any fixed
+shared location in memory form a global ordering.  We can imagine
+inserting the loads from that location into this ordering, by placing
+each load between the store that it reads from and the following
+store.  This leaves the relative positions of loads that read from the
+same store unspecified; let's say they are inserted in program order,
+first for CPU 0, then CPU 1, etc.
+
+You can check that the four coherency rules imply that the rf, co, fr,
+and po-loc relations agree with this global ordering; in other words,
+whenever we have X ->rf Y or X ->co Y or X ->fr Y or X ->po-loc Y, the
+X event comes before the Y event in the global ordering.  The LKMM's
+"coherence" axiom expresses this by requiring the union of these
+relations not to have any cycles.  This means it must not be possible
+to find events
+
+	X0 -> X1 -> X2 -> ... -> Xn -> X0,
+
+where each of the links is either rf, co, fr, or po-loc.  This has to
+hold if the accesses to the fixed memory location can be ordered as
+cache coherence demands.
+
+Although it is not obvious, it can be shown that the converse is also
+true: This LKMM axiom implies that the four coherency rules are
+obeyed.
+
+
+ATOMIC UPDATES: rmw
+-------------------
+
+What does it mean to say that a read-modify-write (rmw) update, such
+as atomic_inc(&x), is atomic?  It means that the memory location (x in
+this case) does not get altered between the read and the write events
+making up the atomic operation.  In particular, if two CPUs perform
+atomic_inc(&x) concurrently, it must be guaranteed that the final
+value of x will be the initial value plus two.  We should never have
+the following sequence of events:
+
+	CPU 0 loads x obtaining 13;
+					CPU 1 loads x obtaining 13;
+	CPU 0 stores 14 to x;
+					CPU 1 stores 14 to x;
+
+where the final value of x is wrong (14 rather than 15).
+
+In this example, CPU 0's increment effectively gets lost because it
+occurs in between CPU 1's load and store.  To put it another way, the
+problem is that the position of CPU 0's store in x's coherence order
+is between the store that CPU 1 reads from and the store that CPU 1
+performs.
+
+The same analysis applies to all atomic update operations.  Therefore,
+to enforce atomicity the LKMM requires that atomic updates follow this
+rule: Whenever R and W are the read and write events composing an
+atomic read-modify-write and W' is the write event which R reads from,
+there must not be any stores coming between W' and W in the coherence
+order.  Equivalently,
+
+	(R ->rmw W) implies (there is no X with R ->fr X and X ->co W),
+
+where the rmw relation links the read and write events making up each
+atomic update.  This is what the LKMM's "atomic" axiom says.
+
+
+THE PRESERVED PROGRAM ORDER RELATION: ppo
+-----------------------------------------
+
+There are many situations where a CPU is obligated to execute two
+instructions in program order.  We amalgamate them into the ppo (for
+"preserved program order") relation, which links the po-earlier
+instruction to the po-later instruction and is thus a sub-relation of
+po.
+
+The operational model already includes a description of one such
+situation: Fences are a source of ppo links.  Suppose X and Y are
+memory accesses with X ->po Y; then the CPU must execute X before Y if
+any of the following hold:
+
+	A strong (smp_mb() or synchronize_rcu()) fence occurs between
+	X and Y;
+
+	X and Y are both stores and an smp_wmb() fence occurs between
+	them;
+
+	X and Y are both loads and an smp_rmb() fence occurs between
+	them;
+
+	X is also an acquire fence, such as smp_load_acquire();
+
+	Y is also a release fence, such as smp_store_release().
+
+Another possibility, not mentioned earlier but discussed in the next
+section, is:
+
+	X and Y are both loads, X ->addr Y (i.e., there is an address
+	dependency from X to Y), and an smp_read_barrier_depends()
+	fence occurs between them.
+
+Dependencies can also cause instructions to be executed in program
+order.  This is uncontroversial when the second instruction is a
+store; either a data, address, or control dependency from a load R to
+a store W will force the CPU to execute R before W.  This is very
+simply because the CPU cannot tell the memory subsystem about W's
+store before it knows what value should be stored (in the case of a
+data dependency), what location it should be stored into (in the case
+of an address dependency), or whether the store should actually take
+place (in the case of a control dependency).
+
+Dependencies to load instructions are more problematic.  To begin with,
+there is no such thing as a data dependency to a load.  Next, a CPU
+has no reason to respect a control dependency to a load, because it
+can always satisfy the second load speculatively before the first, and
+then ignore the result if it turns out that the second load shouldn't
+be executed after all.  And lastly, the real difficulties begin when
+we consider address dependencies to loads.
+
+To be fair about it, all Linux-supported architectures do execute
+loads in program order if there is an address dependency between them.
+After all, a CPU cannot ask the memory subsystem to load a value from
+a particular location before it knows what that location is.  However,
+the split-cache design used by Alpha can cause it to behave in a way
+that looks as if the loads were executed out of order (see the next
+section for more details).  For this reason, the LKMM does not include
+address dependencies between read events in the ppo relation unless an
+smp_read_barrier_depends() fence is present.
+
+On the other hand, dependencies can indirectly affect the ordering of
+two loads.  This happens when there is a dependency from a load to a
+store and a second, po-later load reads from that store:
+
+	R ->dep W ->rfi R',
+
+where the dep link can be either an address or a data dependency.  In
+this situation we know it is possible for the CPU to execute R' before
+W, because it can forward the value that W will store to R'.  But it
+cannot execute R' before R, because it cannot forward the value before
+it knows what that value is, or that W and R' do access the same
+location.  However, if there is merely a control dependency between R
+and W then the CPU can speculatively forward W to R' before executing
+R; if the speculation turns out to be wrong then the CPU merely has to
+restart or abandon R'.
+
+(In theory, a CPU might forward a store to a load when it runs across
+an address dependency like this:
+
+	r1 = READ_ONCE(ptr);
+	WRITE_ONCE(*r1, 17);
+	r2 = READ_ONCE(*r1);
+
+because it could tell that the store and the second load access the
+same location even before it knows what the location's address is.
+However, none of the architectures supported by the Linux kernel do
+this.)
+
+Two memory accesses of the same location must always be executed in
+program order if the second access is a store.  Thus, if we have
+
+	R ->po-loc W
+
+(the po-loc link says that R comes before W in program order and they
+access the same location), the CPU is obliged to execute W after R.
+If it executed W first then the memory subsystem would respond to R's
+read request with the value stored by W (or an even later store), in
+violation of the read-write coherence rule.  Similarly, if we had
+
+	W ->po-loc W'
+
+and the CPU executed W' before W, then the memory subsystem would put
+W' before W in the coherence order.  It would effectively cause W to
+overwrite W', in violation of the write-write coherence rule.
+(Interestingly, an early ARMv8 memory model, now obsolete, proposed
+allowing out-of-order writes like this to occur.  The model avoided
+violating the write-write coherence rule by requiring the CPU not to
+send the W write to the memory subsystem at all!)
+
+There is one last example of preserved program order in the LKMM: when
+a load-acquire reads from an earlier store-release.  For example:
+
+	smp_store_release(&x, 123);
+	r1 = smp_load_acquire(&x);
+
+If the smp_load_acquire() ends up obtaining the 123 value that was
+stored by the smp_store_release(), the LKMM says that the load must be
+executed after the store; the store cannot be forwarded to the load.
+This requirement does not arise from the operational model, but it
+yields correct predictions on all architectures supported by the Linux
+kernel, although for differing reasons.
+
+On some architectures, including x86 and ARMv8, it is true that the
+store cannot be forwarded to the load.  On others, including PowerPC
+and ARMv7, smp_store_release() generates object code that starts with
+a fence and smp_load_acquire() generates object code that ends with a
+fence.  The upshot is that even though the store may be forwarded to
+the load, it is still true that any instruction preceding the store
+will be executed before the load or any following instructions, and
+the store will be executed before any instruction following the load.
+
+
+AND THEN THERE WAS ALPHA
+------------------------
+
+As mentioned above, the Alpha architecture is unique in that it does
+not appear to respect address dependencies to loads.  This means that
+code such as the following:
+
+	int x = 0;
+	int y = -1;
+	int *ptr = &y;
+
+	P0()
+	{
+		WRITE_ONCE(x, 1);
+		smp_wmb();
+		WRITE_ONCE(ptr, &x);
+	}
+
+	P1()
+	{
+		int *r1;
+		int r2;
+
+		r1 = READ_ONCE(ptr);
+		r2 = READ_ONCE(*r1);
+	}
+
+can malfunction on Alpha systems.  It is quite possible that r1 = &x
+and r2 = 0 at the end, in spite of the address dependency.
+
+At first glance this doesn't seem to make sense.  We know that the
+smp_wmb() forces P0's store to x to propagate to P1 before the store
+to ptr does.  And since P1 can't execute its second load
+until it knows what location to load from, i.e., after executing its
+first load, the value x = 1 must have propagated to P1 before the
+second load executed.  So why doesn't r2 end up equal to 1?
+
+The answer lies in the Alpha's split local caches.  Although the two
+stores do reach P1's local cache in the proper order, it can happen
+that the first store is processed by a busy part of the cache while
+the second store is processed by an idle part.  As a result, the x = 1
+value may not become available for P1's CPU to read until after the
+ptr = &x value does, leading to the undesirable result above.  The
+final effect is that even though the two loads really are executed in
+program order, it appears that they aren't.
+
+This could not have happened if the local cache had processed the
+incoming stores in FIFO order.  In constrast, other architectures
+maintain at least the appearance of FIFO order.
+
+In practice, this difficulty is solved by inserting an
+smp_read_barrier_depends() fence between P1's two loads.  The effect
+of this fence is to cause the CPU not to execute any po-later
+instructions until after the local cache has finished processing all
+the stores it has already received.  Thus, if the code was changed to:
+
+	P1()
+	{
+		int *r1;
+		int r2;
+
+		r1 = READ_ONCE(ptr);
+		smp_read_barrier_depends();
+		r2 = READ_ONCE(*r1);
+	}
+
+then we would never get r1 = &x and r2 = 0.  By the time P1 executed
+its second load, the x = 1 store would already be fully processed by
+the local cache and available for satisfying the read request.
+
+The LKMM requires that smp_rmb(), acquire fences, and strong fences
+share this property with smp_read_barrier_depends(): They do not allow
+the CPU to execute any po-later instructions (or po-later loads in the
+case of smp_rmb()) until all outstanding stores have been processed by
+the local cache.  In the case of a strong fence, the CPU first has to
+wait for all of its po-earlier stores to propagate to every other CPU
+in the system; then it has to wait for the local cache to process all
+the stores received as of that time -- not just the stores received
+when the strong fence began.
+
+And of course, none of this matters for any architecture other than
+Alpha.
+
+
+THE HAPPENS-BEFORE RELATION: hb
+-------------------------------
+
+The happens-before relation (hb) links memory accesses that have to
+execute in a certain order.  hb includes the ppo relation and two
+others, one of which is rfe.
+
+W ->rfe R implies that W and R are on different CPUs.  It also means
+that W's store must have propagated to R's CPU before R executed;
+otherwise R could not have read the value stored by W.  Therefore W
+must have executed before R, and so we have W ->hb R.
+
+The equivalent fact need not hold if W ->rfi R (i.e., W and R are on
+the same CPU).  As we have already seen, the operational model allows
+W's value to be forwarded to R in such cases, meaning that R may well
+execute before W does.
+
+It's important to understand that neither coe nor fre is included in
+hb, despite their similarities to rfe.  For example, suppose we have
+W ->coe W'.  This means that W and W' are stores to the same location,
+they execute on different CPUs, and W comes before W' in the coherence
+order (i.e., W' overwrites W).  Nevertheless, it is possible for W' to
+execute before W, because the decision as to which store overwrites
+the other is made later by the memory subsystem.  When the stores are
+nearly simultaneous, either one can come out on top.  Similarly,
+R ->fre W means that W overwrites the value which R reads, but it
+doesn't mean that W has to execute after R.  All that's necessary is
+for the memory subsystem not to propagate W to R's CPU until after R
+has executed, which is possible if W executes shortly before R.
+
+The third relation included in hb is like ppo, in that it only links
+events that are on the same CPU.  However it is more difficult to
+explain, because it arises only indirectly from the requirement of
+cache coherence.  The relation is called prop, and it links two events
+on CPU C in situations where a store from some other CPU comes after
+the first event in the coherence order and propagates to C before the
+second event executes.
+
+This is best explained with some examples.  The simplest case looks
+like this:
+
+	int x;
+
+	P0()
+	{
+		int r1;
+
+		WRITE_ONCE(x, 1);
+		r1 = READ_ONCE(x);
+	}
+
+	P1()
+	{
+		WRITE_ONCE(x, 8);
+	}
+
+If r1 = 8 at the end then P0's accesses must have executed in program
+order.  We can deduce this from the operational model; if P0's load
+had executed before its store then the value of the store would have
+been forwarded to the load, so r1 would have ended up equal to 1, not
+8.  In this case there is a prop link from P0's write event to its read
+event, because P1's store came after P0's store in x's coherence
+order, and P1's store propagated to P0 before P0's load executed.
+
+An equally simple case involves two loads of the same location that
+read from different stores:
+
+	int x = 0;
+
+	P0()
+	{
+		int r1, r2;
+
+		r1 = READ_ONCE(x);
+		r2 = READ_ONCE(x);
+	}
+
+	P1()
+	{
+		WRITE_ONCE(x, 9);
+	}
+
+If r1 = 0 and r2 = 9 at the end then P0's accesses must have executed
+in program order.  If the second load had executed before the first
+then the x = 9 store must have been propagated to P0 before the first
+load executed, and so r1 would have been 9 rather than 0.  In this
+case there is a prop link from P0's first read event to its second,
+because P1's store overwrote the value read by P0's first load, and
+P1's store propagated to P0 before P0's second load executed.
+
+Less trivial examples of prop all involve fences.  Unlike the simple
+examples above, they can require that some instructions are executed
+out of program order.  This next one should look familiar:
+
+	int buf = 0, flag = 0;
+
+	P0()
+	{
+		WRITE_ONCE(buf, 1);
+		smp_wmb();
+		WRITE_ONCE(flag, 1);
+	}
+
+	P1()
+	{
+		int r1;
+		int r2;
+
+		r1 = READ_ONCE(flag);
+		r2 = READ_ONCE(buf);
+	}
+
+This is the MP pattern again, with an smp_wmb() fence between the two
+stores.  If r1 = 1 and r2 = 0 at the end then there is a prop link
+from P1's second load to its first (backwards!).  The reason is
+similar to the previous examples: The value P1 loads from buf gets
+overwritten by P0's store to buf, the fence guarantees that the store
+to buf will propagate to P1 before the store to flag does, and the
+store to flag propagates to P1 before P1 reads flag.
+
+The prop link says that in order to obtain the r1 = 1, r2 = 0 result,
+P1 must execute its second load before the first.  Indeed, if the load
+from flag were executed first, then the buf = 1 store would already
+have propagated to P1 by the time P1's load from buf executed, so r2
+would have been 1 at the end, not 0.  (The reasoning holds even for
+Alpha, although the details are more complicated and we will not go
+into them.)
+
+But what if we put an smp_rmb() fence between P1's loads?  The fence
+would force the two loads to be executed in program order, and it
+would generate a cycle in the hb relation: The fence would create a ppo
+link (hence an hb link) from the first load to the second, and the
+prop relation would give an hb link from the second load to the first.
+Since an instruction can't execute before itself, we are forced to
+conclude that if an smp_rmb() fence is added, the r1 = 1, r2 = 0
+outcome is impossible -- as it should be.
+
+The formal definition of the prop relation involves a coe or fre link,
+followed by an arbitrary number of cumul-fence links, ending with an
+rfe link.  You can concoct more exotic examples, containing more than
+one fence, although this quickly leads to diminishing returns in terms
+of complexity.  For instance, here's an example containing a coe link
+followed by two fences and an rfe link, utilizing the fact that
+release fences are A-cumulative:
+
+	int x, y, z;
+
+	P0()
+	{
+		int r0;
+
+		WRITE_ONCE(x, 1);
+		r0 = READ_ONCE(z);
+	}
+
+	P1()
+	{
+		WRITE_ONCE(x, 2);
+		smp_wmb();
+		WRITE_ONCE(y, 1);
+	}
+
+	P2()
+	{
+		int r2;
+
+		r2 = READ_ONCE(y);
+		smp_store_release(&z, 1);
+	}
+
+If x = 2, r0 = 1, and r2 = 1 after this code runs then there is a prop
+link from P0's store to its load.  This is because P0's store gets
+overwritten by P1's store since x = 2 at the end (a coe link), the
+smp_wmb() ensures that P1's store to x propagates to P2 before the
+store to y does (the first fence), the store to y propagates to P2
+before P2's load and store execute, P2's smp_store_release()
+guarantees that the stores to x and y both propagate to P0 before the
+store to z does (the second fence), and P0's load executes after the
+store to z has propagated to P0 (an rfe link).
+
+In summary, the fact that the hb relation links memory access events
+in the order they execute means that it must not have cycles.  This
+requirement is the content of the LKMM's "happens-before" axiom.
+
+The LKMM defines yet another relation connected to times of
+instruction execution, but it is not included in hb.  It relies on the
+particular properties of strong fences, which we cover in the next
+section.
+
+
+THE PROPAGATES-BEFORE RELATION: pb
+----------------------------------
+
+The propagates-before (pb) relation capitalizes on the special
+features of strong fences.  It links two events E and F whenever some
+store is coherence-later than E and propagates to every CPU and to RAM
+before F executes.  The formal definition requires that E be linked to
+F via a coe or fre link, an arbitrary number of cumul-fences, an
+optional rfe link, a strong fence, and an arbitrary number of hb
+links.  Let's see how this definition works out.
+
+Consider first the case where E is a store (implying that the sequence
+of links begins with coe).  Then there are events W, X, Y, and Z such
+that:
+
+	E ->coe W ->cumul-fence* X ->rfe? Y ->strong-fence Z ->hb* F,
+
+where the * suffix indicates an arbitrary number of links of the
+specified type, and the ? suffix indicates the link is optional (Y may
+be equal to X).  Because of the cumul-fence links, we know that W will
+propagate to Y's CPU before X does, hence before Y executes and hence
+before the strong fence executes.  Because this fence is strong, we
+know that W will propagate to every CPU and to RAM before Z executes.
+And because of the hb links, we know that Z will execute before F.
+Thus W, which comes later than E in the coherence order, will
+propagate to every CPU and to RAM before F executes.
+
+The case where E is a load is exactly the same, except that the first
+link in the sequence is fre instead of coe.
+
+The existence of a pb link from E to F implies that E must execute
+before F.  To see why, suppose that F executed first.  Then W would
+have propagated to E's CPU before E executed.  If E was a store, the
+memory subsystem would then be forced to make E come after W in the
+coherence order, contradicting the fact that E ->coe W.  If E was a
+load, the memory subsystem would then be forced to satisfy E's read
+request with the value stored by W or an even later store,
+contradicting the fact that E ->fre W.
+
+A good example illustrating how pb works is the SB pattern with strong
+fences:
+
+	int x = 0, y = 0;
+
+	P0()
+	{
+		int r0;
+
+		WRITE_ONCE(x, 1);
+		smp_mb();
+		r0 = READ_ONCE(y);
+	}
+
+	P1()
+	{
+		int r1;
+
+		WRITE_ONCE(y, 1);
+		smp_mb();
+		r1 = READ_ONCE(x);
+	}
+
+If r0 = 0 at the end then there is a pb link from P0's load to P1's
+load: an fre link from P0's load to P1's store (which overwrites the
+value read by P0), and a strong fence between P1's store and its load.
+In this example, the sequences of cumul-fence and hb links are empty.
+Note that this pb link is not included in hb as an instance of prop,
+because it does not start and end on the same CPU.
+
+Similarly, if r1 = 0 at the end then there is a pb link from P1's load
+to P0's.  This means that if both r1 and r2 were 0 there would be a
+cycle in pb, which is not possible since an instruction cannot execute
+before itself.  Thus, adding smp_mb() fences to the SB pattern
+prevents the r0 = 0, r1 = 0 outcome.
+
+In summary, the fact that the pb relation links events in the order
+they execute means that it cannot have cycles.  This requirement is
+the content of the LKMM's "propagation" axiom.
+
+
+RCU RELATIONS: link, gp-link, rscs-link, and rcu-path
+-----------------------------------------------------
+
+RCU (Read-Copy-Update) is a powerful synchronization mechanism.  It
+rests on two concepts: grace periods and read-side critical sections.
+
+A grace period is the span of time occupied by a call to
+synchronize_rcu().  A read-side critical section (or just critical
+section, for short) is a region of code delimited by rcu_read_lock()
+at the start and rcu_read_unlock() at the end.  Critical sections can
+be nested, although we won't make use of this fact.
+
+As far as memory models are concerned, RCU's main feature is its
+Grace-Period Guarantee, which states that a critical section can never
+span a full grace period.  In more detail, the Guarantee says:
+
+	If a critical section starts before a grace period then it
+	must end before the grace period does.  In addition, every
+	store that propagates to the critical section's CPU before the
+	end of the critical section must propagate to every CPU before
+	the end of the grace period.
+
+	If a critical section ends after a grace period ends then it
+	must start after the grace period does.  In addition, every
+	store that propagates to the grace period's CPU before the
+	start of the grace period must propagate to every CPU before
+	the start of the critical section.
+
+Here is a simple example of RCU in action:
+
+	int x, y;
+
+	P0()
+	{
+		rcu_read_lock();
+		WRITE_ONCE(x, 1);
+		WRITE_ONCE(y, 1);
+		rcu_read_unlock();
+	}
+
+	P1()
+	{
+		int r1, r2;
+
+		r1 = READ_ONCE(x);
+		synchronize_rcu();
+		r2 = READ_ONCE(y);
+	}
+
+The Grace Period Guarantee tells us that when this code runs, it will
+never end with r1 = 1 and r2 = 0.  The reasoning is as follows.  r1 = 1
+means that P0's store to x propagated to P1 before P1 called
+synchronize_rcu(), so P0's critical section must have started before
+P1's grace period.  On the other hand, r2 = 0 means that P0's store to
+y, which occurs before the end of the critical section, did not
+propagate to P1 before the end of the grace period, violating the
+Guarantee.
+
+In the kernel's implementations of RCU, the business about stores
+propagating to every CPU is realized by placing strong fences at
+suitable places in the RCU-related code.  Thus, if a critical section
+starts before a grace period does then the critical section's CPU will
+execute an smp_mb() fence after the end of the critical section and
+some time before the grace period's synchronize_rcu() call returns.
+And if a critical section ends after a grace period does then the
+synchronize_rcu() routine will execute an smp_mb() fence at its start
+and some time before the critical section's opening rcu_read_lock()
+executes.
+
+What exactly do we mean by saying that a critical section "starts
+before" or "ends after" a grace period?  Some aspects of the meaning
+are pretty obvious, as in the example above, but the details aren't
+entirely clear.  The LKMM formalizes this notion by means of a
+relation with the unfortunately generic name "link".  It is a very
+general relation; among other things, X ->link Z includes cases where
+X happens-before or is equal to some event Y which is equal to or
+comes before Z in the coherence order.  Taking Y = Z, this says that
+X ->rfe Z implies X ->link Z, and taking Y = X, it says that X ->fr Z
+and X ->co Z each imply X ->link Z.
+
+The formal definition of the link relation is more than a little
+obscure, and we won't give it here.  It is closely related to the pb
+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 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 ->link F.  In other words, E and F are connected by a
+	grace period followed by an instance of 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 ->link F.  Roughly speaking, this says that some event
+	in the same critical section as E is connected by link to F.
+
+If we think of the 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 says more than this, because it
+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.
+
+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 connections in which the number of gp-link instances is
+>= the number of rscs-link instances.  It does this by defining the
+rcu-path 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 connections
+with at least as many of the former as the latter.  The LKMM's "rcu"
+axiom then says that there are no events E such that E ->rcu-path 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.
+
+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
+question, and let S be the synchronize_rcu() fence event for the grace
+period.  Saying that the critical section starts before S means there
+are events E and F where E is po-after L (which marks the start of the
+critical section), E is "before" F in the sense of the link relation,
+and F is po-before the grace period S:
+
+	L ->po E ->link F ->po S.
+
+Let W be the store mentioned above, let Z come before the end of the
+critical section and witness that W propagates to the critical
+section's CPU by reading from W, and let Y on some arbitrary CPU be a
+witness that W has not propagated to that CPU, where Y happens after
+some event X which is po-after S.  Symbolically, this amounts to:
+
+	S ->po X ->hb* Y ->fr W ->rf Z ->po U.
+
+The fr link from Y to W indicates that W has not propagated to Y's CPU
+at the time that Y executes.  From this, it can be shown (see the
+discussion of the link relation earlier) that X and Z are connected by
+link, yielding:
+
+	S ->po X ->link Z ->po U.
+
+These 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.
+
+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
+time with statement labels added to the memory access instructions:
+
+	int x, y;
+
+	P0()
+	{
+		rcu_read_lock();
+		W: WRITE_ONCE(x, 1);
+		X: WRITE_ONCE(y, 1);
+		rcu_read_unlock();
+	}
+
+	P1()
+	{
+		int r1, r2;
+
+		Y: r1 = READ_ONCE(x);
+		synchronize_rcu();
+		Z: r2 = READ_ONCE(y);
+	}
+
+
+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 ->link X.  In addition, there is a synchronize_rcu() between Y and
+Z, so therefore we have Y ->gp-link X.
+
+If r1 = 1 at the end then P1's load at Y reads from P0's store at W,
+so we have W ->link Y.  In addition, W and X are in the same critical
+section, so therefore we have X ->rscs-link Y.
+
+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.
+
+For contrast, let's see what can happen in a more complicated example:
+
+	int x, y, z;
+
+	P0()
+	{
+		int r0;
+
+		rcu_read_lock();
+		W: r0 = READ_ONCE(x);
+		X: WRITE_ONCE(y, 1);
+		rcu_read_unlock();
+	}
+
+	P1()
+	{
+		int r1;
+
+		Y: r1 = READ_ONCE(y);
+		synchronize_rcu();
+		Z: WRITE_ONCE(z, 1);
+	}
+
+	P2()
+	{
+		int r2;
+
+		rcu_read_lock();
+		U: r2 = READ_ONCE(z);
+		V: WRITE_ONCE(x, 1);
+		rcu_read_unlock();
+	}
+
+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:
+
+P0			P1			P2
+--------------------	--------------------	--------------------
+rcu_read_lock()
+X: WRITE_ONCE(y, 1)
+			Y: r1 = READ_ONCE(y)
+			synchronize_rcu() starts
+			.			rcu_read_lock()
+			.			V: WRITE_ONCE(x, 1)
+W: r0 = READ_ONCE(x)	.
+rcu_read_unlock()	.
+			synchronize_rcu() ends
+			Z: WRITE_ONCE(z, 1)
+						U: r2 = READ_ONCE(z)
+						rcu_read_unlock()
+
+This requires P0 and P2 to execute their loads and stores out of
+program order, but of course they are allowed to do so.  And as you
+can see, the Grace Period Guarantee is not violated: The critical
+section in P0 both starts before P1's grace period does and ends
+before it does, and the critical section in P2 both starts after P1's
+grace period does and ends after it does.
+
+
+ODDS AND ENDS
+-------------
+
+This section covers material that didn't quite fit anywhere in the
+earlier sections.
+
+The descriptions in this document don't always match the formal
+version of the LKMM exactly.  For example, the actual formal
+definition of the prop relation makes the initial coe or fre part
+optional, and it doesn't require the events linked by the relation to
+be on the same CPU.  These differences are very unimportant; indeed,
+instances where the coe/fre part of prop is missing are of no interest
+because all the other parts (fences and rfe) are already included in
+hb anyway, and where the formal model adds prop into hb, it includes
+an explicit requirement that the events being linked are on the same
+CPU.
+
+Another minor difference has to do with events that are both memory
+accesses and fences, such as those corresponding to smp_load_acquire()
+calls.  In the formal model, these events aren't actually both reads
+and fences; rather, they are read events with an annotation marking
+them as acquires.  (Or write events annotated as releases, in the case
+smp_store_release().)  The final effect is the same.
+
+Although we didn't mention it above, the instruction execution
+ordering provided by the smp_rmb() fence doesn't apply to read events
+that are part of a non-value-returning atomic update.  For instance,
+given:
+
+	atomic_inc(&x);
+	smp_rmb();
+	r1 = READ_ONCE(y);
+
+it is not guaranteed that the load from y will execute after the
+update to x.  This is because the ARMv8 architecture allows
+non-value-returning atomic operations effectively to be executed off
+the CPU.  Basically, the CPU tells the memory subsystem to increment
+x, and then the increment is carried out by the memory hardware with
+no further involvement from the CPU.  Since the CPU doesn't ever read
+the value of x, there is nothing for the smp_rmb() fence to act on.
+
+The LKMM defines a few extra synchronization operations in terms of
+things we have already covered.  In particular, rcu_dereference() and
+lockless_dereference() are both treated as a READ_ONCE() followed by
+smp_read_barrier_depends() -- which also happens to be how they are
+defined in include/linux/rcupdate.h and include/linux/compiler.h,
+respectively.
+
+There are a few oddball fences which need special treatment:
+smp_mb__before_atomic(), smp_mb__after_atomic(), and
+smp_mb__after_spinlock().  The LKMM uses fence events with special
+annotations for them; they act as strong fences just like smp_mb()
+except for the sets of events that they order.  Instead of ordering
+all po-earlier events against all po-later events, as smp_mb() does,
+they behave as follows:
+
+	smp_mb__before_atomic() orders all po-earlier events against
+	po-later atomic updates and the events following them;
+
+	smp_mb__after_atomic() orders po-earlier atomic updates and
+	the events preceding them against all po-later events;
+
+	smp_mb_after_spinlock() orders po-earlier lock acquisition
+	events and the events preceding them against all po-later
+	events.
+
+The LKMM includes locking.  In fact, there is special code for locking
+in the formal model, added in order to make tools run faster.
+However, this special code is intended to be exactly equivalent to
+concepts we have already covered.  A spinlock_t variable is treated
+the same as an int, and spin_lock(&s) is treated the same as:
+
+	while (cmpxchg_acquire(&s, 0, 1) != 0)
+		cpu_relax();
+
+which waits until s is equal to 0 and then atomically sets it to 1,
+and where the read part of the atomic update is also an acquire fence.
+An alternate way to express the same thing would be:
+
+	r = xchg_acquire(&s, 1);
+
+along with a requirement that at the end, r = 0.  spin_unlock(&s) is
+treated the same as:
+
+	smp_store_release(&s, 0);
+
+Interestingly, RCU and locking each introduce the possibility of
+deadlock.  When faced with code sequences such as:
+
+	spin_lock(&s);
+	spin_lock(&s);
+	spin_unlock(&s);
+	spin_unlock(&s);
+
+or:
+
+	rcu_read_lock();
+	synchronize_rcu();
+	rcu_read_unlock();
+
+what does the LKMM have to say?  Answer: It says there are no allowed
+executions at all, which makes sense.  But this can also lead to
+misleading results, because if a piece of code has multiple possible
+executions, some of which deadlock, the model will report only on the
+non-deadlocking executions.  For example:
+
+	int x, y;
+
+	P0()
+	{
+		int r0;
+
+		WRITE_ONCE(x, 1);
+		r0 = READ_ONCE(y);
+	}
+
+	P1()
+	{
+		rcu_read_lock();
+		if (READ_ONCE(x) > 0) {
+			WRITE_ONCE(y, 36);
+			synchronize_rcu();
+		}
+		rcu_read_unlock();
+	}
+
+Is it possible to end up with r0 = 36 at the end?  The LKMM will tell
+you it is not, but the model won't mention that this is because P1
+will self-deadlock in the executions where it stores 36 in y.

tools/memory-model/Documentation/recipes.txt

···
+This document provides "recipes", that is, litmus tests for commonly
+occurring situations, as well as a few that illustrate subtly broken but
+attractive nuisances.  Many of these recipes include example code from
+v4.13 of the Linux kernel.
+
+The first section covers simple special cases, the second section
+takes off the training wheels to cover more involved examples,
+and the third section provides a few rules of thumb.
+
+
+Simple special cases
+====================
+
+This section presents two simple special cases, the first being where
+there is only one CPU or only one memory location is accessed, and the
+second being use of that old concurrency workhorse, locking.
+
+
+Single CPU or single memory location
+------------------------------------
+
+If there is only one CPU on the one hand or only one variable
+on the other, the code will execute in order.  There are (as
+usual) some things to be careful of:
+
+1.	Some aspects of the C language are unordered.  For example,
+	in the expression "f(x) + g(y)", the order in which f and g are
+	called is not defined; the object code is allowed to use either
+	order or even to interleave the computations.
+
+2.	Compilers are permitted to use the "as-if" rule.  That is, a
+	compiler can emit whatever code it likes for normal accesses,
+	as long as the results of a single-threaded execution appear
+	just as if the compiler had followed all the relevant rules.
+	To see this, compile with a high level of optimization and run
+	the debugger on the resulting binary.
+
+3.	If there is only one variable but multiple CPUs, that variable
+	must be properly aligned and all accesses to that variable must
+	be full sized.	Variables that straddle cachelines or pages void
+	your full-ordering warranty, as do undersized accesses that load
+	from or store to only part of the variable.
+
+4.	If there are multiple CPUs, accesses to shared variables should
+	use READ_ONCE() and WRITE_ONCE() or stronger to prevent load/store
+	tearing, load/store fusing, and invented loads and stores.
+	There are exceptions to this rule, including:
+
+	i.	When there is no possibility of a given shared variable
+		being updated by some other CPU, for example, while
+		holding the update-side lock, reads from that variable
+		need not use READ_ONCE().
+
+	ii.	When there is no possibility of a given shared variable
+		being either read or updated by other CPUs, for example,
+		when running during early boot, reads from that variable
+		need not use READ_ONCE() and writes to that variable
+		need not use WRITE_ONCE().
+
+
+Locking
+-------
+
+Locking is well-known and straightforward, at least if you don't think
+about it too hard.  And the basic rule is indeed quite simple: Any CPU that
+has acquired a given lock sees any changes previously seen or made by any
+CPU before it released that same lock.  Note that this statement is a bit
+stronger than "Any CPU holding a given lock sees all changes made by any
+CPU during the time that CPU was holding this same lock".  For example,
+consider the following pair of code fragments:
+
+	/* See MP+polocks.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		spin_lock(&mylock);
+		WRITE_ONCE(y, 1);
+		spin_unlock(&mylock);
+	}
+
+	void CPU1(void)
+	{
+		spin_lock(&mylock);
+		r0 = READ_ONCE(y);
+		spin_unlock(&mylock);
+		r1 = READ_ONCE(x);
+	}
+
+The basic rule guarantees that if CPU0() acquires mylock before CPU1(),
+then both r0 and r1 must be set to the value 1.  This also has the
+consequence that if the final value of r0 is equal to 1, then the final
+value of r1 must also be equal to 1.  In contrast, the weaker rule would
+say nothing about the final value of r1.
+
+The converse to the basic rule also holds, as illustrated by the
+following litmus test:
+
+	/* See MP+porevlocks.litmus. */
+	void CPU0(void)
+	{
+		r0 = READ_ONCE(y);
+		spin_lock(&mylock);
+		r1 = READ_ONCE(x);
+		spin_unlock(&mylock);
+	}
+
+	void CPU1(void)
+	{
+		spin_lock(&mylock);
+		WRITE_ONCE(x, 1);
+		spin_unlock(&mylock);
+		WRITE_ONCE(y, 1);
+	}
+
+This converse to the basic rule guarantees that if CPU0() acquires
+mylock before CPU1(), then both r0 and r1 must be set to the value 0.
+This also has the consequence that if the final value of r1 is equal
+to 0, then the final value of r0 must also be equal to 0.  In contrast,
+the weaker rule would say nothing about the final value of r0.
+
+These examples show only a single pair of CPUs, but the effects of the
+locking basic rule extend across multiple acquisitions of a given lock
+across multiple CPUs.
+
+However, it is not necessarily the case that accesses ordered by
+locking will be seen as ordered by CPUs not holding that lock.
+Consider this example:
+
+	/* See Z6.0+pooncelock+pooncelock+pombonce.litmus. */
+	void CPU0(void)
+	{
+		spin_lock(&mylock);
+		WRITE_ONCE(x, 1);
+		WRITE_ONCE(y, 1);
+		spin_unlock(&mylock);
+	}
+
+	void CPU1(void)
+	{
+		spin_lock(&mylock);
+		r0 = READ_ONCE(y);
+		WRITE_ONCE(z, 1);
+		spin_unlock(&mylock);
+	}
+
+	void CPU2(void)
+	{
+		WRITE_ONCE(z, 2);
+		smp_mb();
+		r1 = READ_ONCE(x);
+	}
+
+Counter-intuitive though it might be, it is quite possible to have
+the final value of r0 be 1, the final value of z be 2, and the final
+value of r1 be 0.  The reason for this surprising outcome is that
+CPU2() never acquired the lock, and thus did not benefit from the
+lock's ordering properties.
+
+Ordering can be extended to CPUs not holding the lock by careful use
+of smp_mb__after_spinlock():
+
+	/* See Z6.0+pooncelock+poonceLock+pombonce.litmus. */
+	void CPU0(void)
+	{
+		spin_lock(&mylock);
+		WRITE_ONCE(x, 1);
+		WRITE_ONCE(y, 1);
+		spin_unlock(&mylock);
+	}
+
+	void CPU1(void)
+	{
+		spin_lock(&mylock);
+		smp_mb__after_spinlock();
+		r0 = READ_ONCE(y);
+		WRITE_ONCE(z, 1);
+		spin_unlock(&mylock);
+	}
+
+	void CPU2(void)
+	{
+		WRITE_ONCE(z, 2);
+		smp_mb();
+		r1 = READ_ONCE(x);
+	}
+
+This addition of smp_mb__after_spinlock() strengthens the lock acquisition
+sufficiently to rule out the counter-intuitive outcome.
+
+
+Taking off the training wheels
+==============================
+
+This section looks at more complex examples, including message passing,
+load buffering, release-acquire chains, store buffering.
+Many classes of litmus tests have abbreviated names, which may be found
+here: https://www.cl.cam.ac.uk/~pes20/ppc-supplemental/test6.pdf
+
+
+Message passing (MP)
+--------------------
+
+The MP pattern has one CPU execute a pair of stores to a pair of variables
+and another CPU execute a pair of loads from this same pair of variables,
+but in the opposite order.  The goal is to avoid the counter-intuitive
+outcome in which the first load sees the value written by the second store
+but the second load does not see the value written by the first store.
+In the absence of any ordering, this goal may not be met, as can be seen
+in the MP+poonceonces.litmus litmus test.  This section therefore looks at
+a number of ways of meeting this goal.
+
+
+Release and acquire
+~~~~~~~~~~~~~~~~~~~
+
+Use of smp_store_release() and smp_load_acquire() is one way to force
+the desired MP ordering.  The general approach is shown below:
+
+	/* See MP+pooncerelease+poacquireonce.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		smp_store_release(&y, 1);
+	}
+
+	void CPU1(void)
+	{
+		r0 = smp_load_acquire(&y);
+		r1 = READ_ONCE(x);
+	}
+
+The smp_store_release() macro orders any prior accesses against the
+store, while the smp_load_acquire macro orders the load against any
+subsequent accesses.  Therefore, if the final value of r0 is the value 1,
+the final value of r1 must also be the value 1.
+
+The init_stack_slab() function in lib/stackdepot.c uses release-acquire
+in this way to safely initialize of a slab of the stack.  Working out
+the mutual-exclusion design is left as an exercise for the reader.
+
+
+Assign and dereference
+~~~~~~~~~~~~~~~~~~~~~~
+
+Use of rcu_assign_pointer() and rcu_dereference() is quite similar to the
+use of smp_store_release() and smp_load_acquire(), except that both
+rcu_assign_pointer() and rcu_dereference() operate on RCU-protected
+pointers.  The general approach is shown below:
+
+	/* See MP+onceassign+derefonce.litmus. */
+	int z;
+	int *y = &z;
+	int x;
+
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		rcu_assign_pointer(y, &x);
+	}
+
+	void CPU1(void)
+	{
+		rcu_read_lock();
+		r0 = rcu_dereference(y);
+		r1 = READ_ONCE(*r0);
+		rcu_read_unlock();
+	}
+
+In this example, if the final value of r0 is &x then the final value of
+r1 must be 1.
+
+The rcu_assign_pointer() macro has the same ordering properties as does
+smp_store_release(), but the rcu_dereference() macro orders the load only
+against later accesses that depend on the value loaded.  A dependency
+is present if the value loaded determines the address of a later access
+(address dependency, as shown above), the value written by a later store
+(data dependency), or whether or not a later store is executed in the
+first place (control dependency).  Note that the term "data dependency"
+is sometimes casually used to cover both address and data dependencies.
+
+In lib/prime_numbers.c, the expand_to_next_prime() function invokes
+rcu_assign_pointer(), and the next_prime_number() function invokes
+rcu_dereference().  This combination mediates access to a bit vector
+that is expanded as additional primes are needed.
+
+
+Write and read memory barriers
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+It is usually better to use smp_store_release() instead of smp_wmb()
+and to use smp_load_acquire() instead of smp_rmb().  However, the older
+smp_wmb() and smp_rmb() APIs are still heavily used, so it is important
+to understand their use cases.  The general approach is shown below:
+
+	/* See MP+wmbonceonce+rmbonceonce.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		smp_wmb();
+		WRITE_ONCE(y, 1);
+	}
+
+	void CPU1(void)
+	{
+		r0 = READ_ONCE(y);
+		smp_rmb();
+		r1 = READ_ONCE(x);
+	}
+
+The smp_wmb() macro orders prior stores against later stores, and the
+smp_rmb() macro orders prior loads against later loads.  Therefore, if
+the final value of r0 is 1, the final value of r1 must also be 1.
+
+The the xlog_state_switch_iclogs() function in fs/xfs/xfs_log.c contains
+the following write-side code fragment:
+
+	log->l_curr_block -= log->l_logBBsize;
+	ASSERT(log->l_curr_block >= 0);
+	smp_wmb();
+	log->l_curr_cycle++;
+
+And the xlog_valid_lsn() function in fs/xfs/xfs_log_priv.h contains
+the corresponding read-side code fragment:
+
+	cur_cycle = ACCESS_ONCE(log->l_curr_cycle);
+	smp_rmb();
+	cur_block = ACCESS_ONCE(log->l_curr_block);
+
+Alternatively, consider the following comment in function
+perf_output_put_handle() in kernel/events/ring_buffer.c:
+
+	 *   kernel				user
+	 *
+	 *   if (LOAD ->data_tail) {		LOAD ->data_head
+	 *			(A)		smp_rmb()	(C)
+	 *	STORE $data			LOAD $data
+	 *	smp_wmb()	(B)		smp_mb()	(D)
+	 *	STORE ->data_head		STORE ->data_tail
+	 *   }
+
+The B/C pairing is an example of the MP pattern using smp_wmb() on the
+write side and smp_rmb() on the read side.
+
+Of course, given that smp_mb() is strictly stronger than either smp_wmb()
+or smp_rmb(), any code fragment that would work with smp_rmb() and
+smp_wmb() would also work with smp_mb() replacing either or both of the
+weaker barriers.
+
+
+Load buffering (LB)
+-------------------
+
+The LB pattern has one CPU load from one variable and then store to a
+second, while another CPU loads from the second variable and then stores
+to the first.  The goal is to avoid the counter-intuitive situation where
+each load reads the value written by the other CPU's store.  In the
+absence of any ordering it is quite possible that this may happen, as
+can be seen in the LB+poonceonces.litmus litmus test.
+
+One way of avoiding the counter-intuitive outcome is through the use of a
+control dependency paired with a full memory barrier:
+
+	/* See LB+ctrlonceonce+mbonceonce.litmus. */
+	void CPU0(void)
+	{
+		r0 = READ_ONCE(x);
+		if (r0)
+			WRITE_ONCE(y, 1);
+	}
+
+	void CPU1(void)
+	{
+		r1 = READ_ONCE(y);
+		smp_mb();
+		WRITE_ONCE(x, 1);
+	}
+
+This pairing of a control dependency in CPU0() with a full memory
+barrier in CPU1() prevents r0 and r1 from both ending up equal to 1.
+
+The A/D pairing from the ring-buffer use case shown earlier also
+illustrates LB.  Here is a repeat of the comment in
+perf_output_put_handle() in kernel/events/ring_buffer.c, showing a
+control dependency on the kernel side and a full memory barrier on
+the user side:
+
+	 *   kernel				user
+	 *
+	 *   if (LOAD ->data_tail) {		LOAD ->data_head
+	 *			(A)		smp_rmb()	(C)
+	 *	STORE $data			LOAD $data
+	 *	smp_wmb()	(B)		smp_mb()	(D)
+	 *	STORE ->data_head		STORE ->data_tail
+	 *   }
+	 *
+	 * Where A pairs with D, and B pairs with C.
+
+The kernel's control dependency between the load from ->data_tail
+and the store to data combined with the user's full memory barrier
+between the load from data and the store to ->data_tail prevents
+the counter-intuitive outcome where the kernel overwrites the data
+before the user gets done loading it.
+
+
+Release-acquire chains
+----------------------
+
+Release-acquire chains are a low-overhead, flexible, and easy-to-use
+method of maintaining order.  However, they do have some limitations that
+need to be fully understood.  Here is an example that maintains order:
+
+	/* See ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		smp_store_release(&y, 1);
+	}
+
+	void CPU1(void)
+	{
+		r0 = smp_load_acquire(y);
+		smp_store_release(&z, 1);
+	}
+
+	void CPU2(void)
+	{
+		r1 = smp_load_acquire(z);
+		r2 = READ_ONCE(x);
+	}
+
+In this case, if r0 and r1 both have final values of 1, then r2 must
+also have a final value of 1.
+
+The ordering in this example is stronger than it needs to be.  For
+example, ordering would still be preserved if CPU1()'s smp_load_acquire()
+invocation was replaced with READ_ONCE().
+
+It is tempting to assume that CPU0()'s store to x is globally ordered
+before CPU1()'s store to z, but this is not the case:
+
+	/* See Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		smp_store_release(&y, 1);
+	}
+
+	void CPU1(void)
+	{
+		r0 = smp_load_acquire(y);
+		smp_store_release(&z, 1);
+	}
+
+	void CPU2(void)
+	{
+		WRITE_ONCE(z, 2);
+		smp_mb();
+		r1 = READ_ONCE(x);
+	}
+
+One might hope that if the final value of r0 is 1 and the final value
+of z is 2, then the final value of r1 must also be 1, but it really is
+possible for r1 to have the final value of 0.  The reason, of course,
+is that in this version, CPU2() is not part of the release-acquire chain.
+This situation is accounted for in the rules of thumb below.
+
+Despite this limitation, release-acquire chains are low-overhead as
+well as simple and powerful, at least as memory-ordering mechanisms go.
+
+
+Store buffering
+---------------
+
+Store buffering can be thought of as upside-down load buffering, so
+that one CPU first stores to one variable and then loads from a second,
+while another CPU stores to the second variable and then loads from the
+first.  Preserving order requires nothing less than full barriers:
+
+	/* See SB+mbonceonces.litmus. */
+	void CPU0(void)
+	{
+		WRITE_ONCE(x, 1);
+		smp_mb();
+		r0 = READ_ONCE(y);
+	}
+
+	void CPU1(void)
+	{
+		WRITE_ONCE(y, 1);
+		smp_mb();
+		r1 = READ_ONCE(x);
+	}
+
+Omitting either smp_mb() will allow both r0 and r1 to have final
+values of 0, but providing both full barriers as shown above prevents
+this counter-intuitive outcome.
+
+This pattern most famously appears as part of Dekker's locking
+algorithm, but it has a much more practical use within the Linux kernel
+of ordering wakeups.  The following comment taken from waitqueue_active()
+in include/linux/wait.h shows the canonical pattern:
+
+ *      CPU0 - waker                    CPU1 - waiter
+ *
+ *                                      for (;;) {
+ *      @cond = true;                     prepare_to_wait(&wq_head, &wait, state);
+ *      smp_mb();                         // smp_mb() from set_current_state()
+ *      if (waitqueue_active(wq_head))         if (@cond)
+ *        wake_up(wq_head);                      break;
+ *                                        schedule();
+ *                                      }
+ *                                      finish_wait(&wq_head, &wait);
+
+On CPU0, the store is to @cond and the load is in waitqueue_active().
+On CPU1, prepare_to_wait() contains both a store to wq_head and a call
+to set_current_state(), which contains an smp_mb() barrier; the load is
+"if (@cond)".  The full barriers prevent the undesirable outcome where
+CPU1 puts the waiting task to sleep and CPU0 fails to wake it up.
+
+Note that use of locking can greatly simplify this pattern.
+
+
+Rules of thumb
+==============
+
+There might seem to be no pattern governing what ordering primitives are
+needed in which situations, but this is not the case.  There is a pattern
+based on the relation between the accesses linking successive CPUs in a
+given litmus test.  There are three types of linkage:
+
+1.	Write-to-read, where the next CPU reads the value that the
+	previous CPU wrote.  The LB litmus-test patterns contain only
+	this type of relation.	In formal memory-modeling texts, this
+	relation is called "reads-from" and is usually abbreviated "rf".
+
+2.	Read-to-write, where the next CPU overwrites the value that the
+	previous CPU read.  The SB litmus test contains only this type
+	of relation.  In formal memory-modeling texts, this relation is
+	often called "from-reads" and is sometimes abbreviated "fr".
+
+3.	Write-to-write, where the next CPU overwrites the value written
+	by the previous CPU.  The Z6.0 litmus test pattern contains a
+	write-to-write relation between the last access of CPU1() and
+	the first access of CPU2().  In formal memory-modeling texts,
+	this relation is often called "coherence order" and is sometimes
+	abbreviated "co".  In the C++ standard, it is instead called
+	"modification order" and often abbreviated "mo".
+
+The strength of memory ordering required for a given litmus test to
+avoid a counter-intuitive outcome depends on the types of relations
+linking the memory accesses for the outcome in question:
+
+o	If all links are write-to-read links, then the weakest
+	possible ordering within each CPU suffices.  For example, in
+	the LB litmus test, a control dependency was enough to do the
+	job.
+
+o	If all but one of the links are write-to-read links, then a
+	release-acquire chain suffices.  Both the MP and the ISA2
+	litmus tests illustrate this case.
+
+o	If more than one of the links are something other than
+	write-to-read links, then a full memory barrier is required
+	between each successive pair of non-write-to-read links.  This
+	case is illustrated by the Z6.0 litmus tests, both in the
+	locking and in the release-acquire sections.
+
+However, if you find yourself having to stretch these rules of thumb
+to fit your situation, you should consider creating a litmus test and
+running it on the model.

tools/memory-model/Documentation/references.txt

···
+This document provides background reading for memory models and related
+tools.  These documents are aimed at kernel hackers who are interested
+in memory models.
+
+
+Hardware manuals and models
+===========================
+
+o	SPARC International Inc. (Ed.). 1994. "The SPARC Architecture
+	Reference Manual Version 9". SPARC International Inc.
+
+o	Compaq Computer Corporation (Ed.). 2002. "Alpha Architecture
+	Reference Manual".  Compaq Computer Corporation.
+
+o	Intel Corporation (Ed.). 2002. "A Formal Specification of Intel
+	Itanium Processor Family Memory Ordering". Intel Corporation.
+
+o	Intel Corporation (Ed.). 2002. "Intel 64 and IA-32 Architectures
+	Software Developer’s Manual". Intel Corporation.
+
+o	Peter Sewell, Susmit Sarkar, Scott Owens, Francesco Zappa Nardelli,
+	and Magnus O. Myreen. 2010. "x86-TSO: A Rigorous and Usable
+	Programmer's Model for x86 Multiprocessors". Commun. ACM 53, 7
+	(July, 2010), 89-97. http://doi.acm.org/10.1145/1785414.1785443
+
+o	IBM Corporation (Ed.). 2009. "Power ISA Version 2.06". IBM
+	Corporation.
+
+o	ARM Ltd. (Ed.). 2009. "ARM Barrier Litmus Tests and Cookbook".
+	ARM Ltd.
+
+o	Susmit Sarkar, Peter Sewell, Jade Alglave, Luc Maranget, and
+	Derek Williams.  2011. "Understanding POWER Multiprocessors". In
+	Proceedings of the 32Nd ACM SIGPLAN Conference on Programming
+	Language Design and Implementation (PLDI ’11). ACM, New York,
+	NY, USA, 175–186.
+
+o	Susmit Sarkar, Kayvan Memarian, Scott Owens, Mark Batty,
+	Peter Sewell, Luc Maranget, Jade Alglave, and Derek Williams.
+	2012. "Synchronising C/C++ and POWER". In Proceedings of the 33rd
+	ACM SIGPLAN Conference on Programming Language Design and
+	Implementation (PLDI '12). ACM, New York, NY, USA, 311-322.
+
+o	ARM Ltd. (Ed.). 2014. "ARM Architecture Reference Manual (ARMv8,
+	for ARMv8-A architecture profile)". ARM Ltd.
+
+o	Imagination Technologies, LTD. 2015. "MIPS(R) Architecture
+	For Programmers, Volume II-A: The MIPS64(R) Instruction,
+	Set Reference Manual". Imagination Technologies,
+	LTD. https://imgtec.com/?do-download=4302.
+
+o	Shaked Flur, Kathryn E. Gray, Christopher Pulte, Susmit
+	Sarkar, Ali Sezgin, Luc Maranget, Will Deacon, and Peter
+	Sewell. 2016. "Modelling the ARMv8 Architecture, Operationally:
+	Concurrency and ISA". In Proceedings of the 43rd Annual ACM
+	SIGPLAN-SIGACT Symposium on Principles of Programming Languages
+	(POPL ’16). ACM, New York, NY, USA, 608–621.
+
+o	Shaked Flur, Susmit Sarkar, Christopher Pulte, Kyndylan Nienhuis,
+	Luc Maranget, Kathryn E. Gray, Ali Sezgin, Mark Batty, and Peter
+	Sewell. 2017. "Mixed-size Concurrency: ARM, POWER, C/C++11,
+	and SC". In Proceedings of the 44th ACM SIGPLAN Symposium on
+	Principles of Programming Languages (POPL 2017). ACM, New York,
+	NY, USA, 429–442.
+
+
+Linux-kernel memory model
+=========================
+
+o	Andrea Parri, Alan Stern, Luc Maranget, Paul E. McKenney,
+	and Jade Alglave.  2017. "A formal model of
+	Linux-kernel memory ordering - companion webpage".
+	http://moscova.inria.fr/∼maranget/cats7/linux/. (2017). [Online;
+	accessed 30-January-2017].
+
+o	Jade Alglave, Luc Maranget, Paul E. McKenney, Andrea Parri, and
+	Alan Stern.  2017.  "A formal kernel memory-ordering model (part 1)"
+	Linux Weekly News.  https://lwn.net/Articles/718628/
+
+o	Jade Alglave, Luc Maranget, Paul E. McKenney, Andrea Parri, and
+	Alan Stern.  2017.  "A formal kernel memory-ordering model (part 2)"
+	Linux Weekly News.  https://lwn.net/Articles/720550/
+
+
+Memory-model tooling
+====================
+
+o	Daniel Jackson. 2002. "Alloy: A Lightweight Object Modelling
+	Notation". ACM Trans. Softw. Eng. Methodol. 11, 2 (April 2002),
+	256–290. http://doi.acm.org/10.1145/505145.505149
+
+o	Jade Alglave, Luc Maranget, and Michael Tautschnig. 2014. "Herding
+	Cats: Modelling, Simulation, Testing, and Data Mining for Weak
+	Memory". ACM Trans. Program. Lang. Syst. 36, 2, Article 7 (July
+	2014), 7:1–7:74 pages.
+
+o	Jade Alglave, Patrick Cousot, and Luc Maranget. 2016. "Syntax and
+	semantics of the weak consistency model specification language
+	cat". CoRR abs/1608.07531 (2016). http://arxiv.org/abs/1608.07531
+
+
+Memory-model comparisons
+========================
+
+o	Paul E. McKenney, Ulrich Weigand, Andrea Parri, and Boqun
+	Feng. 2016. "Linux-Kernel Memory Model". (6 June 2016).
+	http://open-std.org/JTC1/SC22/WG21/docs/papers/2016/p0124r2.html.

tools/memory-model/MAINTAINERS

···
+LINUX KERNEL MEMORY MODEL
+M:	Alan Stern <[e-mail]>
+M:	Andrea Parri <[e-mail]>
+M:	Will Deacon <[e-mail]>
+M:	Peter Zijlstra <[e-mail]>
+M:	Boqun Feng <[e-mail]>
+M:	Nicholas Piggin <[e-mail]>
+M:	David Howells <[e-mail]>
+M:	Jade Alglave <[e-mail]>
+M:	Luc Maranget <[e-mail]>
+M:	"Paul E. McKenney" <[e-mail]>
+L:	[e-mail]
+S:	Supported
+T:	git git://git.kernel.org/pub/scm/linux/kernel/git/paulmck/linux-rcu.git
+F:	tools/memory-model/

tools/memory-model/README

···
+			=========================
+			LINUX KERNEL MEMORY MODEL
+			=========================
+
+============
+INTRODUCTION
+============
+
+This directory contains the memory model of the Linux kernel, written
+in the "cat" language and executable by the (externally provided)
+"herd7" simulator, which exhaustively explores the state space of
+small litmus tests.
+
+In addition, the "klitmus7" tool (also externally provided) may be used
+to convert a litmus test to a Linux kernel module, which in turn allows
+that litmus test to be exercised within the Linux kernel.
+
+
+============
+REQUIREMENTS
+============
+
+The "herd7" and "klitmus7" tools must be downloaded separately:
+
+  https://github.com/herd/herdtools7
+
+See "herdtools7/INSTALL.md" for installation instructions.
+
+Alternatively, Abhishek Bhardwaj has kindly provided a Docker image
+of these tools at "abhishek40/memory-model".  Abhishek suggests the
+following commands to install and use this image:
+
+  - Users should install Docker for their distribution.
+  - docker run -itd abhishek40/memory-model
+  - docker attach <id-emitted-from-the-previous-command>
+
+Gentoo users might wish to make use of Patrick McLean's package:
+
+  https://gitweb.gentoo.org/repo/gentoo.git/tree/dev-util/herdtools7
+
+These packages may not be up-to-date with respect to the GitHub
+repository.
+
+
+==================
+BASIC USAGE: HERD7
+==================
+
+The memory model is used, in conjunction with "herd7", to exhaustively
+explore the state space of small litmus tests.
+
+For example, to run SB+mbonceonces.litmus against the memory model:
+
+  $ herd7 -conf linux-kernel.cfg litmus-tests/SB+mbonceonces.litmus
+
+Here is the corresponding output:
+
+  Test SB+mbonceonces Allowed
+  States 3
+  0:r0=0; 1:r0=1;
+  0:r0=1; 1:r0=0;
+  0:r0=1; 1:r0=1;
+  No
+  Witnesses
+  Positive: 0 Negative: 3
+  Condition exists (0:r0=0 /\ 1:r0=0)
+  Observation SB+mbonceonces Never 0 3
+  Time SB+mbonceonces 0.01
+  Hash=d66d99523e2cac6b06e66f4c995ebb48
+
+The "Positive: 0 Negative: 3" and the "Never 0 3" each indicate that
+this litmus test's "exists" clause can not be satisfied.
+
+See "herd7 -help" or "herdtools7/doc/" for more information.
+
+
+=====================
+BASIC USAGE: KLITMUS7
+=====================
+
+The "klitmus7" tool converts a litmus test into a Linux kernel module,
+which may then be loaded and run.
+
+For example, to run SB+mbonceonces.litmus against hardware:
+
+  $ mkdir mymodules
+  $ klitmus7 -o mymodules litmus-tests/SB+mbonceonces.litmus
+  $ cd mymodules ; make
+  $ sudo sh run.sh
+
+The corresponding output includes:
+
+  Test SB+mbonceonces Allowed
+  Histogram (3 states)
+  644580  :>0:r0=1; 1:r0=0;
+  644328  :>0:r0=0; 1:r0=1;
+  711092  :>0:r0=1; 1:r0=1;
+  No
+  Witnesses
+  Positive: 0, Negative: 2000000
+  Condition exists (0:r0=0 /\ 1:r0=0) is NOT validated
+  Hash=d66d99523e2cac6b06e66f4c995ebb48
+  Observation SB+mbonceonces Never 0 2000000
+  Time SB+mbonceonces 0.16
+
+The "Positive: 0 Negative: 2000000" and the "Never 0 2000000" indicate
+that during two million trials, the state specified in this litmus
+test's "exists" clause was not reached.
+
+And, as with "herd7", please see "klitmus7 -help" or "herdtools7/doc/"
+for more information.
+
+
+====================
+DESCRIPTION OF FILES
+====================
+
+Documentation/cheatsheet.txt
+	Quick-reference guide to the Linux-kernel memory model.
+
+Documentation/explanation.txt
+	Describes the memory model in detail.
+
+Documentation/recipes.txt
+	Lists common memory-ordering patterns.
+
+Documentation/references.txt
+	Provides background reading.
+
+linux-kernel.bell
+	Categorizes the relevant instructions, including memory
+	references, memory barriers, atomic read-modify-write operations,
+	lock acquisition/release, and RCU operations.
+
+	More formally, this file (1) lists the subtypes of the various
+	event types used by the memory model and (2) performs RCU
+	read-side critical section nesting analysis.
+
+linux-kernel.cat
+	Specifies what reorderings are forbidden by memory references,
+	memory barriers, atomic read-modify-write operations, and RCU.
+
+	More formally, this file specifies what executions are forbidden
+	by the memory model.  Allowed executions are those which
+	satisfy the model's "coherence", "atomic", "happens-before",
+	"propagation", and "rcu" axioms, which are defined in the file.
+
+linux-kernel.cfg
+	Convenience file that gathers the common-case herd7 command-line
+	arguments.
+
+linux-kernel.def
+	Maps from C-like syntax to herd7's internal litmus-test
+	instruction-set architecture.
+
+litmus-tests
+	Directory containing a few representative litmus tests, which
+	are listed in litmus-tests/README.  A great deal more litmus
+	tests are available at https://github.com/paulmckrcu/litmus.
+
+lock.cat
+	Provides a front-end analysis of lock acquisition and release,
+	for example, associating a lock acquisition with the preceding
+	and following releases and checking for self-deadlock.
+
+	More formally, this file defines a performance-enhanced scheme
+	for generation of the possible reads-from and coherence order
+	relations on the locking primitives.
+
+README
+	This file.
+
+
+===========
+LIMITATIONS
+===========
+
+The Linux-kernel memory model has the following limitations:
+
+1.	Compiler optimizations are not modeled.  Of course, the use
+	of READ_ONCE() and WRITE_ONCE() limits the compiler's ability
+	to optimize, but there is Linux-kernel code that uses bare C
+	memory accesses.  Handling this code is on the to-do list.
+	For more information, see Documentation/explanation.txt (in
+	particular, the "THE PROGRAM ORDER RELATION: po AND po-loc"
+	and "A WARNING" sections).
+
+2.	Multiple access sizes for a single variable are not supported,
+	and neither are misaligned or partially overlapping accesses.
+
+3.	Exceptions and interrupts are not modeled.  In some cases,
+	this limitation can be overcome by modeling the interrupt or
+	exception with an additional process.
+
+4.	I/O such as MMIO or DMA is not supported.
+
+5.	Self-modifying code (such as that found in the kernel's
+	alternatives mechanism, function tracer, Berkeley Packet Filter
+	JIT compiler, and module loader) is not supported.
+
+6.	Complete modeling of all variants of atomic read-modify-write
+	operations, locking primitives, and RCU is not provided.
+	For example, call_rcu() and rcu_barrier() are not supported.
+	However, a substantial amount of support is provided for these
+	operations, as shown in the linux-kernel.def file.
+
+The "herd7" tool has some additional limitations of its own, apart from
+the memory model:
+
+1.	Non-trivial data structures such as arrays or structures are
+	not supported.	However, pointers are supported, allowing trivial
+	linked lists to be constructed.
+
+2.	Dynamic memory allocation is not supported, although this can
+	be worked around in some cases by supplying multiple statically
+	allocated variables.
+
+Some of these limitations may be overcome in the future, but others are
+more likely to be addressed by incorporating the Linux-kernel memory model
+into other tools.

tools/memory-model/linux-kernel.bell

···
+// SPDX-License-Identifier: GPL-2.0+
+(*
+ * Copyright (C) 2015 Jade Alglave <[e-mail]>,
+ * Copyright (C) 2016 Luc Maranget <[e-mail]> for Inria
+ * Copyright (C) 2017 Alan Stern <[e-mail]>,
+ *                    Andrea Parri <[e-mail]>
+ *
+ * An earlier version of this file appears in the companion webpage for
+ * "Frightening small children and disconcerting grown-ups: Concurrency
+ * in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
+ * which is to appear in ASPLOS 2018.
+ *)
+
+"Linux kernel memory model"
+
+enum Accesses = 'once (*READ_ONCE,WRITE_ONCE,ACCESS_ONCE*) ||
+		'release (*smp_store_release*) ||
+		'acquire (*smp_load_acquire*) ||
+		'noreturn (* R of non-return RMW *)
+instructions R[{'once,'acquire,'noreturn}]
+instructions W[{'once,'release}]
+instructions RMW[{'once,'acquire,'release}]
+
+enum Barriers = 'wmb (*smp_wmb*) ||
+		'rmb (*smp_rmb*) ||
+		'mb (*smp_mb*) ||
+		'rb_dep (*smp_read_barrier_depends*) ||
+		'rcu-lock (*rcu_read_lock*)  ||
+		'rcu-unlock (*rcu_read_unlock*) ||
+		'sync-rcu (*synchronize_rcu*) ||
+		'before_atomic (*smp_mb__before_atomic*) ||
+		'after_atomic (*smp_mb__after_atomic*) ||
+		'after_spinlock (*smp_mb__after_spinlock*)
+instructions F[Barriers]
+
+(* Compute matching pairs of nested Rcu-lock and Rcu-unlock *)
+let matched = let rec
+	    unmatched-locks = Rcu-lock \ domain(matched)
+	and unmatched-unlocks = Rcu-unlock \ range(matched)
+	and unmatched = unmatched-locks | unmatched-unlocks
+	and unmatched-po = [unmatched] ; po ; [unmatched]
+	and unmatched-locks-to-unlocks =
+		[unmatched-locks] ; po ; [unmatched-unlocks]
+	and matched = matched | (unmatched-locks-to-unlocks \
+		(unmatched-po ; unmatched-po))
+	in matched
+
+(* Validate nesting *)
+flag ~empty Rcu-lock \ domain(matched) as unbalanced-rcu-locking
+flag ~empty Rcu-unlock \ range(matched) as unbalanced-rcu-locking
+
+(* Outermost level of nesting only *)
+let crit = matched \ (po^-1 ; matched ; po^-1)

tools/memory-model/linux-kernel.cat

···
+// SPDX-License-Identifier: GPL-2.0+
+(*
+ * Copyright (C) 2015 Jade Alglave <[e-mail]>,
+ * Copyright (C) 2016 Luc Maranget <[e-mail]> for Inria
+ * Copyright (C) 2017 Alan Stern <[e-mail]>,
+ *                    Andrea Parri <[e-mail]>
+ *
+ * An earlier version of this file appears in the companion webpage for
+ * "Frightening small children and disconcerting grown-ups: Concurrency
+ * in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
+ * which is to appear in ASPLOS 2018.
+ *)
+
+"Linux kernel memory model"
+
+(*
+ * File "lock.cat" handles locks and is experimental.
+ * It can be replaced by include "cos.cat" for tests that do not use locks.
+ *)
+
+include "lock.cat"
+
+(*******************)
+(* Basic relations *)
+(*******************)
+
+(* Fences *)
+let rb-dep = [R] ; fencerel(Rb_dep) ; [R]
+let rmb = [R \ Noreturn] ; fencerel(Rmb) ; [R \ Noreturn]
+let wmb = [W] ; fencerel(Wmb) ; [W]
+let mb = ([M] ; fencerel(Mb) ; [M]) |
+	([M] ; fencerel(Before_atomic) ; [RMW] ; po? ; [M]) |
+	([M] ; po? ; [RMW] ; fencerel(After_atomic) ; [M]) |
+	([M] ; po? ; [LKW] ; fencerel(After_spinlock) ; [M])
+let gp = po ; [Sync-rcu] ; po?
+
+let strong-fence = mb | gp
+
+(* Release Acquire *)
+let acq-po = [Acquire] ; po ; [M]
+let po-rel = [M] ; po ; [Release]
+let rfi-rel-acq = [Release] ; rfi ; [Acquire]
+
+(**********************************)
+(* Fundamental coherence ordering *)
+(**********************************)
+
+(* Sequential Consistency Per Variable *)
+let com = rf | co | fr
+acyclic po-loc | com as coherence
+
+(* Atomic Read-Modify-Write *)
+empty rmw & (fre ; coe) as atomic
+
+(**********************************)
+(* Instruction execution ordering *)
+(**********************************)
+
+(* Preserved Program Order *)
+let dep = addr | data
+let rwdep = (dep | ctrl) ; [W]
+let overwrite = co | fr
+let to-w = rwdep | (overwrite & int)
+let rrdep = addr | (dep ; rfi)
+let strong-rrdep = rrdep+ & rb-dep
+let to-r = strong-rrdep | rfi-rel-acq
+let fence = strong-fence | wmb | po-rel | rmb | acq-po
+let ppo = rrdep* ; (to-r | to-w | fence)
+
+(* Propagation: Ordering from release operations and strong fences. *)
+let A-cumul(r) = rfe? ; r
+let cumul-fence = A-cumul(strong-fence | po-rel) | wmb
+let prop = (overwrite & ext)? ; cumul-fence* ; rfe?
+
+(*
+ * Happens Before: Ordering from the passage of time.
+ * No fences needed here for prop because relation confined to one process.
+ *)
+let hb = ppo | rfe | ((prop \ id) & int)
+acyclic hb as happens-before
+
+(****************************************)
+(* Write and fence propagation ordering *)
+(****************************************)
+
+(* Propagation: Each non-rf link needs a strong fence. *)
+let pb = prop ; strong-fence ; hb*
+acyclic pb as propagation
+
+(*******)
+(* RCU *)
+(*******)
+
+(*
+ * Effect of read-side critical section proceeds from the rcu_read_lock()
+ * onward on the one hand and from the rcu_read_unlock() backwards on the
+ * other hand.
+ *)
+let rscs = po ; crit^-1 ; po?
+
+(*
+ * The synchronize_rcu() strong fence is special in that it can order not
+ * one but two non-rf relations, but only in conjunction with an RCU
+ * read-side critical section.
+ *)
+let link = hb* ; pb* ; prop
+
+(* Chains that affect the RCU grace-period guarantee *)
+let gp-link = gp ; link
+let rscs-link = rscs ; link
+
+(*
+ * A cycle containing at least as many grace periods as RCU read-side
+ * critical sections is forbidden.
+ *)
+let rec rcu-path =
+	gp-link |
+	(gp-link ; rscs-link) |
+	(rscs-link ; gp-link) |
+	(rcu-path ; rcu-path) |
+	(gp-link ; rcu-path ; rscs-link) |
+	(rscs-link ; rcu-path ; gp-link)
+
+irreflexive rcu-path as rcu

tools/memory-model/linux-kernel.cfg

···
+macros linux-kernel.def
+bell linux-kernel.bell
+model linux-kernel.cat
+graph columns
+squished true
+showevents noregs
+movelabel true
+fontsize 8
+xscale 2.0
+yscale 1.5
+arrowsize 0.8
+showinitrf false
+showfinalrf false
+showinitwrites false
+splines spline
+pad 0.1
+edgeattr hb,color,indigo
+edgeattr co,color,blue
+edgeattr mb,color,darkgreen
+edgeattr wmb,color,darkgreen
+edgeattr rmb,color,darkgreen

tools/memory-model/linux-kernel.def

···
+// SPDX-License-Identifier: GPL-2.0+
+//
+// An earlier version of this file appears in the companion webpage for
+// "Frightening small children and disconcerting grown-ups: Concurrency
+// in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
+// which is to appear in ASPLOS 2018.
+
+// ONCE
+READ_ONCE(X) __load{once}(X)
+WRITE_ONCE(X,V) { __store{once}(X,V); }
+
+// Release Acquire and friends
+smp_store_release(X,V) { __store{release}(*X,V); }
+smp_load_acquire(X) __load{acquire}(*X)
+rcu_assign_pointer(X,V) { __store{release}(X,V); }
+lockless_dereference(X) __load{lderef}(X)
+rcu_dereference(X) __load{deref}(X)
+
+// Fences
+smp_mb() { __fence{mb} ; }
+smp_rmb() { __fence{rmb} ; }
+smp_wmb() { __fence{wmb} ; }
+smp_read_barrier_depends() { __fence{rb_dep}; }
+smp_mb__before_atomic() { __fence{before_atomic} ; }
+smp_mb__after_atomic() { __fence{after_atomic} ; }
+smp_mb__after_spinlock() { __fence{after_spinlock} ; }
+
+// Exchange
+xchg(X,V)  __xchg{mb}(X,V)
+xchg_relaxed(X,V) __xchg{once}(X,V)
+xchg_release(X,V) __xchg{release}(X,V)
+xchg_acquire(X,V) __xchg{acquire}(X,V)
+cmpxchg(X,V,W) __cmpxchg{mb}(X,V,W)
+cmpxchg_relaxed(X,V,W) __cmpxchg{once}(X,V,W)
+cmpxchg_acquire(X,V,W) __cmpxchg{acquire}(X,V,W)
+cmpxchg_release(X,V,W) __cmpxchg{release}(X,V,W)
+
+// Spinlocks
+spin_lock(X) { __lock(X) ; }
+spin_unlock(X) { __unlock(X) ; }
+spin_trylock(X) __trylock(X)
+
+// RCU
+rcu_read_lock() { __fence{rcu-lock}; }
+rcu_read_unlock() { __fence{rcu-unlock};}
+synchronize_rcu() { __fence{sync-rcu}; }
+synchronize_rcu_expedited() { __fence{sync-rcu}; }
+
+// Atomic
+atomic_read(X) READ_ONCE(*X)
+atomic_set(X,V) { WRITE_ONCE(*X,V) ; }
+atomic_read_acquire(X) smp_load_acquire(X)
+atomic_set_release(X,V) { smp_store_release(X,V); }
+
+atomic_add(V,X) { __atomic_op(X,+,V) ; }
+atomic_sub(V,X) { __atomic_op(X,-,V) ; }
+atomic_inc(X)   { __atomic_op(X,+,1) ; }
+atomic_dec(X)   { __atomic_op(X,-,1) ; }
+
+atomic_add_return(V,X) __atomic_op_return{mb}(X,+,V)
+atomic_add_return_relaxed(V,X) __atomic_op_return{once}(X,+,V)
+atomic_add_return_acquire(V,X) __atomic_op_return{acquire}(X,+,V)
+atomic_add_return_release(V,X) __atomic_op_return{release}(X,+,V)
+atomic_fetch_add(V,X) __atomic_fetch_op{mb}(X,+,V)
+atomic_fetch_add_relaxed(V,X) __atomic_fetch_op{once}(X,+,V)
+atomic_fetch_add_acquire(V,X) __atomic_fetch_op{acquire}(X,+,V)
+atomic_fetch_add_release(V,X) __atomic_fetch_op{release}(X,+,V)
+
+atomic_inc_return(X) __atomic_op_return{mb}(X,+,1)
+atomic_inc_return_relaxed(X) __atomic_op_return{once}(X,+,1)
+atomic_inc_return_acquire(X) __atomic_op_return{acquire}(X,+,1)
+atomic_inc_return_release(X) __atomic_op_return{release}(X,+,1)
+atomic_fetch_inc(X) __atomic_fetch_op{mb}(X,+,1)
+atomic_fetch_inc_relaxed(X) __atomic_fetch_op{once}(X,+,1)
+atomic_fetch_inc_acquire(X) __atomic_fetch_op{acquire}(X,+,1)
+atomic_fetch_inc_release(X) __atomic_fetch_op{release}(X,+,1)
+
+atomic_sub_return(V,X) __atomic_op_return{mb}(X,-,V)
+atomic_sub_return_relaxed(V,X) __atomic_op_return{once}(X,-,V)
+atomic_sub_return_acquire(V,X) __atomic_op_return{acquire}(X,-,V)
+atomic_sub_return_release(V,X) __atomic_op_return{release}(X,-,V)
+atomic_fetch_sub(V,X) __atomic_fetch_op{mb}(X,-,V)
+atomic_fetch_sub_relaxed(V,X) __atomic_fetch_op{once}(X,-,V)
+atomic_fetch_sub_acquire(V,X) __atomic_fetch_op{acquire}(X,-,V)
+atomic_fetch_sub_release(V,X) __atomic_fetch_op{release}(X,-,V)
+
+atomic_dec_return(X) __atomic_op_return{mb}(X,-,1)
+atomic_dec_return_relaxed(X) __atomic_op_return{once}(X,-,1)
+atomic_dec_return_acquire(X) __atomic_op_return{acquire}(X,-,1)
+atomic_dec_return_release(X) __atomic_op_return{release}(X,-,1)
+atomic_fetch_dec(X) __atomic_fetch_op{mb}(X,-,1)
+atomic_fetch_dec_relaxed(X) __atomic_fetch_op{once}(X,-,1)
+atomic_fetch_dec_acquire(X) __atomic_fetch_op{acquire}(X,-,1)
+atomic_fetch_dec_release(X) __atomic_fetch_op{release}(X,-,1)
+
+atomic_xchg(X,V) __xchg{mb}(X,V)
+atomic_xchg_relaxed(X,V) __xchg{once}(X,V)
+atomic_xchg_release(X,V) __xchg{release}(X,V)
+atomic_xchg_acquire(X,V) __xchg{acquire}(X,V)
+atomic_cmpxchg(X,V,W) __cmpxchg{mb}(X,V,W)
+atomic_cmpxchg_relaxed(X,V,W) __cmpxchg{once}(X,V,W)
+atomic_cmpxchg_acquire(X,V,W) __cmpxchg{acquire}(X,V,W)
+atomic_cmpxchg_release(X,V,W) __cmpxchg{release}(X,V,W)
+
+atomic_sub_and_test(V,X) __atomic_op_return{mb}(X,-,V) == 0
+atomic_dec_and_test(X)  __atomic_op_return{mb}(X,-,1) == 0
+atomic_inc_and_test(X)  __atomic_op_return{mb}(X,+,1) == 0
+atomic_add_negative(V,X) __atomic_op_return{mb}(X,+,V) < 0

tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus

···
+C CoRR+poonceonce+Once
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*x);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0)

tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus

···
+C CoRW+poonceonce+Once
+
+{}
+
+P0(int *x)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x)
+{
+	WRITE_ONCE(*x, 2);
+}
+
+exists (x=2 /\ 0:r0=2)

tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus

···
+C CoWR+poonceonce+Once
+
+{}
+
+P0(int *x)
+{
+	int r0;
+
+	WRITE_ONCE(*x, 1);
+	r0 = READ_ONCE(*x);
+}
+
+P1(int *x)
+{
+	WRITE_ONCE(*x, 2);
+}
+
+exists (x=1 /\ 0:r0=2)

tools/memory-model/litmus-tests/CoWW+poonceonce.litmus

···
+C CoWW+poonceonce
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*x, 2);
+}
+
+exists (x=1)

tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus

···
+C IRIW+mbonceonces+OnceOnce
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*x);
+	smp_mb();
+	r1 = READ_ONCE(*y);
+}
+
+P2(int *y)
+{
+	WRITE_ONCE(*y, 1);
+}
+
+P3(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	smp_mb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0 /\ 3:r0=1 /\ 3:r1=0)

tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus

···
+C IRIW+poonceonces+OnceOnce
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*x);
+	r1 = READ_ONCE(*y);
+}
+
+P2(int *y)
+{
+	WRITE_ONCE(*y, 1);
+}
+
+P3(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0 /\ 3:r0=1 /\ 3:r1=0)

tools/memory-model/litmus-tests/ISA2+poonceonces.litmus

···
+C ISA2+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *y, int *z)
+{
+	int r0;
+
+	r0 = READ_ONCE(*y);
+	WRITE_ONCE(*z, 1);
+}
+
+P2(int *x, int *z)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*z);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

tools/memory-model/litmus-tests/ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus

···
+C ISA2+pooncerelease+poacquirerelease+poacquireonce
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	smp_store_release(y, 1);
+}
+
+P1(int *y, int *z)
+{
+	int r0;
+
+	r0 = smp_load_acquire(y);
+	smp_store_release(z, 1);
+}
+
+P2(int *x, int *z)
+{
+	int r0;
+	int r1;
+
+	r0 = smp_load_acquire(z);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus

···
+C LB+ctrlonceonce+mbonceonce
+
+{}
+
+P0(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	if (r0)
+		WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*y);
+	smp_mb();
+	WRITE_ONCE(*x, 1);
+}
+
+exists (0:r0=1 /\ 1:r0=1)

tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus

···
+C LB+poacquireonce+pooncerelease
+
+{}
+
+P0(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	smp_store_release(y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = smp_load_acquire(y);
+	WRITE_ONCE(*x, 1);
+}
+
+exists (0:r0=1 /\ 1:r0=1)

tools/memory-model/litmus-tests/LB+poonceonces.litmus

···
+C LB+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*y);
+	WRITE_ONCE(*x, 1);
+}
+
+exists (0:r0=1 /\ 1:r0=1)

tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus

···
+C MP+onceassign+derefonce.litmus
+
+{
+y=z;
+z=0;
+}
+
+P0(int *x, int **y)
+{
+	WRITE_ONCE(*x, 1);
+	rcu_assign_pointer(*y, x);
+}
+
+P1(int *x, int **y)
+{
+	int *r0;
+	int r1;
+
+	rcu_read_lock();
+	r0 = rcu_dereference(*y);
+	r1 = READ_ONCE(*r0);
+	rcu_read_unlock();
+}
+
+exists (1:r0=x /\ 1:r1=0)

tools/memory-model/litmus-tests/MP+polocks.litmus

···
+C MP+polocks
+
+{}
+
+P0(int *x, int *y, spinlock_t *mylock)
+{
+	WRITE_ONCE(*x, 1);
+	spin_lock(mylock);
+	WRITE_ONCE(*y, 1);
+	spin_unlock(mylock);
+}
+
+P1(int *x, int *y, spinlock_t *mylock)
+{
+	int r0;
+	int r1;
+
+	spin_lock(mylock);
+	r0 = READ_ONCE(*y);
+	spin_unlock(mylock);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0)

tools/memory-model/litmus-tests/MP+poonceonces.litmus

···
+C MP+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0)

tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus

···
+C MP+pooncerelease+poacquireonce
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	smp_store_release(y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = smp_load_acquire(y);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0)

tools/memory-model/litmus-tests/MP+porevlocks.litmus

···
+C MP+porevlocks
+
+{}
+
+P0(int *x, int *y, spinlock_t *mylock)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	spin_lock(mylock);
+	r1 = READ_ONCE(*x);
+	spin_unlock(mylock);
+}
+
+P1(int *x, int *y, spinlock_t *mylock)
+{
+	spin_lock(mylock);
+	WRITE_ONCE(*x, 1);
+	spin_unlock(mylock);
+	WRITE_ONCE(*y, 1);
+}
+
+exists (0:r0=1 /\ 0:r1=0)

tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus

···
+C MP+wmbonceonce+rmbonceonce
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	smp_wmb();
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	smp_rmb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 1:r1=0)

tools/memory-model/litmus-tests/R+mbonceonces.litmus

···
+C R+mbonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	smp_mb();
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*y, 2);
+	smp_mb();
+	r0 = READ_ONCE(*x);
+}
+
+exists (y=2 /\ 1:r0=0)

tools/memory-model/litmus-tests/R+poonceonces.litmus

···
+C R+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*y, 2);
+	r0 = READ_ONCE(*x);
+}
+
+exists (y=2 /\ 1:r0=0)

tools/memory-model/litmus-tests/README

···
+This directory contains the following litmus tests:
+
+CoRR+poonceonce+Once.litmus
+	Test of read-read coherence, that is, whether or not two
+	successive reads from the same variable are ordered.
+
+CoRW+poonceonce+Once.litmus
+	Test of read-write coherence, that is, whether or not a read
+	from a given variable followed by a write to that same variable
+	are ordered.
+
+CoWR+poonceonce+Once.litmus
+	Test of write-read coherence, that is, whether or not a write
+	to a given variable followed by a read from that same variable
+	are ordered.
+
+CoWW+poonceonce.litmus
+	Test of write-write coherence, that is, whether or not two
+	successive writes to the same variable are ordered.
+
+IRIW+mbonceonces+OnceOnce.litmus
+	Test of independent reads from independent writes with smp_mb()
+	between each pairs of reads.  In other words, is smp_mb()
+	sufficient to cause two different reading processes to agree on
+	the order of a pair of writes, where each write is to a different
+	variable by a different process.
+
+IRIW+poonceonces+OnceOnce.litmus
+	Test of independent reads from independent writes with nothing
+	between each pairs of reads.  In other words, is anything at all
+	needed to cause two different reading processes to agree on the
+	order of a pair of writes, where each write is to a different
+	variable by a different process.
+
+ISA2+poonceonces.litmus
+	As below, but with store-release replaced with WRITE_ONCE()
+	and load-acquire replaced with READ_ONCE().
+
+ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus
+	Can a release-acquire chain order a prior store against
+	a later load?
+
+LB+ctrlonceonce+mbonceonce.litmus
+	Does a control dependency and an smp_mb() suffice for the
+	load-buffering litmus test, where each process reads from one
+	of two variables then writes to the other?
+
+LB+poacquireonce+pooncerelease.litmus
+	Does a release-acquire pair suffice for the load-buffering
+	litmus test, where each process reads from one of two variables then
+	writes to the other?
+
+LB+poonceonces.litmus
+	As above, but with store-release replaced with WRITE_ONCE()
+	and load-acquire replaced with READ_ONCE().
+
+MP+onceassign+derefonce.litmus
+	As below, but with rcu_assign_pointer() and an rcu_dereference().
+
+MP+polocks.litmus
+	As below, but with the second access of the writer process
+	and the first access of reader process protected by a lock.
+
+MP+poonceonces.litmus
+	As below, but without the smp_rmb() and smp_wmb().
+
+MP+pooncerelease+poacquireonce.litmus
+	As below, but with a release-acquire chain.
+
+MP+porevlocks.litmus
+	As below, but with the first access of the writer process
+	and the second access of reader process protected by a lock.
+
+MP+wmbonceonce+rmbonceonce.litmus
+	Does a smp_wmb() (between the stores) and an smp_rmb() (between
+	the loads) suffice for the message-passing litmus test, where one
+	process writes data and then a flag, and the other process reads
+	the flag and then the data.  (This is similar to the ISA2 tests,
+	but with two processes instead of three.)
+
+R+mbonceonces.litmus
+	This is the fully ordered (via smp_mb()) version of one of
+	the classic counterintuitive litmus tests that illustrates the
+	effects of store propagation delays.
+
+R+poonceonces.litmus
+	As above, but without the smp_mb() invocations.
+
+SB+mbonceonces.litmus
+	This is the fully ordered (again, via smp_mb() version of store
+	buffering, which forms the core of Dekker's mutual-exclusion
+	algorithm.
+
+SB+poonceonces.litmus
+	As above, but without the smp_mb() invocations.
+
+S+poonceonces.litmus
+	As below, but without the smp_wmb() and acquire load.
+
+S+wmbonceonce+poacquireonce.litmus
+	Can a smp_wmb(), instead of a release, and an acquire order
+	a prior store against a subsequent store?
+
+WRC+poonceonces+Once.litmus
+WRC+pooncerelease+rmbonceonce+Once.litmus
+	These two are members of an extension of the MP litmus-test class
+	in which the first write is moved to a separate process.
+
+Z6.0+pooncelock+pooncelock+pombonce.litmus
+	Is the ordering provided by a spin_unlock() and a subsequent
+	spin_lock() sufficient to make ordering apparent to accesses
+	by a process not holding the lock?
+
+Z6.0+pooncelock+poonceLock+pombonce.litmus
+	As above, but with smp_mb__after_spinlock() immediately
+	following the spin_lock().
+
+Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus
+	Is the ordering provided by a release-acquire chain sufficient
+	to make ordering apparent to accesses by a process that does
+	not participate in that release-acquire chain?
+
+A great many more litmus tests are available here:
+
+	https://github.com/paulmckrcu/litmus

tools/memory-model/litmus-tests/S+poonceonces.litmus

···
+C S+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 2);
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*y);
+	WRITE_ONCE(*x, 1);
+}
+
+exists (x=2 /\ 1:r0=1)

tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus

···
+C S+wmbonceonce+poacquireonce
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 2);
+	smp_wmb();
+	WRITE_ONCE(*y, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = smp_load_acquire(y);
+	WRITE_ONCE(*x, 1);
+}
+
+exists (x=2 /\ 1:r0=1)

tools/memory-model/litmus-tests/SB+mbonceonces.litmus

···
+C SB+mbonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*x, 1);
+	smp_mb();
+	r0 = READ_ONCE(*y);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*y, 1);
+	smp_mb();
+	r0 = READ_ONCE(*x);
+}
+
+exists (0:r0=0 /\ 1:r0=0)

tools/memory-model/litmus-tests/SB+poonceonces.litmus

···
+C SB+poonceonces
+
+{}
+
+P0(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*x, 1);
+	r0 = READ_ONCE(*y);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	WRITE_ONCE(*y, 1);
+	r0 = READ_ONCE(*x);
+}
+
+exists (0:r0=0 /\ 1:r0=0)

tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus

···
+C WRC+poonceonces+Once
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	WRITE_ONCE(*y, 1);
+}
+
+P2(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

tools/memory-model/litmus-tests/WRC+pooncerelease+rmbonceonce+Once.litmus

···
+C WRC+pooncerelease+rmbonceonce+Once
+
+{}
+
+P0(int *x)
+{
+	WRITE_ONCE(*x, 1);
+}
+
+P1(int *x, int *y)
+{
+	int r0;
+
+	r0 = READ_ONCE(*x);
+	smp_store_release(y, 1);
+}
+
+P2(int *x, int *y)
+{
+	int r0;
+	int r1;
+
+	r0 = READ_ONCE(*y);
+	smp_rmb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

tools/memory-model/litmus-tests/Z6.0+pooncelock+poonceLock+pombonce.litmus

···
+C Z6.0+pooncelock+poonceLock+pombonce
+
+{}
+
+P0(int *x, int *y, spinlock_t *mylock)
+{
+	spin_lock(mylock);
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*y, 1);
+	spin_unlock(mylock);
+}
+
+P1(int *y, int *z, spinlock_t *mylock)
+{
+	int r0;
+
+	spin_lock(mylock);
+	smp_mb__after_spinlock();
+	r0 = READ_ONCE(*y);
+	WRITE_ONCE(*z, 1);
+	spin_unlock(mylock);
+}
+
+P2(int *x, int *z)
+{
+	int r1;
+
+	WRITE_ONCE(*z, 2);
+	smp_mb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ z=2 /\ 2:r1=0)

tools/memory-model/litmus-tests/Z6.0+pooncelock+pooncelock+pombonce.litmus

···
+C Z6.0+pooncelock+pooncelock+pombonce
+
+{}
+
+P0(int *x, int *y, spinlock_t *mylock)
+{
+	spin_lock(mylock);
+	WRITE_ONCE(*x, 1);
+	WRITE_ONCE(*y, 1);
+	spin_unlock(mylock);
+}
+
+P1(int *y, int *z, spinlock_t *mylock)
+{
+	int r0;
+
+	spin_lock(mylock);
+	r0 = READ_ONCE(*y);
+	WRITE_ONCE(*z, 1);
+	spin_unlock(mylock);
+}
+
+P2(int *x, int *z)
+{
+	int r1;
+
+	WRITE_ONCE(*z, 2);
+	smp_mb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ z=2 /\ 2:r1=0)

tools/memory-model/litmus-tests/Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus

···
+C Z6.0+pooncerelease+poacquirerelease+mbonceonce
+
+{}
+
+P0(int *x, int *y)
+{
+	WRITE_ONCE(*x, 1);
+	smp_store_release(y, 1);
+}
+
+P1(int *y, int *z)
+{
+	int r0;
+
+	r0 = smp_load_acquire(y);
+	smp_store_release(z, 1);
+}
+
+P2(int *x, int *z)
+{
+	int r1;
+
+	WRITE_ONCE(*z, 2);
+	smp_mb();
+	r1 = READ_ONCE(*x);
+}
+
+exists (1:r0=1 /\ z=2 /\ 2:r1=0)

tools/memory-model/lock.cat

···
+// SPDX-License-Identifier: GPL-2.0+
+(*
+ * Copyright (C) 2016 Luc Maranget <[e-mail]> for Inria
+ * Copyright (C) 2017 Alan Stern <[e-mail]>
+ *)
+
+(* Generate coherence orders and handle lock operations *)
+
+include "cross.cat"
+
+(* From lock reads to their partner lock writes *)
+let lk-rmw = ([LKR] ; po-loc ; [LKW]) \ (po ; po)
+let rmw = rmw | lk-rmw
+
+(*
+ * A paired LKR must always see an unlocked value; spin_lock() calls nested
+ * inside a critical section (for the same lock) always deadlock.
+ *)
+empty ([LKW] ; po-loc ; [domain(lk-rmw)]) \ (po-loc ; [UL] ; po-loc)
+	as lock-nest
+
+(* The litmus test is invalid if an LKW event is not part of an RMW pair *)
+flag ~empty LKW \ range(lk-rmw) as unpaired-LKW
+
+(* This will be allowed if we implement spin_is_locked() *)
+flag ~empty LKR \ domain(lk-rmw) as unpaired-LKR
+
+(* There should be no R or W accesses to spinlocks *)
+let ALL-LOCKS = LKR | LKW | UL | LF
+flag ~empty [M \ IW] ; loc ; [ALL-LOCKS] as mixed-lock-accesses
+
+(* The final value of a spinlock should not be tested *)
+flag ~empty [FW] ; loc ; [ALL-LOCKS] as lock-final
+
+
+(*
+ * Put lock operations in their appropriate classes, but leave UL out of W
+ * until after the co relation has been generated.
+ *)
+let R = R | LKR | LF
+let W = W | LKW
+
+let Release = Release | UL
+let Acquire = Acquire | LKR
+
+
+(* Match LKW events to their corresponding UL events *)
+let critical = ([LKW] ; po-loc ; [UL]) \ (po-loc ; [LKW | UL] ; po-loc)
+
+flag ~empty UL \ range(critical) as unmatched-unlock
+
+(* Allow up to one unmatched LKW per location; more must deadlock *)
+let UNMATCHED-LKW = LKW \ domain(critical)
+empty ([UNMATCHED-LKW] ; loc ; [UNMATCHED-LKW]) \ id as unmatched-locks
+
+
+(* rfi for LF events: link each LKW to the LF events in its critical section *)
+let rfi-lf = ([LKW] ; po-loc ; [LF]) \ ([LKW] ; po-loc ; [UL] ; po-loc)
+
+(* rfe for LF events *)
+let all-possible-rfe-lf =
+  (*
+   * Given an LF event r, compute the possible rfe edges for that event
+   * (all those starting from LKW events in other threads),
+   * and then convert that relation to a set of single-edge relations.
+   *)
+  let possible-rfe-lf r =
+    let pair-to-relation p = p ++ 0
+    in map pair-to-relation ((LKW * {r}) & loc & ext)
+  (* Do this for each LF event r that isn't in rfi-lf *)
+  in map possible-rfe-lf (LF \ range(rfi-lf))
+
+(* Generate all rf relations for LF events *)
+with rfe-lf from cross(all-possible-rfe-lf)
+let rf = rf | rfi-lf | rfe-lf
+
+
+(* Generate all co relations, including LKW events but not UL *)
+let co0 = co0 | ([IW] ; loc ; [LKW]) |
+	(([LKW] ; loc ; [UNMATCHED-LKW]) \ [UNMATCHED-LKW])
+include "cos-opt.cat"
+let W = W | UL
+let M = R | W
+
+(* Merge UL events into co *)
+let co = (co | critical | (critical^-1 ; co))+
+let coe = co & ext
+let coi = co & int
+
+(* Merge LKR events into rf *)
+let rf = rf | ([IW | UL] ; singlestep(co) ; lk-rmw^-1)
+let rfe = rf & ext
+let rfi = rf & int
+
+let fr = rf^-1 ; co
+let fre = fr & ext
+let fri = fr & int
+
+show co,rf,fr