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diff --git a/tools/memory-model/Documentation/explanation.txt b/tools/memory-model/Documentation/explanation.txt new file mode 100644 index 000000000..0cbd1ef8f --- /dev/null +++ b/tools/memory-model/Documentation/explanation.txt @@ -0,0 +1,1896 @@ +Explanation of the Linux-Kernel Memory Consistency Model +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +:Author: Alan Stern <stern@rowland.harvard.edu> +:Created: October 2017 + +.. Contents + + 1. INTRODUCTION + 2. BACKGROUND + 3. A SIMPLE EXAMPLE + 4. A SELECTION OF MEMORY MODELS + 5. ORDERING AND CYCLES + 6. EVENTS + 7. THE PROGRAM ORDER RELATION: po AND po-loc + 8. A WARNING + 9. DEPENDENCY RELATIONS: data, addr, and ctrl + 10. THE READS-FROM RELATION: rf, rfi, and rfe + 11. CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe + 12. THE FROM-READS RELATION: fr, fri, and fre + 13. AN OPERATIONAL MODEL + 14. PROPAGATION ORDER RELATION: cumul-fence + 15. DERIVATION OF THE LKMM FROM THE OPERATIONAL MODEL + 16. SEQUENTIAL CONSISTENCY PER VARIABLE + 17. ATOMIC UPDATES: rmw + 18. THE PRESERVED PROGRAM ORDER RELATION: ppo + 19. AND THEN THERE WAS ALPHA + 20. THE HAPPENS-BEFORE RELATION: hb + 21. THE PROPAGATES-BEFORE RELATION: pb + 22. RCU RELATIONS: rcu-link, gp, rscs, rcu-fence, and rb + 23. ODDS AND ENDS + + + +INTRODUCTION +------------ + +The Linux-kernel memory consistency model (LKMM) is rather complex and +obscure. This is particularly evident if you read through the +linux-kernel.bell and linux-kernel.cat files that make up the formal +version of the model; they are extremely terse and their meanings are +far from clear. + +This document describes the ideas underlying the LKMM. It is meant +for people who want to understand how the model was designed. It does +not go into the details of the code in the .bell and .cat files; +rather, it explains in English what the code expresses symbolically. + +Sections 2 (BACKGROUND) through 5 (ORDERING AND CYCLES) are aimed +toward beginners; they explain what memory consistency models are and +the basic notions shared by all such models. People already familiar +with these concepts can skim or skip over them. Sections 6 (EVENTS) +through 12 (THE FROM_READS RELATION) describe the fundamental +relations used in many models. Starting in Section 13 (AN OPERATIONAL +MODEL), the workings of the LKMM itself are covered. + +Warning: The code examples in this document are not written in the +proper format for litmus tests. They don't include a header line, the +initializations are not enclosed in braces, the global variables are +not passed by pointers, and they don't have an "exists" clause at the +end. Converting them to the right format is left as an exercise for +the reader. + + +BACKGROUND +---------- + +A memory consistency model (or just memory model, for short) is +something which predicts, given a piece of computer code running on a +particular kind of system, what values may be obtained by the code's +load instructions. The LKMM makes these predictions for code running +as part of the Linux kernel. + +In practice, people tend to use memory models the other way around. +That is, given a piece of code and a collection of values specified +for the loads, the model will predict whether it is possible for the +code to run in such a way that the loads will indeed obtain the +specified values. Of course, this is just another way of expressing +the same idea. + +For code running on a uniprocessor system, the predictions are easy: +Each load instruction must obtain the value written by the most recent +store instruction accessing the same location (we ignore complicating +factors such as DMA and mixed-size accesses.) But on multiprocessor +systems, with multiple CPUs making concurrent accesses to shared +memory locations, things aren't so simple. + +Different architectures have differing memory models, and the Linux +kernel supports a variety of architectures. The LKMM has to be fairly +permissive, in the sense that any behavior allowed by one of these +architectures also has to be allowed by the LKMM. + + +A SIMPLE EXAMPLE +---------------- + +Here is a simple example to illustrate the basic concepts. Consider +some code running as part of a device driver for an input device. The +driver might contain an interrupt handler which collects data from the +device, stores it in a buffer, and sets a flag to indicate the buffer +is full. Running concurrently on a different CPU might be a part of +the driver code being executed by a process in the midst of a read(2) +system call. This code tests the flag to see whether the buffer is +ready, and if it is, copies the data back to userspace. The buffer +and the flag are memory locations shared between the two CPUs. + +We can abstract out the important pieces of the driver code as follows +(the reason for using WRITE_ONCE() and READ_ONCE() instead of simple +assignment statements is discussed later): + + int buf = 0, flag = 0; + + P0() + { + WRITE_ONCE(buf, 1); + WRITE_ONCE(flag, 1); + } + + P1() + { + int r1; + int r2 = 0; + + r1 = READ_ONCE(flag); + if (r1) + r2 = READ_ONCE(buf); + } + +Here the P0() function represents the interrupt handler running on one +CPU and P1() represents the read() routine running on another. The +value 1 stored in buf represents input data collected from the device. +Thus, P0 stores the data in buf and then sets flag. Meanwhile, P1 +reads flag into the private variable r1, and if it is set, reads the +data from buf into a second private variable r2 for copying to +userspace. (Presumably if flag is not set then the driver will wait a +while and try again.) + +This pattern of memory accesses, where one CPU stores values to two +shared memory locations and another CPU loads from those locations in +the opposite order, is widely known as the "Message Passing" or MP +pattern. It is typical of memory access patterns in the kernel. + +Please note that this example code is a simplified abstraction. Real +buffers are usually larger than a single integer, real device drivers +usually use sleep and wakeup mechanisms rather than polling for I/O +completion, and real code generally doesn't bother to copy values into +private variables before using them. All that is beside the point; +the idea here is simply to illustrate the overall pattern of memory +accesses by the CPUs. + +A memory model will predict what values P1 might obtain for its loads +from flag and buf, or equivalently, what values r1 and r2 might end up +with after the code has finished running. + +Some predictions are trivial. For instance, no sane memory model would +predict that r1 = 42 or r2 = -7, because neither of those values ever +gets stored in flag or buf. + +Some nontrivial predictions are nonetheless quite simple. For +instance, P1 might run entirely before P0 begins, in which case r1 and +r2 will both be 0 at the end. Or P0 might run entirely before P1 +begins, in which case r1 and r2 will both be 1. + +The interesting predictions concern what might happen when the two +routines run concurrently. One possibility is that P1 runs after P0's +store to buf but before the store to flag. In this case, r1 and r2 +will again both be 0. (If P1 had been designed to read buf +unconditionally then we would instead have r1 = 0 and r2 = 1.) + +However, the most interesting possibility is where r1 = 1 and r2 = 0. +If this were to occur it would mean the driver contains a bug, because +incorrect data would get sent to the user: 0 instead of 1. As it +happens, the LKMM does predict this outcome can occur, and the example +driver code shown above is indeed buggy. + + +A SELECTION OF MEMORY MODELS +---------------------------- + +The first widely cited memory model, and the simplest to understand, +is Sequential Consistency. According to this model, systems behave as +if each CPU executed its instructions in order but with unspecified +timing. In other words, the instructions from the various CPUs get +interleaved in a nondeterministic way, always according to some single +global order that agrees with the order of the instructions in the +program source for each CPU. The model says that the value obtained +by each load is simply the value written by the most recently executed +store to the same memory location, from any CPU. + +For the MP example code shown above, Sequential Consistency predicts +that the undesired result r1 = 1, r2 = 0 cannot occur. The reasoning +goes like this: + + Since r1 = 1, P0 must store 1 to flag before P1 loads 1 from + it, as loads can obtain values only from earlier stores. + + P1 loads from flag before loading from buf, since CPUs execute + their instructions in order. + + P1 must load 0 from buf before P0 stores 1 to it; otherwise r2 + would be 1 since a load obtains its value from the most recent + store to the same address. + + P0 stores 1 to buf before storing 1 to flag, since it executes + its instructions in order. + + Since an instruction (in this case, P1's store to flag) cannot + execute before itself, the specified outcome is impossible. + +However, real computer hardware almost never follows the Sequential +Consistency memory model; doing so would rule out too many valuable +performance optimizations. On ARM and PowerPC architectures, for +instance, the MP example code really does sometimes yield r1 = 1 and +r2 = 0. + +x86 and SPARC follow yet a different memory model: TSO (Total Store +Ordering). This model predicts that the undesired outcome for the MP +pattern cannot occur, but in other respects it differs from Sequential +Consistency. One example is the Store Buffer (SB) pattern, in which +each CPU stores to its own shared location and then loads from the +other CPU's location: + + int x = 0, y = 0; + + P0() + { + int r0; + + WRITE_ONCE(x, 1); + r0 = READ_ONCE(y); + } + + P1() + { + int r1; + + WRITE_ONCE(y, 1); + r1 = READ_ONCE(x); + } + +Sequential Consistency predicts that the outcome r0 = 0, r1 = 0 is +impossible. (Exercise: Figure out the reasoning.) But TSO allows +this outcome to occur, and in fact it does sometimes occur on x86 and +SPARC systems. + +The LKMM was inspired by the memory models followed by PowerPC, ARM, +x86, Alpha, and other architectures. However, it is different in +detail from each of them. + + +ORDERING AND CYCLES +------------------- + +Memory models are all about ordering. Often this is temporal ordering +(i.e., the order in which certain events occur) but it doesn't have to +be; consider for example the order of instructions in a program's +source code. We saw above that Sequential Consistency makes an +important assumption that CPUs execute instructions in the same order +as those instructions occur in the code, and there are many other +instances of ordering playing central roles in memory models. + +The counterpart to ordering is a cycle. Ordering rules out cycles: +It's not possible to have X ordered before Y, Y ordered before Z, and +Z ordered before X, because this would mean that X is ordered before +itself. The analysis of the MP example under Sequential Consistency +involved just such an impossible cycle: + + W: P0 stores 1 to flag executes before + X: P1 loads 1 from flag executes before + Y: P1 loads 0 from buf executes before + Z: P0 stores 1 to buf executes before + W: P0 stores 1 to flag. + +In short, if a memory model requires certain accesses to be ordered, +and a certain outcome for the loads in a piece of code can happen only +if those accesses would form a cycle, then the memory model predicts +that outcome cannot occur. + +The LKMM is defined largely in terms of cycles, as we will see. + + +EVENTS +------ + +The LKMM does not work directly with the C statements that make up +kernel source code. Instead it considers the effects of those +statements in a more abstract form, namely, events. The model +includes three types of events: + + Read events correspond to loads from shared memory, such as + calls to READ_ONCE(), smp_load_acquire(), or + rcu_dereference(). + + Write events correspond to stores to shared memory, such as + calls to WRITE_ONCE(), smp_store_release(), or atomic_set(). + + Fence events correspond to memory barriers (also known as + fences), such as calls to smp_rmb() or rcu_read_lock(). + +These categories are not exclusive; a read or write event can also be +a fence. This happens with functions like smp_load_acquire() or +spin_lock(). However, no single event can be both a read and a write. +Atomic read-modify-write accesses, such as atomic_inc() or xchg(), +correspond to a pair of events: a read followed by a write. (The +write event is omitted for executions where it doesn't occur, such as +a cmpxchg() where the comparison fails.) + +Other parts of the code, those which do not involve interaction with +shared memory, do not give rise to events. Thus, arithmetic and +logical computations, control-flow instructions, or accesses to +private memory or CPU registers are not of central interest to the +memory model. They only affect the model's predictions indirectly. +For example, an arithmetic computation might determine the value that +gets stored to a shared memory location (or in the case of an array +index, the address where the value gets stored), but the memory model +is concerned only with the store itself -- its value and its address +-- not the computation leading up to it. + +Events in the LKMM can be linked by various relations, which we will +describe in the following sections. The memory model requires certain +of these relations to be orderings, that is, it requires them not to +have any cycles. + + +THE PROGRAM ORDER RELATION: po AND po-loc +----------------------------------------- + +The most important relation between events is program order (po). You +can think of it as the order in which statements occur in the source +code after branches are taken into account and loops have been +unrolled. A better description might be the order in which +instructions are presented to a CPU's execution unit. Thus, we say +that X is po-before Y (written as "X ->po Y" in formulas) if X occurs +before Y in the instruction stream. + +This is inherently a single-CPU relation; two instructions executing +on different CPUs are never linked by po. Also, it is by definition +an ordering so it cannot have any cycles. + +po-loc is a sub-relation of po. It links two memory accesses when the +first comes before the second in program order and they access the +same memory location (the "-loc" suffix). + +Although this may seem straightforward, there is one subtle aspect to +program order we need to explain. The LKMM was inspired by low-level +architectural memory models which describe the behavior of machine +code, and it retains their outlook to a considerable extent. The +read, write, and fence events used by the model are close in spirit to +individual machine instructions. Nevertheless, the LKMM describes +kernel code written in C, and the mapping from C to machine code can +be extremely complex. + +Optimizing compilers have great freedom in the way they translate +source code to object code. They are allowed to apply transformations +that add memory accesses, eliminate accesses, combine them, split them +into pieces, or move them around. Faced with all these possibilities, +the LKMM basically gives up. It insists that the code it analyzes +must contain no ordinary accesses to shared memory; all accesses must +be performed using READ_ONCE(), WRITE_ONCE(), or one of the other +atomic or synchronization primitives. These primitives prevent a +large number of compiler optimizations. In particular, it is +guaranteed that the compiler will not remove such accesses from the +generated code (unless it can prove the accesses will never be +executed), it will not change the order in which they occur in the +code (within limits imposed by the C standard), and it will not +introduce extraneous accesses. + +This explains why the MP and SB examples above used READ_ONCE() and +WRITE_ONCE() rather than ordinary memory accesses. Thanks to this +usage, we can be certain that in the MP example, P0's write event to +buf really is po-before its write event to flag, and similarly for the +other shared memory accesses in the examples. + +Private variables are not subject to this restriction. Since they are +not shared between CPUs, they can be accessed normally without +READ_ONCE() or WRITE_ONCE(), and there will be no ill effects. In +fact, they need not even be stored in normal memory at all -- in +principle a private variable could be stored in a CPU register (hence +the convention that these variables have names starting with the +letter 'r'). + + +A WARNING +--------- + +The protections provided by READ_ONCE(), WRITE_ONCE(), and others are +not perfect; and under some circumstances it is possible for the +compiler to undermine the memory model. Here is an example. Suppose +both branches of an "if" statement store the same value to the same +location: + + r1 = READ_ONCE(x); + if (r1) { + WRITE_ONCE(y, 2); + ... /* do something */ + } else { + WRITE_ONCE(y, 2); + ... /* do something else */ + } + +For this code, the LKMM predicts that the load from x will always be +executed before either of the stores to y. However, a compiler could +lift the stores out of the conditional, transforming the code into +something resembling: + + r1 = READ_ONCE(x); + WRITE_ONCE(y, 2); + if (r1) { + ... /* do something */ + } else { + ... /* do something else */ + } + +Given this version of the code, the LKMM would predict that the load +from x could be executed after the store to y. Thus, the memory +model's original prediction could be invalidated by the compiler. + +Another issue arises from the fact that in C, arguments to many +operators and function calls can be evaluated in any order. For +example: + + r1 = f(5) + g(6); + +The object code might call f(5) either before or after g(6); the +memory model cannot assume there is a fixed program order relation +between them. (In fact, if the functions are inlined then the +compiler might even interleave their object code.) + + +DEPENDENCY RELATIONS: data, addr, and ctrl +------------------------------------------ + +We say that two events are linked by a dependency relation when the +execution of the second event depends in some way on a value obtained +from memory by the first. The first event must be a read, and the +value it obtains must somehow affect what the second event does. +There are three kinds of dependencies: data, address (addr), and +control (ctrl). + +A read and a write event are linked by a data dependency if the value +obtained by the read affects the value stored by the write. As a very +simple example: + + int x, y; + + r1 = READ_ONCE(x); + WRITE_ONCE(y, r1 + 5); + +The value stored by the WRITE_ONCE obviously depends on the value +loaded by the READ_ONCE. Such dependencies can wind through +arbitrarily complicated computations, and a write can depend on the +values of multiple reads. + +A read event and another memory access event are linked by an address +dependency if the value obtained by the read affects the location +accessed by the other event. The second event can be either a read or +a write. Here's another simple example: + + int a[20]; + int i; + + r1 = READ_ONCE(i); + r2 = READ_ONCE(a[r1]); + +Here the location accessed by the second READ_ONCE() depends on the +index value loaded by the first. Pointer indirection also gives rise +to address dependencies, since the address of a location accessed +through a pointer will depend on the value read earlier from that +pointer. + +Finally, a read event and another memory access event are linked by a +control dependency if the value obtained by the read affects whether +the second event is executed at all. Simple example: + + int x, y; + + r1 = READ_ONCE(x); + if (r1) + WRITE_ONCE(y, 1984); + +Execution of the WRITE_ONCE() is controlled by a conditional expression +which depends on the value obtained by the READ_ONCE(); hence there is +a control dependency from the load to the store. + +It should be pretty obvious that events can only depend on reads that +come earlier in program order. Symbolically, if we have R ->data X, +R ->addr X, or R ->ctrl X (where R is a read event), then we must also +have R ->po X. It wouldn't make sense for a computation to depend +somehow on a value that doesn't get loaded from shared memory until +later in the code! + + +THE READS-FROM RELATION: rf, rfi, and rfe +----------------------------------------- + +The reads-from relation (rf) links a write event to a read event when +the value loaded by the read is the value that was stored by the +write. In colloquial terms, the load "reads from" the store. We +write W ->rf R to indicate that the load R reads from the store W. We +further distinguish the cases where the load and the store occur on +the same CPU (internal reads-from, or rfi) and where they occur on +different CPUs (external reads-from, or rfe). + +For our purposes, a memory location's initial value is treated as +though it had been written there by an imaginary initial store that +executes on a separate CPU before the program runs. + +Usage of the rf relation implicitly assumes that loads will always +read from a single store. It doesn't apply properly in the presence +of load-tearing, where a load obtains some of its bits from one store +and some of them from another store. Fortunately, use of READ_ONCE() +and WRITE_ONCE() will prevent load-tearing; it's not possible to have: + + int x = 0; + + P0() + { + WRITE_ONCE(x, 0x1234); + } + + P1() + { + int r1; + + r1 = READ_ONCE(x); + } + +and end up with r1 = 0x1200 (partly from x's initial value and partly +from the value stored by P0). + +On the other hand, load-tearing is unavoidable when mixed-size +accesses are used. Consider this example: + + union { + u32 w; + u16 h[2]; + } x; + + P0() + { + WRITE_ONCE(x.h[0], 0x1234); + WRITE_ONCE(x.h[1], 0x5678); + } + + P1() + { + int r1; + + r1 = READ_ONCE(x.w); + } + +If r1 = 0x56781234 (little-endian!) at the end, then P1 must have read +from both of P0's stores. It is possible to handle mixed-size and +unaligned accesses in a memory model, but the LKMM currently does not +attempt to do so. It requires all accesses to be properly aligned and +of the location's actual size. + + +CACHE COHERENCE AND THE COHERENCE ORDER RELATION: co, coi, and coe +------------------------------------------------------------------ + +Cache coherence is a general principle requiring that in a +multi-processor system, the CPUs must share a consistent view of the +memory contents. Specifically, it requires that for each location in +shared memory, the stores to that location must form a single global +ordering which all the CPUs agree on (the coherence order), and this +ordering must be consistent with the program order for accesses to +that location. + +To put it another way, for any variable x, the coherence order (co) of +the stores to x is simply the order in which the stores overwrite one +another. The imaginary store which establishes x's initial value +comes first in the coherence order; the store which directly +overwrites the initial value comes second; the store which overwrites +that value comes third, and so on. + +You can think of the coherence order as being the order in which the +stores reach x's location in memory (or if you prefer a more +hardware-centric view, the order in which the stores get written to +x's cache line). We write W ->co W' if W comes before W' in the +coherence order, that is, if the value stored by W gets overwritten, +directly or indirectly, by the value stored by W'. + +Coherence order is required to be consistent with program order. This +requirement takes the form of four coherency rules: + + Write-write coherence: If W ->po-loc W' (i.e., W comes before + W' in program order and they access the same location), where W + and W' are two stores, then W ->co W'. + + Write-read coherence: If W ->po-loc R, where W is a store and R + is a load, then R must read from W or from some other store + which comes after W in the coherence order. + + Read-write coherence: If R ->po-loc W, where R is a load and W + is a store, then the store which R reads from must come before + W in the coherence order. + + Read-read coherence: If R ->po-loc R', where R and R' are two + loads, then either they read from the same store or else the + store read by R comes before the store read by R' in the + coherence order. + +This is sometimes referred to as sequential consistency per variable, +because it means that the accesses to any single memory location obey +the rules of the Sequential Consistency memory model. (According to +Wikipedia, sequential consistency per variable and cache coherence +mean the same thing except that cache coherence includes an extra +requirement that every store eventually becomes visible to every CPU.) + +Any reasonable memory model will include cache coherence. Indeed, our +expectation of cache coherence is so deeply ingrained that violations +of its requirements look more like hardware bugs than programming +errors: + + int x; + + P0() + { + WRITE_ONCE(x, 17); + WRITE_ONCE(x, 23); + } + +If the final value stored in x after this code ran was 17, you would +think your computer was broken. It would be a violation of the +write-write coherence rule: Since the store of 23 comes later in +program order, it must also come later in x's coherence order and +thus must overwrite the store of 17. + + int x = 0; + + P0() + { + int r1; + + r1 = READ_ONCE(x); + WRITE_ONCE(x, 666); + } + +If r1 = 666 at the end, this would violate the read-write coherence +rule: The READ_ONCE() load comes before the WRITE_ONCE() store in +program order, so it must not read from that store but rather from one +coming earlier in the coherence order (in this case, x's initial +value). + + int x = 0; + + P0() + { + WRITE_ONCE(x, 5); + } + + P1() + { + int r1, r2; + + r1 = READ_ONCE(x); + r2 = READ_ONCE(x); + } + +If r1 = 5 (reading from P0's store) and r2 = 0 (reading from the +imaginary store which establishes x's initial value) at the end, this +would violate the read-read coherence rule: The r1 load comes before +the r2 load in program order, so it must not read from a store that +comes later in the coherence order. + +(As a minor curiosity, if this code had used normal loads instead of +READ_ONCE() in P1, on Itanium it sometimes could end up with r1 = 5 +and r2 = 0! This results from parallel execution of the operations +encoded in Itanium's Very-Long-Instruction-Word format, and it is yet +another motivation for using READ_ONCE() when accessing shared memory +locations.) + +Just like the po relation, co is inherently an ordering -- it is not +possible for a store to directly or indirectly overwrite itself! And +just like with the rf relation, we distinguish between stores that +occur on the same CPU (internal coherence order, or coi) and stores +that occur on different CPUs (external coherence order, or coe). + +On the other hand, stores to different memory locations are never +related by co, just as instructions on different CPUs are never +related by po. Coherence order is strictly per-location, or if you +prefer, each location has its own independent coherence order. + + +THE FROM-READS RELATION: fr, fri, and fre +----------------------------------------- + +The from-reads relation (fr) can be a little difficult for people to +grok. It describes the situation where a load reads a value that gets +overwritten by a store. In other words, we have R ->fr W when the +value that R reads is overwritten (directly or indirectly) by W, or +equivalently, when R reads from a store which comes earlier than W in +the coherence order. + +For example: + + int x = 0; + + P0() + { + int r1; + + r1 = READ_ONCE(x); + WRITE_ONCE(x, 2); + } + +The value loaded from x will be 0 (assuming cache coherence!), and it +gets overwritten by the value 2. Thus there is an fr link from the +READ_ONCE() to the WRITE_ONCE(). If the code contained any later +stores to x, there would also be fr links from the READ_ONCE() to +them. + +As with rf, rfi, and rfe, we subdivide the fr relation into fri (when +the load and the store are on the same CPU) and fre (when they are on +different CPUs). + +Note that the fr relation is determined entirely by the rf and co +relations; it is not independent. Given a read event R and a write +event W for the same location, we will have R ->fr W if and only if +the write which R reads from is co-before W. In symbols, + + (R ->fr W) := (there exists W' with W' ->rf R and W' ->co W). + + +AN OPERATIONAL MODEL +-------------------- + +The LKMM is based on various operational memory models, meaning that +the models arise from an abstract view of how a computer system +operates. Here are the main ideas, as incorporated into the LKMM. + +The system as a whole is divided into the CPUs and a memory subsystem. +The CPUs are responsible for executing instructions (not necessarily +in program order), and they communicate with the memory subsystem. +For the most part, executing an instruction requires a CPU to perform +only internal operations. However, loads, stores, and fences involve +more. + +When CPU C executes a store instruction, it tells the memory subsystem +to store a certain value at a certain location. The memory subsystem +propagates the store to all the other CPUs as well as to RAM. (As a +special case, we say that the store propagates to its own CPU at the +time it is executed.) The memory subsystem also determines where the +store falls in the location's coherence order. In particular, it must +arrange for the store to be co-later than (i.e., to overwrite) any +other store to the same location which has already propagated to CPU C. + +When a CPU executes a load instruction R, it first checks to see +whether there are any as-yet unexecuted store instructions, for the +same location, that come before R in program order. If there are, it +uses the value of the po-latest such store as the value obtained by R, +and we say that the store's value is forwarded to R. Otherwise, the +CPU asks the memory subsystem for the value to load and we say that R +is satisfied from memory. The memory subsystem hands back the value +of the co-latest store to the location in question which has already +propagated to that CPU. + +(In fact, the picture needs to be a little more complicated than this. +CPUs have local caches, and propagating a store to a CPU really means +propagating it to the CPU's local cache. A local cache can take some +time to process the stores that it receives, and a store can't be used +to satisfy one of the CPU's loads until it has been processed. On +most architectures, the local caches process stores in +First-In-First-Out order, and consequently the processing delay +doesn't matter for the memory model. But on Alpha, the local caches +have a partitioned design that results in non-FIFO behavior. We will +discuss this in more detail later.) + +Note that load instructions may be executed speculatively and may be +restarted under certain circumstances. The memory model ignores these +premature executions; we simply say that the load executes at the +final time it is forwarded or satisfied. + +Executing a fence (or memory barrier) instruction doesn't require a +CPU to do anything special other than informing the memory subsystem +about the fence. However, fences do constrain the way CPUs and the +memory subsystem handle other instructions, in two respects. + +First, a fence forces the CPU to execute various instructions in +program order. Exactly which instructions are ordered depends on the +type of fence: + + Strong fences, including smp_mb() and synchronize_rcu(), force + the CPU to execute all po-earlier instructions before any + po-later instructions; + + smp_rmb() forces the CPU to execute all po-earlier loads + before any po-later loads; + + smp_wmb() forces the CPU to execute all po-earlier stores + before any po-later stores; + + Acquire fences, such as smp_load_acquire(), force the CPU to + execute the load associated with the fence (e.g., the load + part of an smp_load_acquire()) before any po-later + instructions; + + Release fences, such as smp_store_release(), force the CPU to + execute all po-earlier instructions before the store + associated with the fence (e.g., the store part of an + smp_store_release()). + +Second, some types of fence affect the way the memory subsystem +propagates stores. When a fence instruction is executed on CPU C: + + For each other CPU C', 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 five requirements, or +axioms: + + Sequential consistency per variable: This requires that the + system obey the four coherency rules. + + Atomicity: This requires that atomic read-modify-write + operations really are atomic, that is, no other stores can + sneak into the middle of such an update. + + Happens-before: This requires that certain instructions are + executed in a specific order. + + Propagation: This requires that certain stores propagate to + CPUs and to RAM in a specific order. + + Rcu: This requires that RCU read-side critical sections and + grace periods obey the rules of RCU, in particular, the + Grace-Period Guarantee. + +The first and second are quite common; they can be found in many +memory models (such as those for C11/C++11). The "happens-before" and +"propagation" axioms have analogs in other memory models as well. The +"rcu" axiom is specific to the LKMM. + +Each of these axioms is discussed below. + + +SEQUENTIAL CONSISTENCY PER VARIABLE +----------------------------------- + +According to the principle of cache coherence, the stores to any fixed +shared location in memory form a global ordering. We can imagine +inserting the loads from that location into this ordering, by placing +each load between the store that it reads from and the following +store. This leaves the relative positions of loads that read from the +same store unspecified; let's say they are inserted in program order, +first for CPU 0, then CPU 1, etc. + +You can check that the four coherency rules imply that the rf, co, fr, +and po-loc relations agree with this global ordering; in other words, +whenever we have X ->rf Y or X ->co Y or X ->fr Y or X ->po-loc Y, the +X event comes before the Y event in the global ordering. The LKMM's +"coherence" axiom expresses this by requiring the union of these +relations not to have any cycles. This means it must not be possible +to find events + + X0 -> X1 -> X2 -> ... -> Xn -> X0, + +where each of the links is either rf, co, fr, or po-loc. This has to +hold if the accesses to the fixed memory location can be ordered as +cache coherence demands. + +Although it is not obvious, it can be shown that the converse is also +true: This LKMM axiom implies that the four coherency rules are +obeyed. + + +ATOMIC UPDATES: rmw +------------------- + +What does it mean to say that a read-modify-write (rmw) update, such +as atomic_inc(&x), is atomic? It means that the memory location (x in +this case) does not get altered between the read and the write events +making up the atomic operation. In particular, if two CPUs perform +atomic_inc(&x) concurrently, it must be guaranteed that the final +value of x will be the initial value plus two. We should never have +the following sequence of events: + + CPU 0 loads x obtaining 13; + CPU 1 loads x obtaining 13; + CPU 0 stores 14 to x; + CPU 1 stores 14 to x; + +where the final value of x is wrong (14 rather than 15). + +In this example, CPU 0's increment effectively gets lost because it +occurs in between CPU 1's load and store. To put it another way, the +problem is that the position of CPU 0's store in x's coherence order +is between the store that CPU 1 reads from and the store that CPU 1 +performs. + +The same analysis applies to all atomic update operations. Therefore, +to enforce atomicity the LKMM requires that atomic updates follow this +rule: Whenever R and W are the read and write events composing an +atomic read-modify-write and W' is the write event which R reads from, +there must not be any stores coming between W' and W in the coherence +order. Equivalently, + + (R ->rmw W) implies (there is no X with R ->fr X and X ->co W), + +where the rmw relation links the read and write events making up each +atomic update. This is what the LKMM's "atomic" axiom says. + + +THE PRESERVED PROGRAM ORDER RELATION: ppo +----------------------------------------- + +There are many situations where a CPU is obligated to execute two +instructions in program order. We amalgamate them into the ppo (for +"preserved program order") relation, which links the po-earlier +instruction to the po-later instruction and is thus a sub-relation of +po. + +The operational model already includes a description of one such +situation: Fences are a source of ppo links. Suppose X and Y are +memory accesses with X ->po Y; then the CPU must execute X before Y if +any of the following hold: + + A strong (smp_mb() or synchronize_rcu()) fence occurs between + X and Y; + + X and Y are both stores and an smp_wmb() fence occurs between + them; + + X and Y are both loads and an smp_rmb() fence occurs between + them; + + X is also an acquire fence, such as smp_load_acquire(); + + Y is also a release fence, such as smp_store_release(). + +Another possibility, not mentioned earlier but discussed in the next +section, is: + + X and Y are both loads, X ->addr Y (i.e., there is an address + dependency from X to Y), and 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!) + +There is one last example of preserved program order in the LKMM: when +a load-acquire reads from an earlier store-release. For example: + + smp_store_release(&x, 123); + r1 = smp_load_acquire(&x); + +If the smp_load_acquire() ends up obtaining the 123 value that was +stored by the smp_store_release(), the LKMM says that the load must be +executed after the store; the store cannot be forwarded to the load. +This requirement does not arise from the operational model, but it +yields correct predictions on all architectures supported by the Linux +kernel, although for differing reasons. + +On some architectures, including x86 and ARMv8, it is true that the +store cannot be forwarded to the load. On others, including PowerPC +and ARMv7, smp_store_release() generates object code that starts with +a fence and smp_load_acquire() generates object code that ends with a +fence. The upshot is that even though the store may be forwarded to +the load, it is still true that any instruction preceding the store +will be executed before the load or any following instructions, and +the store will be executed before any instruction following the load. + + +AND THEN THERE WAS ALPHA +------------------------ + +As mentioned above, the Alpha architecture is unique in that it does +not appear to respect address dependencies to loads. This means that +code such as the following: + + int x = 0; + int y = -1; + int *ptr = &y; + + P0() + { + WRITE_ONCE(x, 1); + smp_wmb(); + WRITE_ONCE(ptr, &x); + } + + P1() + { + int *r1; + int r2; + + r1 = 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 (called smp_read_barrier_depends() and defined as +nothing at all on non-Alpha builds) after every READ_ONCE() and atomic +load. 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 with smp_read_barrier_depends(): They do not allow +the CPU to execute any po-later instructions (or po-later loads in the +case of smp_rmb()) until all outstanding stores have been processed by +the local cache. In the case of a strong fence, the CPU first has to +wait for all of its po-earlier stores to propagate to every other CPU +in the system; then it has to wait for the local cache to process all +the stores received as of that time -- not just the stores received +when the strong fence began. + +And of course, none of this matters for any architecture other than +Alpha. + + +THE HAPPENS-BEFORE RELATION: hb +------------------------------- + +The happens-before relation (hb) links memory accesses that have to +execute in a certain order. hb includes the ppo relation and two +others, one of which is rfe. + +W ->rfe R implies that W and R are on different CPUs. It also means +that W's store must have propagated to R's CPU before R executed; +otherwise R could not have read the value stored by W. Therefore W +must have executed before R, and so we have W ->hb R. + +The equivalent fact need not hold if W ->rfi R (i.e., W and R are on +the same CPU). As we have already seen, the operational model allows +W's value to be forwarded to R in such cases, meaning that R may well +execute before W does. + +It's important to understand that neither coe nor fre is included in +hb, despite their similarities to rfe. For example, suppose we have +W ->coe W'. This means that W and W' are stores to the same location, +they execute on different CPUs, and W comes before W' in the coherence +order (i.e., W' overwrites W). Nevertheless, it is possible for W' to +execute before W, because the decision as to which store overwrites +the other is made later by the memory subsystem. When the stores are +nearly simultaneous, either one can come out on top. Similarly, +R ->fre W means that W overwrites the value which R reads, but it +doesn't mean that W has to execute after R. All that's necessary is +for the memory subsystem not to propagate W to R's CPU until after R +has executed, which is possible if W executes shortly before R. + +The third relation included in hb is like ppo, in that it only links +events that are on the same CPU. However it is more difficult to +explain, because it arises only indirectly from the requirement of +cache coherence. The relation is called prop, and it links two events +on CPU C in situations where a store from some other CPU comes after +the first event in the coherence order and propagates to C before the +second event executes. + +This is best explained with some examples. The simplest case looks +like this: + + int x; + + P0() + { + int r1; + + WRITE_ONCE(x, 1); + r1 = READ_ONCE(x); + } + + P1() + { + WRITE_ONCE(x, 8); + } + +If r1 = 8 at the end then P0's accesses must have executed in program +order. We can deduce this from the operational model; if P0's load +had executed before its store then the value of the store would have +been forwarded to the load, so r1 would have ended up equal to 1, not +8. In this case there is a prop link from P0's write event to its read +event, because P1's store came after P0's store in x's coherence +order, and P1's store propagated to P0 before P0's load executed. + +An equally simple case involves two loads of the same location that +read from different stores: + + int x = 0; + + P0() + { + int r1, r2; + + r1 = READ_ONCE(x); + r2 = READ_ONCE(x); + } + + P1() + { + WRITE_ONCE(x, 9); + } + +If r1 = 0 and r2 = 9 at the end then P0's accesses must have executed +in program order. If the second load had executed before the first +then the x = 9 store must have been propagated to P0 before the first +load executed, and so r1 would have been 9 rather than 0. In this +case there is a prop link from P0's first read event to its second, +because P1's store overwrote the value read by P0's first load, and +P1's store propagated to P0 before P0's second load executed. + +Less trivial examples of prop all involve fences. Unlike the simple +examples above, they can require that some instructions are executed +out of program order. This next one should look familiar: + + int buf = 0, flag = 0; + + P0() + { + WRITE_ONCE(buf, 1); + smp_wmb(); + WRITE_ONCE(flag, 1); + } + + P1() + { + int r1; + int r2; + + r1 = READ_ONCE(flag); + r2 = READ_ONCE(buf); + } + +This is the MP pattern again, with an smp_wmb() fence between the two +stores. If r1 = 1 and r2 = 0 at the end then there is a prop link +from P1's second load to its first (backwards!). The reason is +similar to the previous examples: The value P1 loads from buf gets +overwritten by P0's store to buf, the fence guarantees that the store +to buf will propagate to P1 before the store to flag does, and the +store to flag propagates to P1 before P1 reads flag. + +The prop link says that in order to obtain the r1 = 1, r2 = 0 result, +P1 must execute its second load before the first. Indeed, if the load +from flag were executed first, then the buf = 1 store would already +have propagated to P1 by the time P1's load from buf executed, so r2 +would have been 1 at the end, not 0. (The reasoning holds even for +Alpha, although the details are more complicated and we will not go +into them.) + +But what if we put an smp_rmb() fence between P1's loads? The fence +would force the two loads to be executed in program order, and it +would generate a cycle in the hb relation: The fence would create a ppo +link (hence an hb link) from the first load to the second, and the +prop relation would give an hb link from the second load to the first. +Since an instruction can't execute before itself, we are forced to +conclude that if an smp_rmb() fence is added, the r1 = 1, r2 = 0 +outcome is impossible -- as it should be. + +The formal definition of the prop relation involves a coe or fre link, +followed by an arbitrary number of cumul-fence links, ending with an +rfe link. You can concoct more exotic examples, containing more than +one fence, although this quickly leads to diminishing returns in terms +of complexity. For instance, here's an example containing a coe link +followed by two fences and an rfe link, utilizing the fact that +release fences are A-cumulative: + + int x, y, z; + + P0() + { + int r0; + + WRITE_ONCE(x, 1); + r0 = READ_ONCE(z); + } + + P1() + { + WRITE_ONCE(x, 2); + smp_wmb(); + WRITE_ONCE(y, 1); + } + + P2() + { + int r2; + + r2 = READ_ONCE(y); + smp_store_release(&z, 1); + } + +If x = 2, r0 = 1, and r2 = 1 after this code runs then there is a prop +link from P0's store to its load. This is because P0's store gets +overwritten by P1's store since x = 2 at the end (a coe link), the +smp_wmb() ensures that P1's store to x propagates to P2 before the +store to y does (the first fence), the store to y propagates to P2 +before P2's load and store execute, P2's smp_store_release() +guarantees that the stores to x and y both propagate to P0 before the +store to z does (the second fence), and P0's load executes after the +store to z has propagated to P0 (an rfe link). + +In summary, the fact that the hb relation links memory access events +in the order they execute means that it must not have cycles. This +requirement is the content of the LKMM's "happens-before" axiom. + +The LKMM defines yet another relation connected to times of +instruction execution, but it is not included in hb. It relies on the +particular properties of strong fences, which we cover in the next +section. + + +THE PROPAGATES-BEFORE RELATION: pb +---------------------------------- + +The propagates-before (pb) relation capitalizes on the special +features of strong fences. It links two events E and F whenever some +store is coherence-later than E and propagates to every CPU and to RAM +before F executes. The formal definition requires that E be linked to +F via a coe or fre link, an arbitrary number of cumul-fences, an +optional rfe link, a strong fence, and an arbitrary number of hb +links. Let's see how this definition works out. + +Consider first the case where E is a store (implying that the sequence +of links begins with coe). Then there are events W, X, Y, and Z such +that: + + E ->coe W ->cumul-fence* X ->rfe? Y ->strong-fence Z ->hb* F, + +where the * suffix indicates an arbitrary number of links of the +specified type, and the ? suffix indicates the link is optional (Y may +be equal to X). Because of the cumul-fence links, we know that W will +propagate to Y's CPU before X does, hence before Y executes and hence +before the strong fence executes. Because this fence is strong, we +know that W will propagate to every CPU and to RAM before Z executes. +And because of the hb links, we know that Z will execute before F. +Thus W, which comes later than E in the coherence order, will +propagate to every CPU and to RAM before F executes. + +The case where E is a load is exactly the same, except that the first +link in the sequence is fre instead of coe. + +The existence of a pb link from E to F implies that E must execute +before F. To see why, suppose that F executed first. Then W would +have propagated to E's CPU before E executed. If E was a store, the +memory subsystem would then be forced to make E come after W in the +coherence order, contradicting the fact that E ->coe W. If E was a +load, the memory subsystem would then be forced to satisfy E's read +request with the value stored by W or an even later store, +contradicting the fact that E ->fre W. + +A good example illustrating how pb works is the SB pattern with strong +fences: + + int x = 0, y = 0; + + P0() + { + int r0; + + WRITE_ONCE(x, 1); + smp_mb(); + r0 = READ_ONCE(y); + } + + P1() + { + int r1; + + WRITE_ONCE(y, 1); + smp_mb(); + r1 = READ_ONCE(x); + } + +If r0 = 0 at the end then there is a pb link from P0's load to P1's +load: an fre link from P0's load to P1's store (which overwrites the +value read by P0), and a strong fence between P1's store and its load. +In this example, the sequences of cumul-fence and hb links are empty. +Note that this pb link is not included in hb as an instance of prop, +because it does not start and end on the same CPU. + +Similarly, if r1 = 0 at the end then there is a pb link from P1's load +to P0's. This means that if both r1 and r2 were 0 there would be a +cycle in pb, which is not possible since an instruction cannot execute +before itself. Thus, adding smp_mb() fences to the SB pattern +prevents the r0 = 0, r1 = 0 outcome. + +In summary, the fact that the pb relation links events in the order +they execute means that it cannot have cycles. This requirement is +the content of the LKMM's "propagation" axiom. + + +RCU RELATIONS: rcu-link, gp, rscs, rcu-fence, and rb +---------------------------------------------------- + +RCU (Read-Copy-Update) is a powerful synchronization mechanism. It +rests on two concepts: grace periods and read-side critical sections. + +A grace period is the span of time occupied by a call to +synchronize_rcu(). A read-side critical section (or just critical +section, for short) is a region of code delimited by rcu_read_lock() +at the start and rcu_read_unlock() at the end. Critical sections can +be nested, although we won't make use of this fact. + +As far as memory models are concerned, RCU's main feature is its +Grace-Period Guarantee, which states that a critical section can never +span a full grace period. In more detail, the Guarantee says: + + If a critical section starts before a grace period then it + must end before the grace period does. In addition, every + store that propagates to the critical section's CPU before the + end of the critical section must propagate to every CPU before + the end of the grace period. + + If a critical section ends after a grace period ends then it + must start after the grace period does. In addition, every + store that propagates to the grace period's CPU before the + start of the grace period must propagate to every CPU before + the start of the critical section. + +Here is a simple example of RCU in action: + + int x, y; + + P0() + { + rcu_read_lock(); + WRITE_ONCE(x, 1); + WRITE_ONCE(y, 1); + rcu_read_unlock(); + } + + P1() + { + int r1, r2; + + r1 = READ_ONCE(x); + synchronize_rcu(); + r2 = READ_ONCE(y); + } + +The Grace Period Guarantee tells us that when this code runs, it will +never end with r1 = 1 and r2 = 0. The reasoning is as follows. r1 = 1 +means that P0's store to x propagated to P1 before P1 called +synchronize_rcu(), so P0's critical section must have started before +P1's grace period. On the other hand, r2 = 0 means that P0's store to +y, which occurs before the end of the critical section, did not +propagate to P1 before the end of the grace period, violating the +Guarantee. + +In the kernel's implementations of RCU, the 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": Among other things, X ->rcu-link Z includes cases where X +happens-before or is equal to some event Y which is equal to or comes +before Z in the coherence order. When Y = Z this says that X ->rfe Z +implies X ->rcu-link Z. In addition, when Y = X it says that X ->fr Z +and X ->co Z each imply X ->rcu-link Z. + +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 gp and rscs relations. They bring grace +periods and read-side critical sections into the picture, in the +following way: + + E ->gp F means there is a synchronize_rcu() fence event S such + that E ->po S and either S ->po F or S = F. In simple terms, + there is a grace period po-between E and F. + + E ->rscs F means there is a critical section delimited by an + rcu_read_lock() fence L and an rcu_read_unlock() fence U, such + that E ->po U and either L ->po F or L = F. You can think of + this as saying that E and F are in the same critical section + (in fact, it also allows E to be po-before the start of the + critical section and F to be po-after the end). + +If we think of the rcu-link relation as standing for an extended +"before", then X ->gp Y ->rcu-link Z says that X executes before a +grace period which ends before Z executes. (In fact it covers more +than this, because it also includes cases where X executes before a +grace period and some store propagates to Z's CPU before Z executes +but doesn't propagate to some other CPU until after the grace period +ends.) Similarly, X ->rscs Y ->rcu-link Z says that X is part of (or +before the start of) a critical section which starts before Z +executes. + +The LKMM goes on to define the rcu-fence relation as a sequence of gp +and rscs links separated by rcu-link links, in which the number of gp +links is >= the number of rscs links. For example: + + X ->gp Y ->rcu-link Z ->rscs T ->rcu-link U ->gp V + +would imply that X ->rcu-fence V, because this sequence contains two +gp links and only one rscs link. (It also implies that X ->rcu-fence T +and Z ->rcu-fence V.) On the other hand: + + X ->rscs Y ->rcu-link Z ->rscs T ->rcu-link U ->gp V + +does not imply X ->rcu-fence V, because the sequence contains only +one gp link but two rscs links. + +The rcu-fence relation is important because the Grace Period Guarantee +means that rcu-fence acts kind of like a strong fence. In particular, +if W is a write and we have W ->rcu-fence Z, the Guarantee says that W +will propagate to every CPU before Z executes. + +To prove this in full generality requires some intellectual effort. +We'll consider just a very simple case: + + W ->gp X ->rcu-link Y ->rscs Z. + +This formula means that there is a grace period G and a critical +section C such that: + + 1. W is po-before G; + + 2. X is equal to or po-after G; + + 3. X comes "before" Y in some sense; + + 4. Y is po-before the end of C; + + 5. Z is equal to or po-after the start of C. + +From 2 - 4 we deduce that the grace period G ends before the critical +section C. Then the second part of the Grace Period Guarantee says +not only that G starts before C does, but also that W (which executes +on G's CPU before G starts) must propagate to every CPU before C +starts. In particular, W propagates to every CPU before Z executes +(or finishes executing, in the case where Z is equal to the +rcu_read_lock() fence event which starts C.) This sort of reasoning +can be expanded to handle all the situations covered by rcu-fence. + +Finally, the LKMM defines the RCU-before (rb) relation in terms of +rcu-fence. This is done in essentially the same way as the pb +relation was defined in terms of strong-fence. We will omit the +details; the end result is that E ->rb F implies E must execute before +F, just as E ->pb F does (and for much the same reasons). + +Putting this all together, the LKMM expresses the Grace Period +Guarantee by requiring that the rb relation does not contain a cycle. +Equivalently, this "rcu" axiom requires that there are no events E and +F with E ->rcu-link F ->rcu-fence E. Or to put it a third way, the +axiom requires that there are no cycles consisting of gp and rscs +alternating with rcu-link, where the number of gp links is >= the +number of rscs links. + +Justifying the axiom isn't easy, but it is in fact a valid +formalization of the Grace Period Guarantee. We won't attempt to go +through the detailed argument, but the following analysis gives a +taste of what is involved. Suppose we have a violation of the first +part of the Guarantee: A critical section starts before a grace +period, and some store propagates to the critical section's CPU before +the end of the critical section but doesn't propagate to some other +CPU until after the end of the grace period. + +Putting symbols to these ideas, let L and U be the rcu_read_lock() and +rcu_read_unlock() fence events delimiting the critical section in +question, and let S be the synchronize_rcu() fence event for the grace +period. Saying that the critical section starts before S means there +are events E and F where E is po-after L (which marks the start of the +critical section), E is "before" F in the sense of the rcu-link +relation, and F is po-before the grace period S: + + L ->po E ->rcu-link F ->po S. + +Let W be the store mentioned above, let Z come before the end of the +critical section and witness that W propagates to the critical +section's CPU by reading from W, and let Y on some arbitrary CPU be a +witness that W has not propagated to that CPU, where Y happens after +some event X which is po-after S. Symbolically, this amounts to: + + S ->po X ->hb* Y ->fr W ->rf Z ->po U. + +The fr link from Y to W indicates that W has not propagated to Y's CPU +at the time that Y executes. From this, it can be shown (see the +discussion of the rcu-link relation earlier) that X and Z are related +by rcu-link, yielding: + + S ->po X ->rcu-link Z ->po U. + +The formulas say that S is po-between F and X, hence F ->gp X. They +also say that Z comes before the end of the critical section and E +comes after its start, hence Z ->rscs E. From all this we obtain: + + F ->gp X ->rcu-link Z ->rscs E ->rcu-link F, + +a forbidden cycle. Thus the "rcu" axiom rules out this violation of +the Grace Period Guarantee. + +For something a little more down-to-earth, let's see how the axiom +works out in practice. Consider the RCU code example from above, this +time with statement labels added to the memory access instructions: + + int x, y; + + P0() + { + rcu_read_lock(); + W: WRITE_ONCE(x, 1); + X: WRITE_ONCE(y, 1); + rcu_read_unlock(); + } + + P1() + { + int r1, r2; + + Y: r1 = READ_ONCE(x); + synchronize_rcu(); + Z: r2 = READ_ONCE(y); + } + + +If r2 = 0 at the end then P0's store at X overwrites the value that +P1's load at Z reads from, so we have Z ->fre X and thus Z ->rcu-link X. +In addition, there is a synchronize_rcu() between Y and Z, so therefore +we have Y ->gp Z. + +If r1 = 1 at the end then P1's load at Y reads from P0's store at W, +so we have W ->rcu-link Y. In addition, W and X are in the same critical +section, so therefore we have X ->rscs W. + +Then X ->rscs W ->rcu-link Y ->gp Z ->rcu-link X is a forbidden cycle, +violating the "rcu" axiom. Hence the outcome is not allowed by the +LKMM, as we would expect. + +For contrast, let's see what can happen in a more complicated example: + + int x, y, z; + + P0() + { + int r0; + + rcu_read_lock(); + W: r0 = READ_ONCE(x); + X: WRITE_ONCE(y, 1); + rcu_read_unlock(); + } + + P1() + { + int r1; + + Y: r1 = READ_ONCE(y); + synchronize_rcu(); + Z: WRITE_ONCE(z, 1); + } + + P2() + { + int r2; + + rcu_read_lock(); + U: r2 = READ_ONCE(z); + V: WRITE_ONCE(x, 1); + rcu_read_unlock(); + } + +If r0 = r1 = r2 = 1 at the end, then similar reasoning to before shows +that W ->rscs X ->rcu-link Y ->gp Z ->rcu-link U ->rscs V ->rcu-link W. +However this cycle is not forbidden, because the sequence of relations +contains fewer instances of gp (one) than of rscs (two). Consequently +the outcome is allowed by the LKMM. The following instruction timing +diagram shows how it might actually occur: + +P0 P1 P2 +-------------------- -------------------- -------------------- +rcu_read_lock() +X: WRITE_ONCE(y, 1) + Y: r1 = READ_ONCE(y) + synchronize_rcu() starts + . rcu_read_lock() + . V: WRITE_ONCE(x, 1) +W: r0 = READ_ONCE(x) . +rcu_read_unlock() . + synchronize_rcu() ends + Z: WRITE_ONCE(z, 1) + U: r2 = READ_ONCE(z) + rcu_read_unlock() + +This requires P0 and P2 to execute their loads and stores out of +program order, but of course they are allowed to do so. And as you +can see, the Grace Period Guarantee is not violated: The critical +section in P0 both starts before P1's grace period does and ends +before it does, and the critical section in P2 both starts after P1's +grace period does and ends after it does. + + +ODDS AND ENDS +------------- + +This section covers material that didn't quite fit anywhere in the +earlier sections. + +The descriptions in this document don't always match the formal +version of the LKMM exactly. For example, the actual formal +definition of the prop relation makes the initial coe or fre part +optional, and it doesn't require the events linked by the relation to +be on the same CPU. These differences are very unimportant; indeed, +instances where the coe/fre part of prop is missing are of no interest +because all the other parts (fences and rfe) are already included in +hb anyway, and where the formal model adds prop into hb, it includes +an explicit requirement that the events being linked are on the same +CPU. + +Another minor difference has to do with events that are both memory +accesses and fences, such as those corresponding to smp_load_acquire() +calls. In the formal model, these events aren't actually both reads +and fences; rather, they are read events with an annotation marking +them as acquires. (Or write events annotated as releases, in the case +smp_store_release().) The final effect is the same. + +Although we didn't mention it above, the instruction execution +ordering provided by the smp_rmb() fence doesn't apply to read events +that are part of a non-value-returning atomic update. For instance, +given: + + atomic_inc(&x); + smp_rmb(); + r1 = READ_ONCE(y); + +it is not guaranteed that the load from y will execute after the +update to x. This is because the ARMv8 architecture allows +non-value-returning atomic operations effectively to be executed off +the CPU. Basically, the CPU tells the memory subsystem to increment +x, and then the increment is carried out by the memory hardware with +no further involvement from the CPU. Since the CPU doesn't ever read +the value of x, there is nothing for the smp_rmb() fence to act on. + +The LKMM defines a few extra synchronization operations in terms of +things we have already covered. In particular, rcu_dereference() is +treated as READ_ONCE() and rcu_assign_pointer() is treated as +smp_store_release() -- which is basically how the Linux kernel treats +them. + +There are a few oddball fences which need special treatment: +smp_mb__before_atomic(), smp_mb__after_atomic(), and +smp_mb__after_spinlock(). The LKMM uses fence events with special +annotations for them; they act as strong fences just like smp_mb() +except for the sets of events that they order. Instead of ordering +all po-earlier events against all po-later events, as smp_mb() does, +they behave as follows: + + smp_mb__before_atomic() orders all po-earlier events against + po-later atomic updates and the events following them; + + smp_mb__after_atomic() orders po-earlier atomic updates and + the events preceding them against all po-later events; + + smp_mb_after_spinlock() orders po-earlier lock acquisition + events and the events preceding them against all po-later + events. + +The LKMM includes locking. In fact, there is special code for locking +in the formal model, added in order to make tools run faster. +However, this special code is intended to be exactly equivalent to +concepts we have already covered. A spinlock_t variable is treated +the same as an int, and spin_lock(&s) is treated the same as: + + while (cmpxchg_acquire(&s, 0, 1) != 0) + cpu_relax(); + +which waits until s is equal to 0 and then atomically sets it to 1, +and where the read part of the atomic update is also an acquire fence. +An alternate way to express the same thing would be: + + r = xchg_acquire(&s, 1); + +along with a requirement that at the end, r = 0. spin_unlock(&s) is +treated the same as: + + smp_store_release(&s, 0); + +Interestingly, RCU and locking each introduce the possibility of +deadlock. When faced with code sequences such as: + + spin_lock(&s); + spin_lock(&s); + spin_unlock(&s); + spin_unlock(&s); + +or: + + rcu_read_lock(); + synchronize_rcu(); + rcu_read_unlock(); + +what does the LKMM have to say? Answer: It says there are no allowed +executions at all, which makes sense. But this can also lead to +misleading results, because if a piece of code has multiple possible +executions, some of which deadlock, the model will report only on the +non-deadlocking executions. For example: + + int x, y; + + P0() + { + int r0; + + WRITE_ONCE(x, 1); + r0 = READ_ONCE(y); + } + + P1() + { + rcu_read_lock(); + if (READ_ONCE(x) > 0) { + WRITE_ONCE(y, 36); + synchronize_rcu(); + } + rcu_read_unlock(); + } + +Is it possible to end up with r0 = 36 at the end? The LKMM will tell +you it is not, but the model won't mention that this is because P1 +will self-deadlock in the executions where it stores 36 in y. |