C++ Auto-Vectorize Matrix Multiplication loop

Question

When compiling my source code which does basic matrix-matrix multiplication with auto-vectorization and auto-parallelization enabled, I receive these warnings in console:

Answer 1

The loop carried dependence is on result[i][j].

A solution to your problem would be using a temporary variable when summing up the result and do the update outside the inner-most loop like this:

for (int i = 0; i < dimension; ++i) {
    for (int j = 0; j < dimension; ++j) {
        auto tmp = 0;
        for (int k = 0; k < dimension; ++k) {
            tmp += A[i][k] * B[k][j];
        }
        result[i][j] = tmp;
    }
}

This is going remove the dependence (since there is more read-after-write of result[i][j] and should help the vectorizer doing a better job.