Because this question is highly viewed I decided to add a bit a OpenMP background to help those visiting it
The #pragma omp parallel creates a parallel region with a team of threads, where each thread executes the entire block of code that the parallel region encloses.
From the OpenMP 5.1 one can read a more formal description :
When a thread encounters a parallel construct, a team of threads is
created to execute the parallel region (..). The
thread that encountered the parallel construct becomes the primary
thread of the new team, with a thread number of zero for the duration
of the new parallel region. All threads in the new team, including the
primary thread, execute the region. Once the team is created, the
number of threads in the team remains constant for the duration of
that parallel region.
The #pragma omp parallel for creates a parallel region (as described before), and to the threads of that region the iterations of the loop that it encloses will be assigned, using the default chunk size, and the default schedule which is typically static. Bear in mind, however, that the default schedule might differ among different concrete implementation of the OpenMP standard.
From the OpenMP 5.1 you can read a more formal description :
The worksharing-loop construct specifies that the iterations of one or
more associated loops will be executed in parallel by threads in the
team in the context of their implicit tasks. The iterations are
distributed across threads that already exist in the team that is
executing the parallel region to which the worksharing-loop region
binds.
Moreover,
The parallel loop construct is a shortcut for specifying a parallel
construct containing a loop construct with one or more associated
loops and no other statements.
Or informally, #pragma omp parallel for is a combination of the constructor #pragma omp parallel with #pragma omp for. In your case, this would mean that:
#pragma omp parallel for
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;
}
A team of threads will be created, and to each of those threads will be assigned chunks of the iterations of the outermost loop.
To make it more illustrative, with 4 threads the #pragma omp parallel for with a chunk_size=1 and a static schedule would result in something like:
Code-wise the loop would be transformed to something logically similar to:
for(int i=omp_get_thread_num(); i < n; i+=omp_get_num_threads())
{
c[i]=a[i]+b[i];
}
where omp_get_thread_num()
The omp_get_thread_num routine returns the thread number, within the
current team, of the calling thread.
and omp_get_num_threads()
Returns the number of threads in the current team. In a sequential
section of the program omp_get_num_threads returns 1.
or in other words, for(int i = THREAD_ID; i < n; i += TOTAL_THREADS). With THREAD_ID ranging from 0 to TOTAL_THREADS - 1, and TOTAL_THREADS representing the total number of threads of the team created on the parallel region.
Armed with this knowledge, and looking at your code, one can see that you have a race-condition on the updates of the variables 'x' and 'y'. Those variables are shared among threads and update inside the parallel region, namely:
x += rand_g1;
y += rand_g2;
To solve this race-condition you can use OpenMP' reduction clause:
Specifies that one or more variables that are private to each thread
are the subject of a reduction operation at the end of the parallel
region.
Informally, the reduction clause, will create for each thread a private copy of the variables 'x' and 'y', and at the end of the parallel region perform the summation among all those 'x' and 'y' variables into the original 'x' and 'y' variables from the initial thread.
#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;
}
