How does the `omp ordered` clause ensure sequential execution within a parallel loop in OpenMP?

Understanding the omp ordered Clause

OpenMP's omp ordered clause coordinates thread execution to ensure sequential execution of a code section within a parallel loop. Multiple threads execute concurrently until they encounter the ordered region, where they synchronize and proceed in the same order as they would in a serial loop.

Consider this code:

<code class="cpp">vector<int> v;

#pragma omp parallel for ordered schedule(dynamic, anyChunkSizeGreaterThan1)
for (int i = 0; i < n; ++i){
    ...
    ...
    ...
#pragma omp ordered
    v.push_back(i);
}</code>

This code ensures that the vector v is filled with an ordered list containing n elements.

Thread Synchronization

When threads encounter the omp ordered block, they must wait for the thread executing the lowest possible iteration. This synchronization is critical because it maintains the order of execution specified in the serial loop. The OpenMP runtime library typically assigns the lowest iteration to the first thread that becomes ready to execute.

Influence of Scheduling

While the ordered clause can be used with both dynamic and static scheduling, dynamic scheduling is recommended. With static scheduling, the threads' iterations are defined predetermined, which can lead to thread idling if the lowest iteration is assigned to a thread that has already completed its iterations.

With dynamic scheduling, iterations are assigned at runtime, reducing the likelihood of thread idling. However, it introduces some overhead, so it should only be considered if the time spent on dynamic scheduling is negligible compared to the execution time of the ordered region.

Ordered Execution with Multiple Threads

To illustrate the ordered execution, consider a scenario with three threads and nine iterations, with each thread responsible for three iterations. A static schedule with a chunk size of 1 would result in the following execution timeline:

tid  List of     Timeline
     iterations
0    0,3,6       ==o==o==o
1    1,4,7       ==.o==o==o
2    2,5,8       ==..o==o==o

With dynamic scheduling, the execution timeline would be randomized, as the list of iterations assigned to each thread would not be deterministic.

By using dynamic scheduling with the ordered clause, you achieve concurrency while maintaining the correct execution order within a parallel loop.

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