How Can Array Reduction be Parallelized in OpenMP?

Reducing on an Array in OpenMP

It is not possible to directly perform a reduction on an array in OpenMP. However, there are alternative approaches to achieve array reduction parallelism.

First Method: Private Arrays and Critical Section

This method creates private copies of the array for each thread. Each thread fills in its private array, and a critical section is used to merge the results into the final array.

int A[] = {84, 30, 95, 94, 36, 73, 52, 23, 2, 13};
int S[10] = {0};

#pragma omp parallel
{
    int S_private[10] = {0};
    
    #pragma omp for
    for (int n = 0; n < 10; ++n) {
        for (int m = 0; m <= n; ++m) {
            S_private[n] += A[m];
        }
    }
    
    #pragma omp critical
    {
        for(int n = 0; n < 10; ++n) {
            S[n] += S_private[n];
        }
    }
}

Second Method: Array Expansion and Thread-Independent Accumulation

This method creates an expanded array that spans all threads. Each thread fills in its portion of the array, and then the results are merged without using a critical section. This approach can have cache issues if not used carefully on multi-socket systems.

int A[] = {84, 30, 95, 94, 36, 73, 52, 23, 2, 13};
int S[10] = {0};
int *S_private;

#pragma omp parallel
{
    const int nthreads = omp_get_num_threads();
    const int ithread = omp_get_thread_num();

    #pragma omp single 
    {
        S_private = new int[10 * nthreads];
        for(int i = 0; i < (10 * nthreads); i++) S_private[i] = 0;
    }
    #pragma omp for
    for (int n = 0; n < 10; ++n)
    {
        for (int m = 0; m <= n; ++m){
            S_private[ithread * 10 + n] += A[m];
        }
    }
    #pragma omp for
    for(int i = 0; i < 10; i++) {
        for(int t = 0; t < nthreads; t++) {
            S[i] += S_private[10 * t + i];
        }
    }
}
delete[] S_private;

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