Efficient run-time scheduling for parallelizing partially parallel loops

We propose an efficient run-time technique to find an optimal parallel execution schedule for partially parallel loops in which synchronizations between iterations are needed to ensure correct program semantics. For efficiency, we combine conventional mark phase and scheduler phase into a single parallel scheduler. The scheduler divides the loop iterations into several chunks then executes the iterations in one chunk in parallel. Our scheme not only runs fast but also achieves an optimal schedule. In addition, an atomic bit-vector operation is introduced to avoid global synchronization overhead and ensure the larger wavefront number is kept when the wavefront number of an iteration will be concurrently updated during scheduling.