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#include "mpih" // MPI include file #include <stdioh> int main(int argc, char**argv) { int num_procs; // the number of processes in the group int ID; // a unique identifier ranging from 0 to (num_Procs-1) double local_result; double time_init, time_final, time_elapsed; double min_time, max_time, ave_time; // // Initialize MPI and set up the SPMD program // MPI_Init(&argc,&argv); MPI_Comm_rank(MPI_COMM_WORLD, &ID); MPI_Comm_size (MPI_COMM_WORLD, &num_procs); // // Ensure that all processes are set up and ready to go before timing // runit () // MPI_Barrier(MPI_COMM_WORLD); time_init = MPI_Wtime(); runit(); // a function that we wish to time on each process time_final = MPI_Wtime(); time_elapsed = time_final-time_init; MPI_Reduce (&time_elapsed, &min_time, 1, MPI_DOUBLE, MPI_MIN, 0, MPI_COMM_WORLD); MPI_Reduce (&time_elapsed, &max_time, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD); MPI_Reduce (&time_elapsed, &ave_time, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD); if (ID == 0){ ave_time = ave_time /(double)num_procs;
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printf(" min, ave and max times (secs): %f, %f, %f\n", min_time, ave_time,max_time); } MPI_Finalize(); return 0; }
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Most programmers will never implement their own reductions because the reduction mechanisms available with most parallel programming environments meet their needs Java, however, does not provide a reduction operator, so Java programmers might need to implement their own parallel reductions In any case, the algorithms used for reductions are instructive and well worth the effort to understand
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Figure 617 OpenMP program to time the execution of a function called runit() We use a reduction clause to find sum of the runtimes
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#include <stdioh> #include <omph> // OpenMP include file extern void runit(); int main(int argc, char**argv) { int num_threads; // the number of processes in the group double ave_time=00; #pragma omp parallel reduction(+ : ave_time) num_threads(10) { double local_result; double time_init, time_final, time_elapsed; // The single construct causes one thread to set the value of // the num_threads variable The other threads wait at the // barrier implied by the single construct #pragma omp single num_threads = omp_get_num_threads(); time_init = omp_get wtime(); runit(); // a function that we wish to time on each process time_final = omp_get wtime(); time_elapsed = time_final - time_init; } ave_time += time_elapsed; ave_time = ave_time/(double)num_threads;
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printf(" ave time (secs): % \n", ave_time); return 0; }
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We consider tree based reductions in the following discussion These are the simplest of the scalable parallel reduction algorithms and although not optimal, they expose most of the issues addressed in the more optimal reduction algorithms [CKP 93 + ]
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If the reduction operator is not associative, or cannot be treated as associative without significantly affecting the result, it will likely be necessary to perform the entire reduction serially in a single UE, as sketched in Fig 618 If only one UE needs the result of the reduction, it is probably simplest to have that UE perform the operation; if all UEs need the result, the reduction operation can be followed by a broadcast operation to communicate the result to other UEs For simplicity, the figure shows a situation in which there are as many UEs as data items The solution can be extended to situations in which there are more data items than UEs, but the requirement that all the actual computation be done in a single UE still holds because of the lack of associativity (Clearly this solution completely lacks concurrency; we mention it for the sake of completeness and because it might still be useful and appropriate if the reduction operation represents only a relatively small part of a computation whose other parts do have exploitable concurrency)
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Figure 618 Serial reduction to compute the sum of a(0) through a(3) sum(a(i:j)) denotes the sum of elements i through j of array a
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In this approach, the individual combine two elements operations must be performed in sequence, so it is simplest to have them all performed by a single task Because of the data dependencies (indicated by the arrows in the figure), however, some caution is required if the reduction operation is performed as part of a larger calculation involving multiple concurrent UEs; the UEs not performing the reduction can continue with other work only if they can do so without affecting the computation of the reduction operation (for example, if multiple UEs share access to an array and one of them is computing the sum of the elements of the array, the others should not be simultaneously modifying elements of the array) In a message passing environment, this can usually be accomplished using message passing to enforce the data dependency constraints (that is, the UEs not performing the reduction operation send their data to the single UE actually doing the computation) In other environments, the UEs not performing the reduction operation can be forced to wait by means of a barrier
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