You are given a skeleton sequential program for matrix multiplication below: #in

Question

You are given a skeleton sequential program for matrix multiplication below:

#include

#include

#include                 

#define M 500

#define N 500

int main(int argc, char *argv) {

//set number of threads here

omp_set_num_threads(8);

int i, j, k;

double sum;

double **A, **B, **C;

A = malloc(M*sizeof(double *));

B = malloc(M*sizeof(double *));

C = malloc(M*sizeof(double *));

for (i = 0; i < M; i++) {

  A[i] = malloc(N*sizeof(double));

  B[i] = malloc(N*sizeof(double));

  C[i] = malloc(N*sizeof(double));

}

double start, end;

for (i = 0; i < M; i++) {

   for (j = 0; j < N; j++) {

     A[i][j] = j*1;

     B[i][j] = i*j+2;

     C[i][j] = j-i*2;

   }

}

start = omp_get_wtime();

for (i = 0; i < M; i++) {

  for (j = 0; j < N; j++) {

     sum = 0;

     for (k=0; k < M; k++) {

        sum += A[i][k]*B[k][j];

     }

     C[i][j] = sum;

}

}

end = omp_get_wtime();

printf("Time of computation: %f ", end-start);

         }

You are to parallelize this algorithm in three different ways:

1. Add the necessary pragma to parallelize the outer for loop

2. Remove the pragma for the outer for loop and create a pragma for the middle for loop

3. Add the necessary pragmas to parallelize both the outer and middle for loops

Explanation / Answer

The answer is as follows:

1. Add the necessary pragma to parallelize the outer for loop

start = omp_get_wtime();

#pragma omp parallel for
for (i = 0; i < M; i++) {
  for (j = 0; j < N; j++) {
     sum = 0;
     for (k=0; k < M; k++) {
        sum += A[i][k]*B[k][j];
     }
     C[i][j] = sum;
}
}

end = omp_get_wtime();

2. Remove the pragma for the outer for loop and create a pragma for the middle for loop

start = omp_get_wtime();


for (i = 0; i < M; i++) {
#pragma omp parallel for
  for (j = 0; j < N; j++) {
     sum = 0;
     for (k=0; k < M; k++) {
        sum += A[i][k]*B[k][j];
     }
     C[i][j] = sum;
}
}

end = omp_get_wtime();

3. Add the necessary pragmas to parallelize both the outer and middle for loops

start = omp_get_wtime();

#pragma omp parallel for
for (i = 0; i < M; i++) {
#pragma omp parallel for
  for (j = 0; j < N; j++) {
     sum = 0;
     for (k=0; k < M; k++) {
        sum += A[i][k]*B[k][j];
     }
     C[i][j] = sum;
}
}

end = omp_get_wtime();

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