// list of subtasks in Java

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forked = new FibVL(n - 1, forked); // prepends to list forkedfork(); forked = new FibVL(n - 2, forked); forkedfork(); number = accumulate(forked); } } // Traverse list, joining each subtask and adding to result int accumulate(FibVL list) { int sum = 0; for (FibVL f = list; f != null; f = fnext) { fjoin(); sum += fnumber; } return sum; }
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4416 Callbacks
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Recursive task-based fork/join parallelism may be extended to apply when other local synchronization conditions are used instead of join In the FJTask framework, tjoin() is implemented as an optimized version of:
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while (!tisDone()) yield();
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Method yield here allows the underlying worker thread to process other tasks (More specifically, in the FJTask framework, the thread will process at least one other task if one exists) Any other condition may be used in this construction rather than isDone, as long as you are certain that the predicate being waited for will eventually become true due to the actions of a subtask (or one of its subtasks, and so on) For example, rather than relying on join, task control can rely on counters that keep track of task creation and completion A counter can be incremented on each fork and decremented when the forked task has produced a result This and related counter-based schemes can be attractive choices when subtasks communicate back results via callbacks rather than via access to result fields Counters of this form are small-scale, localized versions of the barriers discussed in 443 Callback-based fork/join designs are seen, for example, in problem-solving algorithms, games, searching, and logic programming In many such applications, the number of subtasks that are forked can vary dynamically, and subtask results are better captured by method calls than by field extraction Callback-based approaches also permit greater asynchrony than techniques such as the linked tasks in 4415 This can lead to better performance when subtasks differ in expected duration, since the result processing of quickly completing subtasks can sometimes overlap with continued processing of longer ones However, this design gives up all result ordering guarantees, and thus is applicable only when subtask result processing is completely independent of the order in which results are produced Callback counters are used in the following class FibVCB, which is not at all well-suited for the problem at hand but serves to exemplify techniques This code illustrates a typical but delicate combination of task-local variables, volatiles, and locking in an effort to keep task control overhead to a minimum:
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class FibVCB extends FJTask { // volatile int number = 0; // as before final FibVCB parent; // is null for outermost call int callbacksExpected = 0; volatile int callbacksReceived = 0; FibVCB(int n, FibVCB p) { number = n; parent = p; } // Callback method invoked by subtasks upon completion synchronized void addToResult(int n) { number += n; ++callbacksReceived; } public void run() { int n = number; // same structure as join-based version
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if (n <= sequentialThreshold) number = seqFib(n); else { // Clear number so subtasks can fill in number = 0; // Establish number of callbacks expected callbacksExpected = 2; new FibVCB(n - 1, this)fork(); new FibVCB(n - 2, this)fork(); // Wait for callbacks from children while (callbacksReceived < callbacksExpected) yield(); } // Call back parent if (parent != null) parentaddToResult(number);
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All mutual exclusion locking is restricted to small code segments protecting field accesses, as must be true for any class in a lightweight task framework Tasks are not allowed to block unless they are sure they will be able to continue soon In particular, this framework unenforceably requires that synchronized blocks not span forks and subsequent joins or yields To help eliminate some synchronization, the callback count is split into two counters, callbacksExpected and callbacksReceived The task is done when they are equal The callbacksExpected counter is used only by the current task, so access need not be synchronized, and it need not be volatile In fact, since exactly two callbacks are always expected in the recursive case and the value is never needed outside the run method, this class could easily be reworked in a way that eliminates all need for this variable However, such a variable is needed in more typical callback-based designs where the number of forks may vary dynamically and may be generated across multiple methods The addToResult callback method must be synchronized to avoid interference problems when subtasks call back at about the same time So long as both number and callbacksReceived are declared as volatile, and callbacksReceived is updated as the last statement of addToResult, the yield loop test need not involve synchronization because it is waiting for a latching threshold that, once reached, will never change (see 3421) We could also define a reworked getAnswer method that uses these mechanics so that it returns an answer if all callbacks have been received However, since this method is designed to be called by external (non-task) clients upon completion of the overall computation, there is no compelling reason to do this The version from the original Fib class suffices Despite these measures, the overhead associated with task control in this version is greater than that of the original version using coInvoke If you were to use it anyway, you would probably choose a slightly larger sequential threshold, and thus exploit slightly less parallelism
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4417 Cancellation In some designs, there is no need for keeping counts of callbacks or exhaustively traversing through subtask lists Instead, tasks complete when any subtask (or one of its subtasks, and so on) arrives at a suitable result In these cases, you can avoid wasting computation by cancelling any subtasks in the midst of producing results that will not be needed The options here are similar to those seen in other situations involving cancellation (see 312) For example, subtasks can regularly invoke a method (perhaps isDone) in their parents that indicates that an answer has already been found, and if so to return early They must also set their own status, so any of their subtasks can do the same This can be implemented here using FJTaskcancel that just prematurely sets isDone status This suppresses execution of tasks that have not yet been started, but has no effect on tasks in the midst of execution unless the tasks' run methods themselves detect updated status and deal with it When an entire set of tasks are all trying to compute a single result, an even simpler strategy suffices: Tasks may regularly check a global (static) variable that indicates completion However, when there are many tasks, and many CPUs, more localized strategies may still be preferable to one that places so much pressure on the underlying system by generating many accesses to the same memory location, especially if it must be accessed under synchronization Additionally, bear in mind that the total overhead associated with cancellation should be less than the cost of just letting small tasks run even if their results are not needed For example, here is a class that solves the classic N-Queens problem, searching for the placement of N queens that do not attack each other on a chessboard of size NxN For simplicity of illustration, it relies on a static Result variable Here tasks check for cancellation only upon entry into the method They will continue looping through possible extensions even if a result has already been found However, the generated tasks will immediately exit This can be slightly wasteful, but may obtain a solution more quickly than a version that checks for completion upon every iteration of every task Note also here that the tasks do not bother joining their subtasks since there is no reason to do so Only the ultimate external caller (in main) needs to wait for a solution; this is supported here by adding standard waiting and notification methods to the Result class (Also, for compactness, this version does not employ any kind of granularity threshold It is easy to add one, for example by directly exploring moves rather than forking subtasks when the number of rows is close to the board size)
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class NQueens extends FJTask { static int boardSize; // fixed after initialization in main // Boards are arrays where each cell represents a row, // and holds the column number of the queen in that row static class Result { // holder for ultimate result private int[] board = null; // non-null when solved synchronized boolean solved() { return board != null; } synchronized void set(int[] b) { // Support use by nonTasks if (board == null) { board = b; notifyAll(); }
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} synchronized int[] await() throws InterruptedException { while (board == null) wait(); return board; }
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} static final Result result = new Result(); public static void main(String[] args) { boardSize = ; FJTaskRunnerGroup tasks = new FJTaskRunnerGroup(); int[] initialBoard = new int[0]; // start with empty board tasksexecute(new NQueens(initialBoard)); int[] board = resultawait(); // } final int[] sofar; // initial configuration }
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NQueens(int[] board) { thissofar = board; public void run() { if (!resultsolved()) { int row = sofarlength; if (row >= boardSize) resultset(sofar); else {
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