OpenMP reductions

Approximation of PI using #pragma omp reduction clause

h = 1.0 / n;
#pragma omp parallel for private(x) shared(n, h) reduction(+:area) 
for (i = 1; i <= n; i++)
{
  x = h * (i - 0.5);
  area += (4.0 / (1.0 + x*x));
}
pi = h * area;

In this example, each threads execute a subset of the iteration count. Each thread has its local private copy of area and at the end of the parallel region they all apply the addition operation (+) so as to generate the final value for area.

Approximation of PI using reductions based on #pragma omp critical

h = 1.0 / n;
#pragma omp parallel for private(x) shared(n, h, area) 
for (i = 1; i <= n; i++)
{
  x = h * (i - 0.5);
  #pragma omp critical
  {
    area += (4.0 / (1.0 + x*x));
  }
}
pi = h * area;

In this example, each threads execute a subset of the iteration count and they accumulate atomically into the shared variable area, which ensures that there are no lost updates.

Approximation of PI using reductions based on #pragma atomic

h = 1.0 / n;
#pragma omp parallel for private(x) shared(n, h, area) 
for (i = 1; i <= n; i++)
{
  x = h * (i - 0.5);
  #pragma atomic
  area += (4.0 / (1.0 + x*x));
}
pi = h * area;

In this example, each threads execute a subset of the iteration count and they accumulate atomically into the shared variable area, which ensures that there are no lost updates. We can use the #pragma atomic in here because the given operation (+=) can be done atomically, which simplifies the readability compared to the usage of the #pragma omp critical.

Approximation of PI hand-crafting the #pragma omp reduction

h = 1.0 / n;

#pragma omp parallel private(x) shared(n, h)
{
  double thread_area = 0;                      // Private / local variable

  #pragma omp for
  for (i = 1; i <= n; i++)
  {
    x = h * (i - 0.5);
    thread_area += (4.0 / (1.0 + x*x));
  }

  #pragma omp atomic                       // Applies the reduction manually
  area += thread_area;                     // All threads aggregate into area
}

pi = h * area;

The threads are spawned in the #pragma omp parallel. Each thread will have an independent/private thread_area that stores its partial addition. The following loop is distributed among threads using #pragma omp for. In this loop, each thread calculates its own thread_area and after this loop, the code sequentially aggregates the area atomically through #pragma omp atomic.