Parallel for loop in openmp

You should make use of the OpenMP reduction clause for x and y:

#pragma omp parallel for reduction(+:x,y)
for (int j=0; j<n; j++) {

    double r=0.0;
    for (int i=0; i < m; i++){

        double rand_g1 = cos(i/double(m));
        double rand_g2 = sin(i/double(m));     

        x += rand_g1;
        y += rand_g2;
        r += sqrt(rand_g1*rand_g1 + rand_g2*rand_g2);
    }
    shifts[j] = r / m;
}

With reduction each thread accumulates its own partial sum in x and y and in the end all partial values are summed together in order to obtain the final values.

Serial version:
25.05s user 0.01s system 99% cpu 25.059 total
OpenMP version w/ OMP_NUM_THREADS=16:
24.76s user 0.02s system 1590% cpu 1.559 total

See – superlinear speed-up 🙂