\documentstyle[12pt,pocs-header]{article} \Scribes{Kathy Knobe and Dan Berkery} \Lecturer{Bill Weihl} \LectureNumber{7} \LectureDate{3 October 1990} \begin{document} \MakeScribeTop \section{Handouts} \begin{itemize} \item Handout 14: Solutions to Problem Set \#1 \item Handout 15: Spec Questions \item Handout 16: Examples of Concurrency \item Problem set \#1 was corrected and returned \end{itemize} The handout of the specification of the hierarchical file system will not be handed out until next week or certainly by the Monday of the following week. \section{Today's Topic: Concurrency} Today's topic is an introduction to concurrency. Concurrent programs can get very hard to understand very quickly even if they are small. Just as for sequential programs we need a way to: \begin{itemize} \item specify concurrent programs \item implement current programs \item and prove them correct \end{itemize} We will talk about these tasks over the next couple of lectures. We will also cover various pragmatic issues that effect performance. Start with a simple example that will illustrate the types of problems that concurrency can cause. \section{Incrementing a Register} We begin with the first example in handout 16: Incrementing a Register. Given a register that has a state s which is an integer, and two operations: \begin{itemize} \item read, that returns the current state and \item write, that sets the current state \end{itemize} The operation we want to perform is an increment. In a sequential system we could perform the increment in three steps: \begin{itemize} \item read the current value into a temporary \item increment that value \item write the updated value back into the register \end{itemize} as shown on page 1 of the handout. Now consider what happens if we have multiple processes accessing this register via the increment procedure. If two processes are executing this procedure concurrently, both could execute the read operation, each could then update the temporary, then both could write back the updated version. The register would only be incremented once instead of twice. This might not be what we had in mind. \section{Atomicity} To analyze this properly, we need to know the low level atomic operations. For some operations Spec defines the level of atomicity, for example, the assignment is atomic once the RHS has been computed. We can infer from this that the Read and Write procedures appear to act atomically by examining their bodies. It is possible, however, to implement read and write as non-atomic operations, for example, by viewing the register as an array of bits and operating on the bits one at a time. If operations of two processes can be interleaved at the level of the individual bits, the result could be practically anything. Therefore we need to know what the atomic operations are; What are those operations that can be performed without any interleaving or interference by any other processes. Without knowing this we can't understand a concurrent program. The way to think about a concurrent program is that the processes each take steps and that they are running asynchronously. The execution of the program is then as follows: at each time step we pick a process and that process does the next atomic step according to its own PC. We then pick the next process to run the next step more or less randomly. The result is interleaving at the level of the atomic operations. A major issue in concurrent programming is how to make complex operations (like increment) appear atomic. In Spec we have atomicity brackets to define larger atomic operations from smaller ones. (Spec uses double brackets. Often in the literature we will see single brackets.) Assume code inside atomicity brackets executes atomically. In the second example in handout 16, assume the read and write are atomic. If the register started with value k and n processors are concurrently executing the increment, the possible result values include any integer from k+1 (if the all read the current value before any of them update it) to k+n (if each processor completes the increment before any other processor reads the current value) and anything in between. Recall if the reads and writes are not atomic then the possible results might be quite different. To bring the point home, suppose the increment is adding money to a bank account. If you and your spouse both increment your account you'd like both operations to have an impact on your balance. This problem appears at all levels of concurrent systems, register operations (as shown here) and at higher levels such as operating systems and data bases etc. The simplest way to make complex operations atomic is to enclose them in atomicity brackets. This feature is not something that most languages provide (although there are some proposed languages that do). One way to implement the atomicity bracket is to not allow any other process to execute their next step while one process is executing code within atomicity brackets. On multiprocessors, this wastes cycles on the idle processors and can have serious impact on performance. Even on uniprocessors we wouldn't want to implement atomicity brackets this way. Suppose that the process performs I/O, the process would have to wait until the I/O is done before execution proceeds. Question: there seem to be different semantics for this atomicity than atomicity discussed previously. If the printing of several variables is enclosed in atomicity brackets does this mean a crash can not occur before the printing is complete? Answer: Good question. In fact, liberal use of atomicity brackets involves more magic that we can really implement. There are two types of atomicity that people tend to talk about. In a sense they are the same. \begin{itemize} \item Atomicity with respect to failures: what are the operations that once you start them are guaranteed to complete even in the presence of crashes (or at least the effect will be that they totally completed or appear as if unstarted) \item Atomicity with respect to concurrency: what are the operations that can not be interrupted by other processes. \end{itemize} But these two views are really the same if you think of crash as a concurrent process that can wake up and crash the system between atomic operations. We need to know what operations will not be interrupted. Remember what Butler said about the disk. We need to be consistent with the real world. We can't say that writing an arbitrarily large amount of data is atomic. Disks don't work that way. Consider the logging techniques that Butler talked about and our answer to question 1 problem set 2. Its clear the we can't just sprinkle atomicity brackets any where we want. If you are writing a specification then atomicity brackets around large segments of code are ok. However, if we write \begin{verbatim} <> \end{verbatim} then we can reason about this as if it is atomic but we still have the task of implementing this as atomic. If we are concerned only about concurrency and not crashes then the implementation of large atomic sections is straightforward. With crashes the problem is more complex. At the start we must determine the model of failures in order to decide what can be done atomically. Consider the appropriate level of abstraction for your task. We can describe implementations at many levels abstraction. \section{Critical Sections} Code that is supposed to run without interference from other processes is called a critical section. This term arises because if that code is interrupted or interleaved with code from another process, the state of the system may become damaged. One safe way to implement a critical section is to insure that nothing else runs concurrently with it. Such an implementation is safe but may perform poorly. The question that arises is: Can we maintain the appearance of atomicity and achieve better performance? To answer this question we must understand the source of the damage. The code sections for P1 and P2 can be interleaved in any way without damage. However, the code for P3 and P4 cannot. \begin{verbatim} P1 P2 s1 x := 1 s4 t1 := a s2 y := z+1 s5 t2 := t1 + b s3 w := t or P3 P4 s1 x := 1 s4 t1 := a s2 y := z+1 s5 t2 := t1 + y s3 w := t \end{verbatim} A problem arises only when the two sections access common state (variables, and values pointed to). If they don't access same state then they can run concurrently. If both access the same state but both are only reading that state we are still ok. Only in the case that at least one is writing and both are accessing do we have a problem. In practice people associate a lock with shared data. If you want to access the data get the lock before accessing the data and release it after done accessing the shared data. If the performance is still not good enough, partition the shared data into subsets and associate a lock with each subset. Then prior to entering a critical section get all the locks that are associated with the state referenced in the critical section. When the critical section is complete the locks are released. All other methods boil down to this. NOTE: these sections do not necessarily run atomically; they just appear to. It is easier to reason about atomic chunks. The larger the atomic chunks, the easier the program is to reason about. Next time we will talk about precise reasoning techniques for concurrent programs. \section{How Locks Work} The approach presented on Page 2 of handout 16 is used in many systems today. Mutex is a standard term in the literature. It stands for mutual exclusion. This spec provides a way to create a new mutex (will be more than one mutex). The state of the mutex is nil if no process is holding a lock or it is the thread name (process id) of the process that is holding the lock. [Aside: There is a confusion between the term process (this has connotation of separate address space) and the term thread. For this class the differences are not critical.] This spec also provides for releasing and acquiring locks. Release atomically sees if the process holding lock is the one asking to release (need some magic to get name of current thread). If the caller to release is the current holder it releases the mutex. Acquire is more subtle. Atomically if current state of the mutex is nil it is set to the name of the current process. This must be done atomically. If it is not done atomically race conditions could occur in which two processes both find it nil and both acquire it. \section{Semantics of Spec} The discussion of the Acquire routine lead to a serious discussion of the Spec semantics mostly pertaining to choice both in and out of atomicity brackets. If we have an atomic statement that can fail (the body of the Acquire can fail if value of mutex is non nil) then the semantics is as if it were implemented with backtracking in order to find a success path through the statement that succeeds. In other words, inside atomicity brackets, we use all the angels and backtracking mechanisms necessary in order to make the right non-deterministic choices so that the statement will succeed. Outside of atomicity brackets, we can choose the next single atomic step based on success or failure of that single step only. That is, for \begin{verbatim} (;;) [] ( ;;) or (;;) [*] ( ;;) \end{verbatim} We can choose option based on the success of the first atomic operation of that option {\tt (s1 or s4 )} only. If we choose the option {\tt (;;)} over the option {\tt( ;;)} then {\tt } must have succeeded. However, if {\tt } fails no backtracking takes place. The program counter remains at {\tt } until (based on updates by other processes) {\tt } succeeds. Two aspects make these semantics rational: We can't backtrack over a completed atomic operation (e.g., {\tt }) since other interleaved processes may have performed subsequent steps based on the completion of that atomic operation. We can't use an oracle or an angel to ensure that all the statements will succeed for an option composed of several atomic operations since after one of the atomic operations completes, other processes could perform actions that affect the guards of the remaining operations. In this example, we can't guarantee the success of {\tt } and {\tt } since after completion of {\tt } another process could update values used in computing the guard for {\tt s2}. The system executes threads, a process can only execute the next atomic step if that step does not fail. Specifically, in the routine Acquire, the statement \begin{verbatim} << m^ = nil => m^ := SELF>> \end{verbatim} the thread executing this statement sits at this statement until it does not fail. More examples follow: \begin{itemize} \item \begin{verbatim} << G1 => S1 [] G2 => S2 >> if G1 => S1 fails then try G2 => S2. \end{verbatim} \item \begin{verbatim} (<>; <

S3>>) [] <> \end{verbatim} Choice is made on the success or failure of {\tt S1} and {\tt S2}. If {\tt S1} succeeds and we choose the first of the two options {\tt P } can still fail. Since this choice is outside atomicity brackets we cannot backtrack. We simply wait at {\tt <

S3>>} until it succeeds. \item If the previous example were changed slightly to \begin{verbatim} (<>; P => S3) [] <> \end{verbatim} then if we choose the first option, we execute {\tt S1} atomically and then try {\tt P}. If {\tt P} fails we wait, as before, until {\tt P} succeeds. However, if {\tt P} succeeds, with the atomicity brackets removed, it is possible that other processes intervene between the success of P and the execution of {\tt S3}. \item \begin{verbatim} << S; P => S3 [] S2 >> \end{verbatim} Here we cannot pick the first choice if {\tt P} fails. %Kathy, this seems to be a repeat of the third item. %\item %By modifying the atomicity brackets in example above we have: %\begin{verbatim} %(<>; P => S3) %[] %<> %\end{verbatim} %Here we can pick the first choice even if {\tt P} fails. We will simply wait %at {\tt P => S3} until {\tt P} succeeds. \item \begin{verbatim} SKIP; false => HAVOC [] SKIP \end{verbatim} Here we could choose the first option since SKIP succeeds but we will wait forever at the predicate 'false.' % Kathy, I could not find a good place to put this in. %[GOES SOMEWHERE] One way to think about this is that atomic statements %are simply relations from input states to output states. Semantics of %a series of non-atomic statements are more complicated. \item \begin{verbatim} <>; <

> => <> [*] <> \end{verbatim} Choice examines only {\tt S1} and {\tt S2} for success. If both fail, it is the choice that is waiting. That is, when either succeed, processing can continue. \end{itemize} \end{document}