Bridging the Gap Between OpenMP and Task-Based Runtime Systems for the Fast Multipole Method

Abstract

With the advent of complex modern architectures, the low-level paradigms long considered sufficient to build High Performance Computing (HPC) numerical codes have met their limits. Achieving efficiency, ensuring portability, while preserving programming tractability on such hardware prompted the HPC community to design new, higher level paradigms while relying on runtime systems to maintain performance. However, the common weakness of these projects is to deeply tie applications to specific expert-only runtime system APIs. The OpenMP specification, which aims at providing common parallel programming means for shared-memory platforms, appears as a good candidate to address this issue thanks to the latest task-based constructs introduced in its revision 4.0. The goal of this paper is to assess the effectiveness and limits of this support for designing a high-performance numerical library, ScalFMM, implementing the fast multipole method (FMM) that we have deeply re-designed with respect to the most advanced features provided by OpenMP 4. We show that OpenMP 4 allows for significant performance improvements over previous OpenMP revisions on recent multicore processors and that extensions to the 4.0 standard allow for strongly improving the performance, bridging the gap with the very high performance that was so far reserved to expert-only runtime system APIs.Index Terms-high performance computing, fast multipole method, runtime system, OpenMP, compiler, parallel programming model, priority, commutativity, multicore architecture ! Algorithm 5: tb-omp4#task#dep scheme with OPENMP 4.0 directives 1 function FMM(tree, kernel) 2 #pragma omp parallel 3 #pragma omp single 4 // Near-field 5 P2P_taskdep(tree, kernel); 18 foreach cell cl in tree.cells[level] do 19 #pragma omp task depend(inout:cl.multipole) \\ 20 depend(in:tree.getChildren(cl.mindex, level).multipole) 21 kernel.M2M(cl.multipole, tree.getChildren(cl.mindex, level).multipole); STARPU directives 1 function FMM(tree, kernel) 2 // Near-field 3 P2P_starpu(tree, kernel);

Impact study of data locality on task-based applications through the Heteroprio scheduler

“…If the edges represent a relation of precedence between the tasks, the resulting graph is a direct acyclic graph of tasks. However, this is not the case when an inter-tasks dependency relation is used, such as a mechanism to express that an operation is commutative (Agullo et al, 2017). In the paper, we consider graphs of the form G = (V, E) with a set of nodes V and a set of edges E. Considering t 1 ,t 2 ∈ V, there exists a relation (t 1 ,t 2 ) ∈ E-also written t 1 !…”

Parallelization of Hierarchical Matrix Algorithms for Electromagnetic Scattering Problems

“…This was before the depend clause was introduced, allowing dependencies between sibling tasks. OpenMP, Cilk and other models are compared for FMM in [66], OpenMP and Klang/StarPU are compared in [1], and different OpenMP implementations and task parallel runtimes are compared with a special focus on locking and synchronization in [4]. A common conclusion from these comparisons is that the commutative clause provided by most task parallel run-time systems is quite important for performance, and that this would be a useful upgrade of OpenMP tasks for the future.…”

On the Performance of Parallel Tasking Runtimes for an Irregular Fast Multipole Method Application

“…Making use of extra data-dependency constructs available in StarPU, Agullo et. al [12], found that performance could be improved over OpenMP.…”