Program structure in Java

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Program structure
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Many task parallel problems can be considered to be loop based Loop based problems are, as the name implies, those in which the tasks are based on the iterations of a loop The best solutions for such problems use the Loop Parallelism pattern This pattern can be particularly simple to implement in programming environments that provide directives for automatically assigning loop iterations to UEs For example, in OpenMP a loop can be parallelized by simply adding a "parallel for" directive with an appropriate schedule clause (one that maximizes efficiency) This solution is especially attractive because OpenMP then guarantees that the resulting program is semantically equivalent to the analogous sequential code (within roundoff error associated with different orderings of floatingpoint operations) For problems in which the target platform is not a good fit with the Loop Parallelism pattern, or for problems in which the model of "all tasks known initially, all tasks must complete" does not apply (either because tasks can be created during the computation or because the computation can terminate without all tasks being complete), this straightforward approach is not the best choice Instead, the best design makes use of a task queue; tasks are placed on the task queue as they are created and
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removed by UEs until the computation is complete The overall program structure can be based on either the Master/Worker pattern or the SPMD pattern The former is particularly appropriate for problems requiring a dynamic schedule In the case in which the computation can terminate before all the tasks are complete, some care must be taken to ensure that the computation ends when it should If we define the termination condition as the condition that when true means the computation is complete either all tasks are complete or some other condition (for example, an acceptable solution has been found by one task) then we want to be sure that (1) the termination condition is eventually met (which, if tasks can be created dynamically, might mean building into it a limit on the total number of tasks created), and (2) when the termination condition is met, the program ends How to ensure the latter is discussed in the Master/Worker and SPMD patterns
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Common idioms
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Most problems for which this pattern is applicable fall into the following two categories Embarrassingly parallel problems are those in which there are no dependencies among the tasks A wide range of problems fall into this category, ranging from rendering frames in a motion picture to statistical sampling in computational physics Because there are no dependencies to manage, the focus is on scheduling the tasks to maximize efficiency In many cases, it is possible to define schedules that automatically and dynamically balance the load among UEs Replicated data or reduction problems are those in which dependencies can be managed by "separating them from the tasks" as described earlier replicating the data at the beginning of computation and combining results when the termination condition is met (usually "all tasks complete") For these problems, the overall solution consists of three phases, one to replicate the data into local variables, one to solve the now independent tasks (using the same techniques used for embarrassingly parallel problems), and one to recombine the results into a single result Examples We will consider two examples of this pattern The first example, an image construction example, is embarrassingly parallel The second example will build on the molecular dynamics example used in several of the Finding Concurrency patterns
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Image construction
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In many image construction problems, each pixel in the image is independent of all the other pixels For example, consider the well known Mandelbrot set [Dou86] This famous image is constructed by coloring each pixel according to the behavior of the quadratic recurrence relation Equation 41
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