HPC - Dot product

The file omp-dot.c contains a serial program that computes the dot product of two arrays v1[] and v2[]. The program receives the array lengths \(n\) as the only parameter on the command line. The arrays are initialized deterministically, so that their scalar product is known awithout computing it explicitly. The dot product of v1[] and v2[] is defined as:

\[ \sum_{i = 0}^{n-1} v1[i] \times v2[i] \]

The goal of this exercise is to parallelize the serial program using the omp parallel construct with the appropriate clauses. It is instructive to begin without using the omp parallel for directive and computing the endpoints of the iterations explicitly. To this aim, let \(P\) be the size of the OpenMP thread pool; partition the arrays into \(P\) blocks of approximately uniform size. Thread \(p\) (\(0 \leq p < P\)) computes the dot product my_p of the subvectors with indices \(\texttt{my_start}, \ldots, \texttt {my_end}-1\):

\[ \texttt{my_p}: = \sum_{i=\texttt{my_start}}^{\texttt{my_end}-1} v1[i] \times v2[i] \]

There are several ways to accumulate partial results. One possibility is to store the value computed by thread \(p\) on partial_p[p], where partial_p[] is an array of length \(P\). In this way each thread writes on different elements of partial_p[] and no race conditions are possible. After the parallel region completes, the master thread computes the final result by summing the content of partial_p[]. Be sure to handle the case where \(n\) is not an integer multiple of \(P\) correctly.

The solution above is instructive but tedious and inefficient. Unless there are specific reasons to do so, in practice you should use the omp parallel for directive with the reduction() clause, and let the compiler take care of everything.

To compile:

    gcc -fopenmp -std=c99 -Wall -Wpedantic omp-dot.c -o omp-dot

To execute:

    ./omp-dot [n]

For example, if you want to use two OpenMP threads:

    OMP_NUM_THREADS=2 ./omp-dot 1000000

File

• omp-dot.c