Consider the Following Code That Adds Two Matrices a and B

question 10

Essay

Consider the following code that adds two matrices A and B and stores the result in a matrix C:
for (i= 0 to 15) {
for (j= 0 to 63) {
C[i][j] = A[i][j] + B[i][j];
}
}
If we had a quad-core multiprocessor, where the elements of the matrices A, B, C are stored in row major order, which one of the following two parallelizations is better and why ? What about when they are stored in column major order ?
(a) For each Pk in {0, 1, 2, 3}:
for (i= 0 to 15) {
for (j= Pk*15 + Pk to (Pk+1)*15 + Pk)
{
// Inner Loop Parallelization C[i][j] = A[i][j] + B[i][j];
}
}
(b) For each Pk in {0, 1, 2, 3}:
for (i= Pk*3 + Pk to (Pk+1)*3 + Pk) {
// Outer Loop Parallelization for (j= 0 to 63) {
C[i][j] = A[i][j] + B[i][j];
}
}

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Definitions:

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