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This pattern is extensively used with the Linda programming environment The tuple space in Linda is ideally suited to programs that use the Master/Worker pattern, as described in depth in [CG91] and in the survey paper [CGMS94] The Master/Worker pattern is used in many distributed computing environments because these systems must deal with extreme levels of unpredictability in the availability of resources The SETI@home project [SET] uses the Master/Worker pattern to utilize volunteers' Internet connected computers to download and analyze radio telescope data as part of the Search for Extraterrestrial Intelligence (SETI) Programs constructed with the Calypso system [BDK95], a distributed computing framework which provides system support for dynamic changes in the set of PEs, also use the Master/Worker pattern A parallel algorithm for detecting repeats in genomic data [RHB03] uses the Master/Worker pattern with MPI on a cluster of dual processor PCs Related Patterns This pattern is closely related to the Loop Parallelism pattern when the loops utilize some form of dynamic scheduling (such as when the schedule (dynamic) clause is used in OpenMP) Implementations of the Fork/Join pattern sometimes use the Master/Worker pattern behind the scenes This pattern is also closely related to algorithms that make use of the nextval function from TCGMSG [Har91, WSG95, LDSH95] The nextval function implements a monotonic counter If the bag of tasks can be mapped onto a fixed range of monotonic indices, the counter provides the bag of tasks and the function of the master is implied by the counter Finally, the owner computes filter discussed in the molecular dynamics example in the SPMD pattern is essentially a variation on the master/worker theme In such an algorithm, all the master would do is set up the bag of tasks (loop iterations) and assign them to UEs, with the assignment of tasks to UEs defined by the filter Because the UEs can essentially perform this assignment themselves (by examining each task with the filter), no explicit master is needed
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56 THE LOOP PARALLELISM PATTERN
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Problem Given a serial program whose runtime is dominated by a set of computationally intensive loops, how can it be translated into a parallel program
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Context The overwhelming majority of programs used in scientific and engineering applications are expressed in terms of iterative constructs; that is, they are loop based Optimizing these programs by focusing strictly on the loops is a tradition dating back to the older vector supercomputers Extending this approach to modern parallel computers suggests a parallel algorithm strategy in which concurrent tasks are identified as iterations of parallelized loops The advantage of structuring a parallel algorithm around parallelized loops is particularly important in problems for which well accepted programs already exist In many cases, it isn't practical to massively restructure an existing program to gain parallel performance This is particularly important when the program (as is frequently the case) contains convoluted code and poorly understood algorithms This pattern addresses ways to structure loop based programs for parallel computation When existing code is available, the goal is to "evolve" a sequential program into a parallel program by a series of transformations on the loops Ideally, all changes are localized to the loops with transformations that remove loop carried dependencies and leave the overall program semantics unchanged (Such transformations are called semantically neutral transformations) Not all problems can be approached in this loop driven manner Clearly, it will only work when the algorithm structure has most, if not all, of the computationally intensive work buried in a manageable number of distinct loops Furthermore, the body of the loop must result in loop iterations that work well as parallel tasks (that is, they are computationally intensive, express sufficient concurrency, and are mostly independent) Not all target computer systems align well with this style of parallel programming If the code cannot be restructured to create effective distributed data structures, some level of support for a shared address space is essential in all but the most trivial cases Finally, Amdahl's law and its requirement to minimize a program's serial fraction often means that loop based approaches are only effective for systems with smaller numbers of PEs Even with these restrictions, this class of parallel algorithms is growing rapidly Because loop based algorithms are the traditional approach in high performance computing and are still dominant in new programs, there is a large backlog of loop based programs that need to be ported to modern parallel computers The OpenMP API was created primarily to support parallelization of these loop driven problems Limitations on the scalability of these algorithms are serious, but acceptable, given that there are orders of magnitude more machines with two or four processors than machines with dozens or hundreds of processors This pattern is particularly relevant for OpenMP programs running on shared memory computers and for problems using the Task Parallelism and Geometric Decomposition patterns Forces
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Sequential equivalence A program that yields identical results (except for round off errors) when executed with one thread or many threads is said to be sequentially equivalent (also known as serially equivalent) Sequentially equivalent code is easier to write, easier to maintain, and lets a single program source code work for serial and parallel machines
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Incremental parallelism (or refactoring) When parallelizing an existing program, it is much easier to end up with a correct parallel program if (1) the parallelization is introduced as a sequence of incremental transformations, one loop at a time, and (2) the transformations don't "break" the program, allowing testing to be carried out after each transformation Memory utilization Good performance requires that the data access patterns implied by the loops mesh well with the memory hierarchy of the system This can be at odds with the previous two forces, causing a programmer to massively restructure loops
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Solution This pattern is closely aligned with the style of parallel programming implied by OpenMP The basic approach consists of the following steps
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Find the bottlenecks Locate the most computationally intensive loops either by inspection of the code, by understanding the performance needs of each subproblem, or through the use of program performance analysis tools The amount of total runtime on representative data sets contained by these loops will ultimately limit the scalability of the parallel program (see Amdahl's law) Eliminate loop carried dependencies The loop iterations must be nearly independent Find dependencies between iterations or read/write accesses and transform the code to remove or mitigate them Finding and removing the dependencies is discussed in the Task Parallelism pattern, while protecting dependencies with synchronization constructs is discussed in the Shared Data pattern Parallelize the loops Split up the iterations among the UEs To maintain sequential equivalence, use semantically neutral directives such as those provided with OpenMP (as described in the OpenMP appendix, Appendix A) Ideally, this should be done to one loop at a time with testing and careful inspection carried out at each point to make sure race conditions or other errors have not been introduced Optimize the loop schedule The iterations must be scheduled for execution by the UEs so the load is evenly balanced Although the right schedule can often be chosen based on a clear understanding of the problem, frequently it is necessary to experiment to find the optimal schedule
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This approach is only effective when the compute times for the loop iterations are large enough to compensate for parallel loop overhead The number of iterations per loop is also important, because having many iterations per UE provides greater scheduling flexibility In some cases, it might be necessary to transform the code to address these issues Two transformations commonly used are the following:
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Merge loops If a problem consists of a sequence of loops that have consistent loop limits, the loops can often be merged into a single loop with more complex loop iterations, as shown in Fig 521 Coalesce nested loops Nested loops can often be combined into a single loop with a larger combined iteration count, as shown in Fig 522 The larger number of iterations can help
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overcome parallel loop overhead, by (1) creating more concurrency to better utilize larger numbers of UEs, and (2) providing additional options for how the iterations are scheduled onto UEs Parallelizing the loops is easily done with OpenMP by using the omp parallel for directive This directive tells the compiler to create a team of threads (the UEs in a shared memory environment) and to split up loop iterations among the team The last loop in Fig 522 is an example of a loop parallelized with OpenMP We describe this directive at a high level in the Implementation Mechanisms design space Syntactic details are included in the OpenMP appendix, Appendix A Notice that in Fig 522 we had to direct the system to create copies of the indices i and j local to each thread The single most common error in using this pattern is to neglect to "privatize" key variables If i and j are shared, then updates of i and j by different UEs can collide and lead to unpredictable results (that is, the program will contain a race condition) Compilers usually will not detect these errors, so programmers must take great care to make sure they avoid these situations
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