1. It is poor practice to hard-code the number 20 multiple times in the code. It would be better to define N = 20 in one place.
2. For a for-loop defined as follows: for (int i12 = 0; i12 <= N; i12++)
the array x12 must have at least N+1 elements. Since this is not the case, the loop should be limited to N elements.
3. The variable f is overwritten with each assignment, so the concrete result is irrelevant here. To ensure the compiler does not optimize away this code, f should be used in some manner. One possible approach is to declare f with the
volatile
keyword.
4. Since the arrays x1 to x12 are not initialized with data, their values are irrelevant.
5. The arrays x1 to x12 can be considered constant since they are only accessed for reading.
6. For precise time measurement in C++, the <chrono> library can be used.
7. Compiler optimization is disabled to ensure that the loops are actually executed.
8. Parallelization with OMP:
#pragma omp parallel for reduction(+:f)
If the compiler supports it, all nested loops can be combined with the collapse option. This creates a single large loop with N^12 iterations, distributed across the available threads.
10. To maximize the program's performance and efficiency, it makes sense to limit the number of threads to the number of logical cores of the system.
11.If more than 20 logical cores are available, outer loops can be combined. With 8 threads, the runtime improves only slightly.
for (int i = 0; i < N * N; i++) {
int i1 = i / N;
int i2 = i % N;
}
Up to 5 loops, I do not see a significant advantage from OMP. After that, the computation time can be significantly reduced with OMP. With OMP, the runtime remains in the double-digit second range for 8 loops, whereas without OMP, it would take impractically long to wait for the result. From the 8th loop onward, it also takes a long time with OMP. I would distribute the computations across additional machines at that point.