Explanation of the Linux-Kernel Memory Consistency Model
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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:Author: Alan Stern <stern@rowland.harvard.edu>
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:Created: October 2017
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.. Contents
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1. INTRODUCTION
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2. BACKGROUND
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3. A SIMPLE EXAMPLE
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4. A SELECTION OF MEMORY MODELS
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5. ORDERING AND CYCLES
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6. EVENTS
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7. THE PROGRAM ORDER RELATION: po AND po-loc
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8. A WARNING
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9. DEPENDENCY RELATIONS: data, addr, and ctrl
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10. THE READS-FROM RELATION: rf, rfi, and rfe
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11. CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe
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12. THE FROM-READS RELATION: fr, fri, and fre
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13. AN OPERATIONAL MODEL
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14. PROPAGATION ORDER RELATION: cumul-fence
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15. DERIVATION OF THE LKMM FROM THE OPERATIONAL MODEL
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16. SEQUENTIAL CONSISTENCY PER VARIABLE
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17. ATOMIC UPDATES: rmw
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18. THE PRESERVED PROGRAM ORDER RELATION: ppo
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19. AND THEN THERE WAS ALPHA
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20. THE HAPPENS-BEFORE RELATION: hb
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21. THE PROPAGATES-BEFORE RELATION: pb
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22. RCU RELATIONS: rcu-link, rcu-gp, rcu-rscsi, rcu-order, rcu-fence, and rb
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23. LOCKING
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24. PLAIN ACCESSES AND DATA RACES
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25. ODDS AND ENDS
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INTRODUCTION
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------------
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The Linux-kernel memory consistency model (LKMM) is rather complex and
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obscure. This is particularly evident if you read through the
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linux-kernel.bell and linux-kernel.cat files that make up the formal
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version of the model; they are extremely terse and their meanings are
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far from clear.
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This document describes the ideas underlying the LKMM. It is meant
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for people who want to understand how the model was designed. It does
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not go into the details of the code in the .bell and .cat files;
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rather, it explains in English what the code expresses symbolically.
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Sections 2 (BACKGROUND) through 5 (ORDERING AND CYCLES) are aimed
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toward beginners; they explain what memory consistency models are and
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the basic notions shared by all such models. People already familiar
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with these concepts can skim or skip over them. Sections 6 (EVENTS)
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through 12 (THE FROM_READS RELATION) describe the fundamental
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relations used in many models. Starting in Section 13 (AN OPERATIONAL
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MODEL), the workings of the LKMM itself are covered.
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Warning: The code examples in this document are not written in the
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proper format for litmus tests. They don't include a header line, the
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initializations are not enclosed in braces, the global variables are
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not passed by pointers, and they don't have an "exists" clause at the
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end. Converting them to the right format is left as an exercise for
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the reader.
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BACKGROUND
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----------
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A memory consistency model (or just memory model, for short) is
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something which predicts, given a piece of computer code running on a
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particular kind of system, what values may be obtained by the code's
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load instructions. The LKMM makes these predictions for code running
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as part of the Linux kernel.
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In practice, people tend to use memory models the other way around.
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That is, given a piece of code and a collection of values specified
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for the loads, the model will predict whether it is possible for the
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code to run in such a way that the loads will indeed obtain the
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specified values. Of course, this is just another way of expressing
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the same idea.
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For code running on a uniprocessor system, the predictions are easy:
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Each load instruction must obtain the value written by the most recent
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store instruction accessing the same location (we ignore complicating
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factors such as DMA and mixed-size accesses.) But on multiprocessor
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systems, with multiple CPUs making concurrent accesses to shared
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memory locations, things aren't so simple.
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Different architectures have differing memory models, and the Linux
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kernel supports a variety of architectures. The LKMM has to be fairly
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permissive, in the sense that any behavior allowed by one of these
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architectures also has to be allowed by the LKMM.
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A SIMPLE EXAMPLE
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----------------
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Here is a simple example to illustrate the basic concepts. Consider
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some code running as part of a device driver for an input device. The
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driver might contain an interrupt handler which collects data from the
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device, stores it in a buffer, and sets a flag to indicate the buffer
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is full. Running concurrently on a different CPU might be a part of
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the driver code being executed by a process in the midst of a read(2)
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system call. This code tests the flag to see whether the buffer is
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ready, and if it is, copies the data back to userspace. The buffer
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and the flag are memory locations shared between the two CPUs.
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We can abstract out the important pieces of the driver code as follows
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(the reason for using WRITE_ONCE() and READ_ONCE() instead of simple
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assignment statements is discussed later):
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int buf = 0, flag = 0;
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P0()
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{
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WRITE_ONCE(buf, 1);
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WRITE_ONCE(flag, 1);
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}
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P1()
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{
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int r1;
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int r2 = 0;
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r1 = READ_ONCE(flag);
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if (r1)
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r2 = READ_ONCE(buf);
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}
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Here the P0() function represents the interrupt handler running on one
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CPU and P1() represents the read() routine running on another. The
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value 1 stored in buf represents input data collected from the device.
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Thus, P0 stores the data in buf and then sets flag. Meanwhile, P1
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reads flag into the private variable r1, and if it is set, reads the
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data from buf into a second private variable r2 for copying to
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userspace. (Presumably if flag is not set then the driver will wait a
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while and try again.)
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This pattern of memory accesses, where one CPU stores values to two
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shared memory locations and another CPU loads from those locations in
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the opposite order, is widely known as the "Message Passing" or MP
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pattern. It is typical of memory access patterns in the kernel.
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Please note that this example code is a simplified abstraction. Real
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buffers are usually larger than a single integer, real device drivers
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usually use sleep and wakeup mechanisms rather than polling for I/O
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completion, and real code generally doesn't bother to copy values into
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private variables before using them. All that is beside the point;
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the idea here is simply to illustrate the overall pattern of memory
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accesses by the CPUs.
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A memory model will predict what values P1 might obtain for its loads
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from flag and buf, or equivalently, what values r1 and r2 might end up
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with after the code has finished running.
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Some predictions are trivial. For instance, no sane memory model would
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predict that r1 = 42 or r2 = -7, because neither of those values ever
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gets stored in flag or buf.
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Some nontrivial predictions are nonetheless quite simple. For
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instance, P1 might run entirely before P0 begins, in which case r1 and
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r2 will both be 0 at the end. Or P0 might run entirely before P1
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begins, in which case r1 and r2 will both be 1.
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The interesting predictions concern what might happen when the two
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routines run concurrently. One possibility is that P1 runs after P0's
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store to buf but before the store to flag. In this case, r1 and r2
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will again both be 0. (If P1 had been designed to read buf
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unconditionally then we would instead have r1 = 0 and r2 = 1.)
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However, the most interesting possibility is where r1 = 1 and r2 = 0.
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If this were to occur it would mean the driver contains a bug, because
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incorrect data would get sent to the user: 0 instead of 1. As it
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happens, the LKMM does predict this outcome can occur, and the example
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driver code shown above is indeed buggy.
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A SELECTION OF MEMORY MODELS
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----------------------------
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The first widely cited memory model, and the simplest to understand,
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is Sequential Consistency. According to this model, systems behave as
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if each CPU executed its instructions in order but with unspecified
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timing. In other words, the instructions from the various CPUs get
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interleaved in a nondeterministic way, always according to some single
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global order that agrees with the order of the instructions in the
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program source for each CPU. The model says that the value obtained
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by each load is simply the value written by the most recently executed
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store to the same memory location, from any CPU.
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For the MP example code shown above, Sequential Consistency predicts
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that the undesired result r1 = 1, r2 = 0 cannot occur. The reasoning
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goes like this:
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Since r1 = 1, P0 must store 1 to flag before P1 loads 1 from
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it, as loads can obtain values only from earlier stores.
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P1 loads from flag before loading from buf, since CPUs execute
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their instructions in order.
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P1 must load 0 from buf before P0 stores 1 to it; otherwise r2
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would be 1 since a load obtains its value from the most recent
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store to the same address.
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P0 stores 1 to buf before storing 1 to flag, since it executes
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its instructions in order.
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Since an instruction (in this case, P0's store to flag) cannot
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execute before itself, the specified outcome is impossible.
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However, real computer hardware almost never follows the Sequential
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Consistency memory model; doing so would rule out too many valuable
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performance optimizations. On ARM and PowerPC architectures, for
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instance, the MP example code really does sometimes yield r1 = 1 and
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r2 = 0.
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x86 and SPARC follow yet a different memory model: TSO (Total Store
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Ordering). This model predicts that the undesired outcome for the MP
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pattern cannot occur, but in other respects it differs from Sequential
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Consistency. One example is the Store Buffer (SB) pattern, in which
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each CPU stores to its own shared location and then loads from the
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other CPU's location:
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int x = 0, y = 0;
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P0()
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{
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int r0;
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WRITE_ONCE(x, 1);
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r0 = READ_ONCE(y);
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}
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P1()
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{
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int r1;
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WRITE_ONCE(y, 1);
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r1 = READ_ONCE(x);
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}
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Sequential Consistency predicts that the outcome r0 = 0, r1 = 0 is
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impossible. (Exercise: Figure out the reasoning.) But TSO allows
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this outcome to occur, and in fact it does sometimes occur on x86 and
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SPARC systems.
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The LKMM was inspired by the memory models followed by PowerPC, ARM,
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x86, Alpha, and other architectures. However, it is different in
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detail from each of them.
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ORDERING AND CYCLES
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-------------------
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Memory models are all about ordering. Often this is temporal ordering
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(i.e., the order in which certain events occur) but it doesn't have to
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be; consider for example the order of instructions in a program's
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source code. We saw above that Sequential Consistency makes an
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important assumption that CPUs execute instructions in the same order
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as those instructions occur in the code, and there are many other
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instances of ordering playing central roles in memory models.
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The counterpart to ordering is a cycle. Ordering rules out cycles:
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It's not possible to have X ordered before Y, Y ordered before Z, and
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Z ordered before X, because this would mean that X is ordered before
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itself. The analysis of the MP example under Sequential Consistency
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involved just such an impossible cycle:
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W: P0 stores 1 to flag executes before
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X: P1 loads 1 from flag executes before
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Y: P1 loads 0 from buf executes before
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Z: P0 stores 1 to buf executes before
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W: P0 stores 1 to flag.
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In short, if a memory model requires certain accesses to be ordered,
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and a certain outcome for the loads in a piece of code can happen only
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if those accesses would form a cycle, then the memory model predicts
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that outcome cannot occur.
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The LKMM is defined largely in terms of cycles, as we will see.
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EVENTS
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------
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The LKMM does not work directly with the C statements that make up
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kernel source code. Instead it considers the effects of those
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statements in a more abstract form, namely, events. The model
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includes three types of events:
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Read events correspond to loads from shared memory, such as
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calls to READ_ONCE(), smp_load_acquire(), or
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rcu_dereference().
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Write events correspond to stores to shared memory, such as
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calls to WRITE_ONCE(), smp_store_release(), or atomic_set().
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Fence events correspond to memory barriers (also known as
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fences), such as calls to smp_rmb() or rcu_read_lock().
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These categories are not exclusive; a read or write event can also be
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a fence. This happens with functions like smp_load_acquire() or
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spin_lock(). However, no single event can be both a read and a write.
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Atomic read-modify-write accesses, such as atomic_inc() or xchg(),
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correspond to a pair of events: a read followed by a write. (The
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write event is omitted for executions where it doesn't occur, such as
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a cmpxchg() where the comparison fails.)
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Other parts of the code, those which do not involve interaction with
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shared memory, do not give rise to events. Thus, arithmetic and
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logical computations, control-flow instructions, or accesses to
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private memory or CPU registers are not of central interest to the
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memory model. They only affect the model's predictions indirectly.
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For example, an arithmetic computation might determine the value that
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gets stored to a shared memory location (or in the case of an array
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index, the address where the value gets stored), but the memory model
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is concerned only with the store itself -- its value and its address
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-- not the computation leading up to it.
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Events in the LKMM can be linked by various relations, which we will
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describe in the following sections. The memory model requires certain
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of these relations to be orderings, that is, it requires them not to
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have any cycles.
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THE PROGRAM ORDER RELATION: po AND po-loc
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-----------------------------------------
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The most important relation between events is program order (po). You
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can think of it as the order in which statements occur in the source
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code after branches are taken into account and loops have been
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unrolled. A better description might be the order in which
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instructions are presented to a CPU's execution unit. Thus, we say
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that X is po-before Y (written as "X ->po Y" in formulas) if X occurs
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before Y in the instruction stream.
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This is inherently a single-CPU relation; two instructions executing
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on different CPUs are never linked by po. Also, it is by definition
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an ordering so it cannot have any cycles.
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po-loc is a sub-relation of po. It links two memory accesses when the
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first comes before the second in program order and they access the
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same memory location (the "-loc" suffix).
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Although this may seem straightforward, there is one subtle aspect to
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program order we need to explain. The LKMM was inspired by low-level
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architectural memory models which describe the behavior of machine
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code, and it retains their outlook to a considerable extent. The
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read, write, and fence events used by the model are close in spirit to
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individual machine instructions. Nevertheless, the LKMM describes
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kernel code written in C, and the mapping from C to machine code can
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be extremely complex.
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Optimizing compilers have great freedom in the way they translate
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source code to object code. They are allowed to apply transformations
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that add memory accesses, eliminate accesses, combine them, split them
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into pieces, or move them around. The use of READ_ONCE(), WRITE_ONCE(),
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or one of the other atomic or synchronization primitives prevents a
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large number of compiler optimizations. In particular, it is guaranteed
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that the compiler will not remove such accesses from the generated code
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(unless it can prove the accesses will never be executed), it will not
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change the order in which they occur in the code (within limits imposed
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by the C standard), and it will not introduce extraneous accesses.
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The MP and SB examples above used READ_ONCE() and WRITE_ONCE() rather
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than ordinary memory accesses. Thanks to this usage, we can be certain
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that in the MP example, the compiler won't reorder P0's write event to
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buf and P0's write event to flag, and similarly for the other shared
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memory accesses in the examples.
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Since private variables are not shared between CPUs, they can be
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accessed normally without READ_ONCE() or WRITE_ONCE(). In fact, they
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need not even be stored in normal memory at all -- in principle a
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private variable could be stored in a CPU register (hence the convention
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that these variables have names starting with the letter 'r').
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A WARNING
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---------
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The protections provided by READ_ONCE(), WRITE_ONCE(), and others are
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not perfect; and under some circumstances it is possible for the
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compiler to undermine the memory model. Here is an example. Suppose
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both branches of an "if" statement store the same value to the same
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location:
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r1 = READ_ONCE(x);
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if (r1) {
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WRITE_ONCE(y, 2);
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... /* do something */
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} else {
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WRITE_ONCE(y, 2);
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... /* do something else */
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}
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For this code, the LKMM predicts that the load from x will always be
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executed before either of the stores to y. However, a compiler could
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lift the stores out of the conditional, transforming the code into
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something resembling:
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r1 = READ_ONCE(x);
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WRITE_ONCE(y, 2);
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if (r1) {
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... /* do something */
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} else {
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... /* do something else */
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}
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Given this version of the code, the LKMM would predict that the load
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from x could be executed after the store to y. Thus, the memory
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model's original prediction could be invalidated by the compiler.
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Another issue arises from the fact that in C, arguments to many
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operators and function calls can be evaluated in any order. For
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example:
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r1 = f(5) + g(6);
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The object code might call f(5) either before or after g(6); the
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memory model cannot assume there is a fixed program order relation
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between them. (In fact, if the function calls are inlined then the
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compiler might even interleave their object code.)
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DEPENDENCY RELATIONS: data, addr, and ctrl
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------------------------------------------
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We say that two events are linked by a dependency relation when the
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execution of the second event depends in some way on a value obtained
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from memory by the first. The first event must be a read, and the
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value it obtains must somehow affect what the second event does.
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There are three kinds of dependencies: data, address (addr), and
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control (ctrl).
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A read and a write event are linked by a data dependency if the value
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obtained by the read affects the value stored by the write. As a very
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simple example:
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int x, y;
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r1 = READ_ONCE(x);
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WRITE_ONCE(y, r1 + 5);
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The value stored by the WRITE_ONCE obviously depends on the value
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loaded by the READ_ONCE. Such dependencies can wind through
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arbitrarily complicated computations, and a write can depend on the
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values of multiple reads.
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A read event and another memory access event are linked by an address
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dependency if the value obtained by the read affects the location
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accessed by the other event. The second event can be either a read or
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a write. Here's another simple example:
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int a[20];
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int i;
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r1 = READ_ONCE(i);
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r2 = READ_ONCE(a[r1]);
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Here the location accessed by the second READ_ONCE() depends on the
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index value loaded by the first. Pointer indirection also gives rise
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to address dependencies, since the address of a location accessed
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through a pointer will depend on the value read earlier from that
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pointer.
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Finally, a read event and another memory access event are linked by a
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control dependency if the value obtained by the read affects whether
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the second event is executed at all. Simple example:
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int x, y;
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r1 = READ_ONCE(x);
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if (r1)
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WRITE_ONCE(y, 1984);
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Execution of the WRITE_ONCE() is controlled by a conditional expression
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which depends on the value obtained by the READ_ONCE(); hence there is
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a control dependency from the load to the store.
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It should be pretty obvious that events can only depend on reads that
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come earlier in program order. Symbolically, if we have R ->data X,
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R ->addr X, or R ->ctrl X (where R is a read event), then we must also
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have R ->po X. It wouldn't make sense for a computation to depend
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somehow on a value that doesn't get loaded from shared memory until
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later in the code!
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THE READS-FROM RELATION: rf, rfi, and rfe
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-----------------------------------------
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|
The reads-from relation (rf) links a write event to a read event when
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the value loaded by the read is the value that was stored by the
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write. In colloquial terms, the load "reads from" the store. We
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write W ->rf R to indicate that the load R reads from the store W. We
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further distinguish the cases where the load and the store occur on
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the same CPU (internal reads-from, or rfi) and where they occur on
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different CPUs (external reads-from, or rfe).
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For our purposes, a memory location's initial value is treated as
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though it had been written there by an imaginary initial store that
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executes on a separate CPU before the main program runs.
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Usage of the rf relation implicitly assumes that loads will always
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read from a single store. It doesn't apply properly in the presence
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of load-tearing, where a load obtains some of its bits from one store
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and some of them from another store. Fortunately, use of READ_ONCE()
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and WRITE_ONCE() will prevent load-tearing; it's not possible to have:
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|
int x = 0;
|
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P0()
|
{
|
WRITE_ONCE(x, 0x1234);
|
}
|
|
P1()
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{
|
int r1;
|
|
r1 = READ_ONCE(x);
|
}
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|
and end up with r1 = 0x1200 (partly from x's initial value and partly
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from the value stored by P0).
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|
On the other hand, load-tearing is unavoidable when mixed-size
|
accesses are used. Consider this example:
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|
union {
|
u32 w;
|
u16 h[2];
|
} x;
|
|
P0()
|
{
|
WRITE_ONCE(x.h[0], 0x1234);
|
WRITE_ONCE(x.h[1], 0x5678);
|
}
|
|
P1()
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{
|
int r1;
|
|
r1 = READ_ONCE(x.w);
|
}
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|
If r1 = 0x56781234 (little-endian!) at the end, then P1 must have read
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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.
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|
CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe
|
------------------------------------------------------------------
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|
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
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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
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that location.
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|
To put it another way, for any variable x, the coherence order (co) of
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the stores to x is simply the order in which the stores overwrite one
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another. The imaginary store which establishes x's initial value
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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.
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|
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
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x's cache line). We write W ->co W' if W comes before W' in the
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coherence order, that is, if the value stored by W gets overwritten,
|
directly or indirectly, by the value stored by W'.
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|
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
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and W' are two stores, then W ->co W'.
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|
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.
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|
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.
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|
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', smp_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).
|
|
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 six 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.
|
|
Plain-coherence: This requires that plain memory accesses
|
(those not using READ_ONCE(), WRITE_ONCE(), etc.) must obey
|
the operational model's rules regarding cache coherence.
|
|
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" and "plain-coherence" axioms are 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 obliged 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 X is a READ_ONCE() or an atomic
|
access.
|
|
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). The kernel includes a workaround for this
|
problem when the loads come from READ_ONCE(), and therefore the LKMM
|
includes address dependencies to loads in the ppo relation.
|
|
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!)
|
|
|
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 = ptr;
|
r2 = READ_ONCE(*r1);
|
}
|
|
can malfunction on Alpha systems (notice that P1 uses an ordinary load
|
to read ptr instead of READ_ONCE()). 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. By contrast, other architectures
|
maintain at least the appearance of FIFO order.
|
|
In practice, this difficulty is solved by inserting a special fence
|
between P1's two loads when the kernel is compiled for the Alpha
|
architecture. In fact, as of version 4.15, the kernel automatically
|
adds this fence after every READ_ONCE() and atomic load on Alpha. The
|
effect of the 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);
|
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. Thus
|
we have yet another reason why shared data should always be read with
|
READ_ONCE() or another synchronization primitive rather than accessed
|
directly.
|
|
The LKMM requires that smp_rmb(), acquire fences, and strong fences
|
share this property: 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 cumul-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 cumul-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 cumul-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: rcu-link, rcu-gp, rcu-rscsi, rcu-order, rcu-fence, and rb
|
------------------------------------------------------------------------
|
|
RCU (Read-Copy-Update) is a powerful synchronization mechanism. It
|
rests on two concepts: grace periods and read-side critical sections.
|
|
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:
|
|
For any critical section C and any grace period G, at least
|
one of the following statements must hold:
|
|
(1) C ends before G does, and in addition, every store that
|
propagates to C's CPU before the end of C must propagate to
|
every CPU before G ends.
|
|
(2) G starts before C does, and in addition, every store that
|
propagates to G's CPU before the start of G must propagate
|
to every CPU before C starts.
|
|
In particular, it is not possible for a critical section to both start
|
before and end after a grace period.
|
|
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, contrary to part (2) of the Guarantee. 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, contrary to part (1). Together the results violate
|
the Guarantee.
|
|
In the kernel's implementations of RCU, the requirements for stores
|
to propagate to every CPU are fulfilled 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 the
|
rcu-link relation. rcu-link encompasses a very general notion of
|
"before": If E and F are RCU fence events (i.e., rcu_read_lock(),
|
rcu_read_unlock(), or synchronize_rcu()) then among other things,
|
E ->rcu-link F includes cases where E is po-before some memory-access
|
event X, F is po-after some memory-access event Y, and we have any of
|
X ->rfe Y, X ->co Y, or X ->fr Y.
|
|
The formal definition of the rcu-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 rcu-link is the information in the preceding paragraph.
|
|
The LKMM also defines the rcu-gp and rcu-rscsi relations. They bring
|
grace periods and read-side critical sections into the picture, in the
|
following way:
|
|
E ->rcu-gp F means that E and F are in fact the same event,
|
and that event is a synchronize_rcu() fence (i.e., a grace
|
period).
|
|
E ->rcu-rscsi F means that E and F are the rcu_read_unlock()
|
and rcu_read_lock() fence events delimiting some read-side
|
critical section. (The 'i' at the end of the name emphasizes
|
that this relation is "inverted": It links the end of the
|
critical section to the start.)
|
|
If we think of the rcu-link relation as standing for an extended
|
"before", then X ->rcu-gp Y ->rcu-link Z roughly says that X is a
|
grace period which ends before Z begins. (In fact it covers more than
|
this, because it also includes cases where some store propagates to
|
Z's CPU before Z begins but doesn't propagate to some other CPU until
|
after X ends.) Similarly, X ->rcu-rscsi Y ->rcu-link Z says that X is
|
the end of a critical section which starts before Z begins.
|
|
The LKMM goes on to define the rcu-order relation as a sequence of
|
rcu-gp and rcu-rscsi links separated by rcu-link links, in which the
|
number of rcu-gp links is >= the number of rcu-rscsi links. For
|
example:
|
|
X ->rcu-gp Y ->rcu-link Z ->rcu-rscsi T ->rcu-link U ->rcu-gp V
|
|
would imply that X ->rcu-order V, because this sequence contains two
|
rcu-gp links and one rcu-rscsi link. (It also implies that
|
X ->rcu-order T and Z ->rcu-order V.) On the other hand:
|
|
X ->rcu-rscsi Y ->rcu-link Z ->rcu-rscsi T ->rcu-link U ->rcu-gp V
|
|
does not imply X ->rcu-order V, because the sequence contains only
|
one rcu-gp link but two rcu-rscsi links.
|
|
The rcu-order relation is important because the Grace Period Guarantee
|
means that rcu-order links act kind of like strong fences. In
|
particular, E ->rcu-order F implies not only that E begins before F
|
ends, but also that any write po-before E will propagate to every CPU
|
before any instruction po-after F can execute. (However, it does not
|
imply that E must execute before F; in fact, each synchronize_rcu()
|
fence event is linked to itself by rcu-order as a degenerate case.)
|
|
To prove this in full generality requires some intellectual effort.
|
We'll consider just a very simple case:
|
|
G ->rcu-gp W ->rcu-link Z ->rcu-rscsi F.
|
|
This formula means that G and W are the same event (a grace period),
|
and there are events X, Y and a read-side critical section C such that:
|
|
1. G = W is po-before or equal to X;
|
|
2. X comes "before" Y in some sense (including rfe, co and fr);
|
|
3. Y is po-before Z;
|
|
4. Z is the rcu_read_unlock() event marking the end of C;
|
|
5. F is the rcu_read_lock() event marking the start of C.
|
|
From 1 - 4 we deduce that the grace period G ends before the critical
|
section C. Then part (2) of the Grace Period Guarantee says not only
|
that G starts before C does, but also that any write which executes on
|
G's CPU before G starts must propagate to every CPU before C starts.
|
In particular, the write propagates to every CPU before F finishes
|
executing and hence before any instruction po-after F can execute.
|
This sort of reasoning can be extended to handle all the situations
|
covered by rcu-order.
|
|
The rcu-fence relation is a simple extension of rcu-order. While
|
rcu-order only links certain fence events (calls to synchronize_rcu(),
|
rcu_read_lock(), or rcu_read_unlock()), rcu-fence links any events
|
that are separated by an rcu-order link. This is analogous to the way
|
the strong-fence relation links events that are separated by an
|
smp_mb() fence event (as mentioned above, rcu-order links act kind of
|
like strong fences). Written symbolically, X ->rcu-fence Y means
|
there are fence events E and F such that:
|
|
X ->po E ->rcu-order F ->po Y.
|
|
From the discussion above, we see this implies not only that X
|
executes before Y, but also (if X is a store) that X propagates to
|
every CPU before Y executes. Thus rcu-fence is sort of a
|
"super-strong" fence: Unlike the original strong fences (smp_mb() and
|
synchronize_rcu()), rcu-fence is able to link events on different
|
CPUs. (Perhaps this fact should lead us to say that rcu-fence isn't
|
really a fence at all!)
|
|
Finally, the LKMM defines the RCU-before (rb) relation in terms of
|
rcu-fence. This is done in essentially the same way as the pb
|
relation was defined in terms of strong-fence. We will omit the
|
details; the end result is that E ->rb F implies E must execute
|
before F, just as E ->pb F does (and for much the same reasons).
|
|
Putting this all together, the LKMM expresses the Grace Period
|
Guarantee by requiring that the rb relation does not contain a cycle.
|
Equivalently, this "rcu" axiom requires that there are no events E
|
and F with E ->rcu-link F ->rcu-order E. Or to put it a third way,
|
the axiom requires that there are no cycles consisting of rcu-gp and
|
rcu-rscsi alternating with rcu-link, where the number of rcu-gp links
|
is >= the number of rcu-rscsi links.
|
|
Justifying the axiom isn't easy, but it is in fact a valid
|
formalization of the Grace Period Guarantee. We won't attempt to go
|
through the detailed argument, but the following analysis gives a
|
taste of what is involved. Suppose both parts of the Guarantee are
|
violated: 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 Q and R where Q is po-after L (which marks the start of the
|
critical section), Q is "before" R in the sense used by the rcu-link
|
relation, and R is po-before the grace period S. Thus we have:
|
|
L ->rcu-link S.
|
|
Let W be the store mentioned above, let Y 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 Z on some arbitrary CPU be a
|
witness that W has not propagated to that CPU, where Z happens after
|
some event X which is po-after S. Symbolically, this amounts to:
|
|
S ->po X ->hb* Z ->fr W ->rf Y ->po U.
|
|
The fr link from Z to W indicates that W has not propagated to Z's CPU
|
at the time that Z executes. From this, it can be shown (see the
|
discussion of the rcu-link relation earlier) that S and U are related
|
by rcu-link:
|
|
S ->rcu-link U.
|
|
Since S is a grace period we have S ->rcu-gp S, and since L and U are
|
the start and end of the critical section C we have U ->rcu-rscsi L.
|
From this we obtain:
|
|
S ->rcu-gp S ->rcu-link U ->rcu-rscsi L ->rcu-link S,
|
|
a forbidden cycle. Thus the "rcu" axiom rules out this violation of
|
the Grace Period Guarantee.
|
|
For something a little more down-to-earth, let's see how the axiom
|
works out in practice. Consider the RCU code example from above, this
|
time with statement labels added:
|
|
int x, y;
|
|
P0()
|
{
|
L: rcu_read_lock();
|
X: WRITE_ONCE(x, 1);
|
Y: WRITE_ONCE(y, 1);
|
U: rcu_read_unlock();
|
}
|
|
P1()
|
{
|
int r1, r2;
|
|
Z: r1 = READ_ONCE(x);
|
S: synchronize_rcu();
|
W: r2 = READ_ONCE(y);
|
}
|
|
|
If r2 = 0 at the end then P0's store at Y overwrites the value that
|
P1's load at W reads from, so we have W ->fre Y. Since S ->po W and
|
also Y ->po U, we get S ->rcu-link U. In addition, S ->rcu-gp S
|
because S is a grace period.
|
|
If r1 = 1 at the end then P1's load at Z reads from P0's store at X,
|
so we have X ->rfe Z. Together with L ->po X and Z ->po S, this
|
yields L ->rcu-link S. And since L and U are the start and end of a
|
critical section, we have U ->rcu-rscsi L.
|
|
Then U ->rcu-rscsi L ->rcu-link S ->rcu-gp S ->rcu-link U is a
|
forbidden cycle, violating the "rcu" axiom. Hence the outcome is not
|
allowed by the LKMM, as we would expect.
|
|
For contrast, let's see what can happen in a more complicated example:
|
|
int x, y, z;
|
|
P0()
|
{
|
int r0;
|
|
L0: rcu_read_lock();
|
r0 = READ_ONCE(x);
|
WRITE_ONCE(y, 1);
|
U0: rcu_read_unlock();
|
}
|
|
P1()
|
{
|
int r1;
|
|
r1 = READ_ONCE(y);
|
S1: synchronize_rcu();
|
WRITE_ONCE(z, 1);
|
}
|
|
P2()
|
{
|
int r2;
|
|
L2: rcu_read_lock();
|
r2 = READ_ONCE(z);
|
WRITE_ONCE(x, 1);
|
U2: rcu_read_unlock();
|
}
|
|
If r0 = r1 = r2 = 1 at the end, then similar reasoning to before shows
|
that U0 ->rcu-rscsi L0 ->rcu-link S1 ->rcu-gp S1 ->rcu-link U2 ->rcu-rscsi
|
L2 ->rcu-link U0. However this cycle is not forbidden, because the
|
sequence of relations contains fewer instances of rcu-gp (one) than of
|
rcu-rscsi (two). Consequently the outcome is allowed by the LKMM.
|
The following instruction timing diagram shows how it might actually
|
occur:
|
|
P0 P1 P2
|
-------------------- -------------------- --------------------
|
rcu_read_lock()
|
WRITE_ONCE(y, 1)
|
r1 = READ_ONCE(y)
|
synchronize_rcu() starts
|
. rcu_read_lock()
|
. WRITE_ONCE(x, 1)
|
r0 = READ_ONCE(x) .
|
rcu_read_unlock() .
|
synchronize_rcu() ends
|
WRITE_ONCE(z, 1)
|
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.
|
|
Addendum: The LKMM now supports SRCU (Sleepable Read-Copy-Update) in
|
addition to normal RCU. The ideas involved are much the same as
|
above, with new relations srcu-gp and srcu-rscsi added to represent
|
SRCU grace periods and read-side critical sections. There is a
|
restriction on the srcu-gp and srcu-rscsi links that can appear in an
|
rcu-order sequence (the srcu-rscsi links must be paired with srcu-gp
|
links having the same SRCU domain with proper nesting); the details
|
are relatively unimportant.
|
|
|
LOCKING
|
-------
|
|
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 more or less equivalent
|
to concepts we have already covered. A spinlock_t variable is treated
|
the same as an int, and spin_lock(&s) is treated almost the same as:
|
|
while (cmpxchg_acquire(&s, 0, 1) != 0)
|
cpu_relax();
|
|
This waits until s is equal to 0 and then atomically sets it to 1,
|
and the read part of the cmpxchg operation acts as 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. Similarly,
|
spin_trylock(&s) is treated almost the same as:
|
|
return !cmpxchg_acquire(&s, 0, 1);
|
|
which atomically sets s to 1 if it is currently equal to 0 and returns
|
true if it succeeds (the read part of the cmpxchg operation acts as an
|
acquire fence only if the operation is successful). spin_unlock(&s)
|
is treated almost the same as:
|
|
smp_store_release(&s, 0);
|
|
The "almost" qualifiers above need some explanation. In the LKMM, the
|
store-release in a spin_unlock() and the load-acquire which forms the
|
first half of the atomic rmw update in a spin_lock() or a successful
|
spin_trylock() -- we can call these things lock-releases and
|
lock-acquires -- have two properties beyond those of ordinary releases
|
and acquires.
|
|
First, when a lock-acquire reads from a lock-release, the LKMM
|
requires that every instruction po-before the lock-release must
|
execute before any instruction po-after the lock-acquire. This would
|
naturally hold if the release and acquire operations were on different
|
CPUs, but the LKMM says it holds even when they are on the same CPU.
|
For example:
|
|
int x, y;
|
spinlock_t s;
|
|
P0()
|
{
|
int r1, r2;
|
|
spin_lock(&s);
|
r1 = READ_ONCE(x);
|
spin_unlock(&s);
|
spin_lock(&s);
|
r2 = READ_ONCE(y);
|
spin_unlock(&s);
|
}
|
|
P1()
|
{
|
WRITE_ONCE(y, 1);
|
smp_wmb();
|
WRITE_ONCE(x, 1);
|
}
|
|
Here the second spin_lock() reads from the first spin_unlock(), and
|
therefore the load of x must execute before the load of y. Thus we
|
cannot have r1 = 1 and r2 = 0 at the end (this is an instance of the
|
MP pattern).
|
|
This requirement does not apply to ordinary release and acquire
|
fences, only to lock-related operations. For instance, suppose P0()
|
in the example had been written as:
|
|
P0()
|
{
|
int r1, r2, r3;
|
|
r1 = READ_ONCE(x);
|
smp_store_release(&s, 1);
|
r3 = smp_load_acquire(&s);
|
r2 = READ_ONCE(y);
|
}
|
|
Then the CPU would be allowed to forward the s = 1 value from the
|
smp_store_release() to the smp_load_acquire(), executing the
|
instructions in the following order:
|
|
r3 = smp_load_acquire(&s); // Obtains r3 = 1
|
r2 = READ_ONCE(y);
|
r1 = READ_ONCE(x);
|
smp_store_release(&s, 1); // Value is forwarded
|
|
and thus it could load y before x, obtaining r2 = 0 and r1 = 1.
|
|
Second, when a lock-acquire reads from a lock-release, and some other
|
stores W and W' occur po-before the lock-release and po-after the
|
lock-acquire respectively, the LKMM requires that W must propagate to
|
each CPU before W' does. For example, consider:
|
|
int x, y;
|
spinlock_t x;
|
|
P0()
|
{
|
spin_lock(&s);
|
WRITE_ONCE(x, 1);
|
spin_unlock(&s);
|
}
|
|
P1()
|
{
|
int r1;
|
|
spin_lock(&s);
|
r1 = READ_ONCE(x);
|
WRITE_ONCE(y, 1);
|
spin_unlock(&s);
|
}
|
|
P2()
|
{
|
int r2, r3;
|
|
r2 = READ_ONCE(y);
|
smp_rmb();
|
r3 = READ_ONCE(x);
|
}
|
|
If r1 = 1 at the end then the spin_lock() in P1 must have read from
|
the spin_unlock() in P0. Hence the store to x must propagate to P2
|
before the store to y does, so we cannot have r2 = 1 and r3 = 0.
|
|
These two special requirements for lock-release and lock-acquire do
|
not arise from the operational model. Nevertheless, kernel developers
|
have come to expect and rely on them because they do hold on all
|
architectures supported by the Linux kernel, albeit for various
|
differing reasons.
|
|
|
PLAIN ACCESSES AND DATA RACES
|
-----------------------------
|
|
In the LKMM, memory accesses such as READ_ONCE(x), atomic_inc(&y),
|
smp_load_acquire(&z), and so on are collectively referred to as
|
"marked" accesses, because they are all annotated with special
|
operations of one kind or another. Ordinary C-language memory
|
accesses such as x or y = 0 are simply called "plain" accesses.
|
|
Early versions of the LKMM had nothing to say about plain accesses.
|
The C standard allows compilers to assume that the variables affected
|
by plain accesses are not concurrently read or written by any other
|
threads or CPUs. This leaves compilers free to implement all manner
|
of transformations or optimizations of code containing plain accesses,
|
making such code very difficult for a memory model to handle.
|
|
Here is just one example of a possible pitfall:
|
|
int a = 6;
|
int *x = &a;
|
|
P0()
|
{
|
int *r1;
|
int r2 = 0;
|
|
r1 = x;
|
if (r1 != NULL)
|
r2 = READ_ONCE(*r1);
|
}
|
|
P1()
|
{
|
WRITE_ONCE(x, NULL);
|
}
|
|
On the face of it, one would expect that when this code runs, the only
|
possible final values for r2 are 6 and 0, depending on whether or not
|
P1's store to x propagates to P0 before P0's load from x executes.
|
But since P0's load from x is a plain access, the compiler may decide
|
to carry out the load twice (for the comparison against NULL, then again
|
for the READ_ONCE()) and eliminate the temporary variable r1. The
|
object code generated for P0 could therefore end up looking rather
|
like this:
|
|
P0()
|
{
|
int r2 = 0;
|
|
if (x != NULL)
|
r2 = READ_ONCE(*x);
|
}
|
|
And now it is obvious that this code runs the risk of dereferencing a
|
NULL pointer, because P1's store to x might propagate to P0 after the
|
test against NULL has been made but before the READ_ONCE() executes.
|
If the original code had said "r1 = READ_ONCE(x)" instead of "r1 = x",
|
the compiler would not have performed this optimization and there
|
would be no possibility of a NULL-pointer dereference.
|
|
Given the possibility of transformations like this one, the LKMM
|
doesn't try to predict all possible outcomes of code containing plain
|
accesses. It is instead content to determine whether the code
|
violates the compiler's assumptions, which would render the ultimate
|
outcome undefined.
|
|
In technical terms, the compiler is allowed to assume that when the
|
program executes, there will not be any data races. A "data race"
|
occurs when there are two memory accesses such that:
|
|
1. they access the same location,
|
|
2. at least one of them is a store,
|
|
3. at least one of them is plain,
|
|
4. they occur on different CPUs (or in different threads on the
|
same CPU), and
|
|
5. they execute concurrently.
|
|
In the literature, two accesses are said to "conflict" if they satisfy
|
1 and 2 above. We'll go a little farther and say that two accesses
|
are "race candidates" if they satisfy 1 - 4. Thus, whether or not two
|
race candidates actually do race in a given execution depends on
|
whether they are concurrent.
|
|
The LKMM tries to determine whether a program contains race candidates
|
which may execute concurrently; if it does then the LKMM says there is
|
a potential data race and makes no predictions about the program's
|
outcome.
|
|
Determining whether two accesses are race candidates is easy; you can
|
see that all the concepts involved in the definition above are already
|
part of the memory model. The hard part is telling whether they may
|
execute concurrently. The LKMM takes a conservative attitude,
|
assuming that accesses may be concurrent unless it can prove they
|
are not.
|
|
If two memory accesses aren't concurrent then one must execute before
|
the other. Therefore the LKMM decides two accesses aren't concurrent
|
if they can be connected by a sequence of hb, pb, and rb links
|
(together referred to as xb, for "executes before"). However, there
|
are two complicating factors.
|
|
If X is a load and X executes before a store Y, then indeed there is
|
no danger of X and Y being concurrent. After all, Y can't have any
|
effect on the value obtained by X until the memory subsystem has
|
propagated Y from its own CPU to X's CPU, which won't happen until
|
some time after Y executes and thus after X executes. But if X is a
|
store, then even if X executes before Y it is still possible that X
|
will propagate to Y's CPU just as Y is executing. In such a case X
|
could very well interfere somehow with Y, and we would have to
|
consider X and Y to be concurrent.
|
|
Therefore when X is a store, for X and Y to be non-concurrent the LKMM
|
requires not only that X must execute before Y but also that X must
|
propagate to Y's CPU before Y executes. (Or vice versa, of course, if
|
Y executes before X -- then Y must propagate to X's CPU before X
|
executes if Y is a store.) This is expressed by the visibility
|
relation (vis), where X ->vis Y is defined to hold if there is an
|
intermediate event Z such that:
|
|
X is connected to Z by a possibly empty sequence of
|
cumul-fence links followed by an optional rfe link (if none of
|
these links are present, X and Z are the same event),
|
|
and either:
|
|
Z is connected to Y by a strong-fence link followed by a
|
possibly empty sequence of xb links,
|
|
or:
|
|
Z is on the same CPU as Y and is connected to Y by a possibly
|
empty sequence of xb links (again, if the sequence is empty it
|
means Z and Y are the same event).
|
|
The motivations behind this definition are straightforward:
|
|
cumul-fence memory barriers force stores that are po-before
|
the barrier to propagate to other CPUs before stores that are
|
po-after the barrier.
|
|
An rfe link from an event W to an event R says that R reads
|
from W, which certainly means that W must have propagated to
|
R's CPU before R executed.
|
|
strong-fence memory barriers force stores that are po-before
|
the barrier, or that propagate to the barrier's CPU before the
|
barrier executes, to propagate to all CPUs before any events
|
po-after the barrier can execute.
|
|
To see how this works out in practice, consider our old friend, the MP
|
pattern (with fences and statement labels, but without the conditional
|
test):
|
|
int buf = 0, flag = 0;
|
|
P0()
|
{
|
X: WRITE_ONCE(buf, 1);
|
smp_wmb();
|
W: WRITE_ONCE(flag, 1);
|
}
|
|
P1()
|
{
|
int r1;
|
int r2 = 0;
|
|
Z: r1 = READ_ONCE(flag);
|
smp_rmb();
|
Y: r2 = READ_ONCE(buf);
|
}
|
|
The smp_wmb() memory barrier gives a cumul-fence link from X to W, and
|
assuming r1 = 1 at the end, there is an rfe link from W to Z. This
|
means that the store to buf must propagate from P0 to P1 before Z
|
executes. Next, Z and Y are on the same CPU and the smp_rmb() fence
|
provides an xb link from Z to Y (i.e., it forces Z to execute before
|
Y). Therefore we have X ->vis Y: X must propagate to Y's CPU before Y
|
executes.
|
|
The second complicating factor mentioned above arises from the fact
|
that when we are considering data races, some of the memory accesses
|
are plain. Now, although we have not said so explicitly, up to this
|
point most of the relations defined by the LKMM (ppo, hb, prop,
|
cumul-fence, pb, and so on -- including vis) apply only to marked
|
accesses.
|
|
There are good reasons for this restriction. The compiler is not
|
allowed to apply fancy transformations to marked accesses, and
|
consequently each such access in the source code corresponds more or
|
less directly to a single machine instruction in the object code. But
|
plain accesses are a different story; the compiler may combine them,
|
split them up, duplicate them, eliminate them, invent new ones, and
|
who knows what else. Seeing a plain access in the source code tells
|
you almost nothing about what machine instructions will end up in the
|
object code.
|
|
Fortunately, the compiler isn't completely free; it is subject to some
|
limitations. For one, it is not allowed to introduce a data race into
|
the object code if the source code does not already contain a data
|
race (if it could, memory models would be useless and no multithreaded
|
code would be safe!). For another, it cannot move a plain access past
|
a compiler barrier.
|
|
A compiler barrier is a kind of fence, but as the name implies, it
|
only affects the compiler; it does not necessarily have any effect on
|
how instructions are executed by the CPU. In Linux kernel source
|
code, the barrier() function is a compiler barrier. It doesn't give
|
rise directly to any machine instructions in the object code; rather,
|
it affects how the compiler generates the rest of the object code.
|
Given source code like this:
|
|
... some memory accesses ...
|
barrier();
|
... some other memory accesses ...
|
|
the barrier() function ensures that the machine instructions
|
corresponding to the first group of accesses will all end po-before
|
any machine instructions corresponding to the second group of accesses
|
-- even if some of the accesses are plain. (Of course, the CPU may
|
then execute some of those accesses out of program order, but we
|
already know how to deal with such issues.) Without the barrier()
|
there would be no such guarantee; the two groups of accesses could be
|
intermingled or even reversed in the object code.
|
|
The LKMM doesn't say much about the barrier() function, but it does
|
require that all fences are also compiler barriers. In addition, it
|
requires that the ordering properties of memory barriers such as
|
smp_rmb() or smp_store_release() apply to plain accesses as well as to
|
marked accesses.
|
|
This is the key to analyzing data races. Consider the MP pattern
|
again, now using plain accesses for buf:
|
|
int buf = 0, flag = 0;
|
|
P0()
|
{
|
U: buf = 1;
|
smp_wmb();
|
X: WRITE_ONCE(flag, 1);
|
}
|
|
P1()
|
{
|
int r1;
|
int r2 = 0;
|
|
Y: r1 = READ_ONCE(flag);
|
if (r1) {
|
smp_rmb();
|
V: r2 = buf;
|
}
|
}
|
|
This program does not contain a data race. Although the U and V
|
accesses are race candidates, the LKMM can prove they are not
|
concurrent as follows:
|
|
The smp_wmb() fence in P0 is both a compiler barrier and a
|
cumul-fence. It guarantees that no matter what hash of
|
machine instructions the compiler generates for the plain
|
access U, all those instructions will be po-before the fence.
|
Consequently U's store to buf, no matter how it is carried out
|
at the machine level, must propagate to P1 before X's store to
|
flag does.
|
|
X and Y are both marked accesses. Hence an rfe link from X to
|
Y is a valid indicator that X propagated to P1 before Y
|
executed, i.e., X ->vis Y. (And if there is no rfe link then
|
r1 will be 0, so V will not be executed and ipso facto won't
|
race with U.)
|
|
The smp_rmb() fence in P1 is a compiler barrier as well as a
|
fence. It guarantees that all the machine-level instructions
|
corresponding to the access V will be po-after the fence, and
|
therefore any loads among those instructions will execute
|
after the fence does and hence after Y does.
|
|
Thus U's store to buf is forced to propagate to P1 before V's load
|
executes (assuming V does execute), ruling out the possibility of a
|
data race between them.
|
|
This analysis illustrates how the LKMM deals with plain accesses in
|
general. Suppose R is a plain load and we want to show that R
|
executes before some marked access E. We can do this by finding a
|
marked access X such that R and X are ordered by a suitable fence and
|
X ->xb* E. If E was also a plain access, we would also look for a
|
marked access Y such that X ->xb* Y, and Y and E are ordered by a
|
fence. We describe this arrangement by saying that R is
|
"post-bounded" by X and E is "pre-bounded" by Y.
|
|
In fact, we go one step further: Since R is a read, we say that R is
|
"r-post-bounded" by X. Similarly, E would be "r-pre-bounded" or
|
"w-pre-bounded" by Y, depending on whether E was a store or a load.
|
This distinction is needed because some fences affect only loads
|
(i.e., smp_rmb()) and some affect only stores (smp_wmb()); otherwise
|
the two types of bounds are the same. And as a degenerate case, we
|
say that a marked access pre-bounds and post-bounds itself (e.g., if R
|
above were a marked load then X could simply be taken to be R itself.)
|
|
The need to distinguish between r- and w-bounding raises yet another
|
issue. When the source code contains a plain store, the compiler is
|
allowed to put plain loads of the same location into the object code.
|
For example, given the source code:
|
|
x = 1;
|
|
the compiler is theoretically allowed to generate object code that
|
looks like:
|
|
if (x != 1)
|
x = 1;
|
|
thereby adding a load (and possibly replacing the store entirely).
|
For this reason, whenever the LKMM requires a plain store to be
|
w-pre-bounded or w-post-bounded by a marked access, it also requires
|
the store to be r-pre-bounded or r-post-bounded, so as to handle cases
|
where the compiler adds a load.
|
|
(This may be overly cautious. We don't know of any examples where a
|
compiler has augmented a store with a load in this fashion, and the
|
Linux kernel developers would probably fight pretty hard to change a
|
compiler if it ever did this. Still, better safe than sorry.)
|
|
Incidentally, the other tranformation -- augmenting a plain load by
|
adding in a store to the same location -- is not allowed. This is
|
because the compiler cannot know whether any other CPUs might perform
|
a concurrent load from that location. Two concurrent loads don't
|
constitute a race (they can't interfere with each other), but a store
|
does race with a concurrent load. Thus adding a store might create a
|
data race where one was not already present in the source code,
|
something the compiler is forbidden to do. Augmenting a store with a
|
load, on the other hand, is acceptable because doing so won't create a
|
data race unless one already existed.
|
|
The LKMM includes a second way to pre-bound plain accesses, in
|
addition to fences: an address dependency from a marked load. That
|
is, in the sequence:
|
|
p = READ_ONCE(ptr);
|
r = *p;
|
|
the LKMM says that the marked load of ptr pre-bounds the plain load of
|
*p; the marked load must execute before any of the machine
|
instructions corresponding to the plain load. This is a reasonable
|
stipulation, since after all, the CPU can't perform the load of *p
|
until it knows what value p will hold. Furthermore, without some
|
assumption like this one, some usages typical of RCU would count as
|
data races. For example:
|
|
int a = 1, b;
|
int *ptr = &a;
|
|
P0()
|
{
|
b = 2;
|
rcu_assign_pointer(ptr, &b);
|
}
|
|
P1()
|
{
|
int *p;
|
int r;
|
|
rcu_read_lock();
|
p = rcu_dereference(ptr);
|
r = *p;
|
rcu_read_unlock();
|
}
|
|
(In this example the rcu_read_lock() and rcu_read_unlock() calls don't
|
really do anything, because there aren't any grace periods. They are
|
included merely for the sake of good form; typically P0 would call
|
synchronize_rcu() somewhere after the rcu_assign_pointer().)
|
|
rcu_assign_pointer() performs a store-release, so the plain store to b
|
is definitely w-post-bounded before the store to ptr, and the two
|
stores will propagate to P1 in that order. However, rcu_dereference()
|
is only equivalent to READ_ONCE(). While it is a marked access, it is
|
not a fence or compiler barrier. Hence the only guarantee we have
|
that the load of ptr in P1 is r-pre-bounded before the load of *p
|
(thus avoiding a race) is the assumption about address dependencies.
|
|
This is a situation where the compiler can undermine the memory model,
|
and a certain amount of care is required when programming constructs
|
like this one. In particular, comparisons between the pointer and
|
other known addresses can cause trouble. If you have something like:
|
|
p = rcu_dereference(ptr);
|
if (p == &x)
|
r = *p;
|
|
then the compiler just might generate object code resembling:
|
|
p = rcu_dereference(ptr);
|
if (p == &x)
|
r = x;
|
|
or even:
|
|
rtemp = x;
|
p = rcu_dereference(ptr);
|
if (p == &x)
|
r = rtemp;
|
|
which would invalidate the memory model's assumption, since the CPU
|
could now perform the load of x before the load of ptr (there might be
|
a control dependency but no address dependency at the machine level).
|
|
Finally, it turns out there is a situation in which a plain write does
|
not need to be w-post-bounded: when it is separated from the other
|
race-candidate access by a fence. At first glance this may seem
|
impossible. After all, to be race candidates the two accesses must
|
be on different CPUs, and fences don't link events on different CPUs.
|
Well, normal fences don't -- but rcu-fence can! Here's an example:
|
|
int x, y;
|
|
P0()
|
{
|
WRITE_ONCE(x, 1);
|
synchronize_rcu();
|
y = 3;
|
}
|
|
P1()
|
{
|
rcu_read_lock();
|
if (READ_ONCE(x) == 0)
|
y = 2;
|
rcu_read_unlock();
|
}
|
|
Do the plain stores to y race? Clearly not if P1 reads a non-zero
|
value for x, so let's assume the READ_ONCE(x) does obtain 0. This
|
means that the read-side critical section in P1 must finish executing
|
before the grace period in P0 does, because RCU's Grace-Period
|
Guarantee says that otherwise P0's store to x would have propagated to
|
P1 before the critical section started and so would have been visible
|
to the READ_ONCE(). (Another way of putting it is that the fre link
|
from the READ_ONCE() to the WRITE_ONCE() gives rise to an rcu-link
|
between those two events.)
|
|
This means there is an rcu-fence link from P1's "y = 2" store to P0's
|
"y = 3" store, and consequently the first must propagate from P1 to P0
|
before the second can execute. Therefore the two stores cannot be
|
concurrent and there is no race, even though P1's plain store to y
|
isn't w-post-bounded by any marked accesses.
|
|
Putting all this material together yields the following picture. For
|
race-candidate stores W and W', where W ->co W', the LKMM says the
|
stores don't race if W can be linked to W' by a
|
|
w-post-bounded ; vis ; w-pre-bounded
|
|
sequence. If W is plain then they also have to be linked by an
|
|
r-post-bounded ; xb* ; w-pre-bounded
|
|
sequence, and if W' is plain then they also have to be linked by a
|
|
w-post-bounded ; vis ; r-pre-bounded
|
|
sequence. For race-candidate load R and store W, the LKMM says the
|
two accesses don't race if R can be linked to W by an
|
|
r-post-bounded ; xb* ; w-pre-bounded
|
|
sequence or if W can be linked to R by a
|
|
w-post-bounded ; vis ; r-pre-bounded
|
|
sequence. For the cases involving a vis link, the LKMM also accepts
|
sequences in which W is linked to W' or R by a
|
|
strong-fence ; xb* ; {w and/or r}-pre-bounded
|
|
sequence with no post-bounding, and in every case the LKMM also allows
|
the link simply to be a fence with no bounding at all. If no sequence
|
of the appropriate sort exists, the LKMM says that the accesses race.
|
|
There is one more part of the LKMM related to plain accesses (although
|
not to data races) we should discuss. Recall that many relations such
|
as hb are limited to marked accesses only. As a result, the
|
happens-before, propagates-before, and rcu axioms (which state that
|
various relation must not contain a cycle) doesn't apply to plain
|
accesses. Nevertheless, we do want to rule out such cycles, because
|
they don't make sense even for plain accesses.
|
|
To this end, the LKMM imposes three extra restrictions, together
|
called the "plain-coherence" axiom because of their resemblance to the
|
rules used by the operational model to ensure cache coherence (that
|
is, the rules governing the memory subsystem's choice of a store to
|
satisfy a load request and its determination of where a store will
|
fall in the coherence order):
|
|
If R and W are race candidates and it is possible to link R to
|
W by one of the xb* sequences listed above, then W ->rfe R is
|
not allowed (i.e., a load cannot read from a store that it
|
executes before, even if one or both is plain).
|
|
If W and R are race candidates and it is possible to link W to
|
R by one of the vis sequences listed above, then R ->fre W is
|
not allowed (i.e., if a store is visible to a load then the
|
load must read from that store or one coherence-after it).
|
|
If W and W' are race candidates and it is possible to link W
|
to W' by one of the vis sequences listed above, then W' ->co W
|
is not allowed (i.e., if one store is visible to a second then
|
the second must come after the first in the coherence order).
|
|
This is the extent to which the LKMM deals with plain accesses.
|
Perhaps it could say more (for example, plain accesses might
|
contribute to the ppo relation), but at the moment it seems that this
|
minimal, conservative approach is good enough.
|
|
|
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() is
|
treated as READ_ONCE() and rcu_assign_pointer() is treated as
|
smp_store_release() -- which is basically how the Linux kernel treats
|
them.
|
|
Although we said that plain accesses are not linked by the ppo
|
relation, they do contribute to it indirectly. Namely, when there is
|
an address dependency from a marked load R to a plain store W,
|
followed by smp_wmb() and then a marked store W', the LKMM creates a
|
ppo link from R to W'. The reasoning behind this is perhaps a little
|
shaky, but essentially it says there is no way to generate object code
|
for this source code in which W' could execute before R. Just as with
|
pre-bounding by address dependencies, it is possible for the compiler
|
to undermine this relation if sufficient care is not taken.
|
|
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.
|
|
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.
|
