--- /dev/null
+Explanation of the Linux-Kernel Memory Model
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+:Author: Alan Stern <stern@rowland.harvard.edu>
+: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.
--- /dev/null
+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.
projects / linux-2.6-microblaze.git / commitdiff