A Comparison of High-Level Programming Choices for Incomplete Sparse Factorization Across Different Architectures

Abstract

All many-core systems require fine-grained shared memory parallelism, however the most efficient way to extract such parallelism is far from trivial. Fine-grained parallel algorithms face various performance trade-offs related to tasking, accesses to global data-structures, and use of shared cache. While programming models provide high level abstractions, such as data and task parallelism, algorithmic choices still remain open on how to best implement irregular algorithms, such as sparse factorizations, while taking into account the trade-offs mentioned above. In this paper, we compare these performance trade-offs for task and data parallelism on different hardware architectures such as Intel Sandy Bridge, Intel Xeon Phi, and IBM Power8. We do this by comparing the scaling of a new task-parallel incomplete sparse Cholesky factorization called Tacho and a new data-parallel incomplete sparse LU factorization called Basker. Both solvers utilize Kokkos programming model and were developed within the ShyLU package of Trilinos. Using these two codes we demonstrate how high-level programming changes affect performance and overhead costs on multiple multi/many-core systems. We find that Kokkos is able to provide comparable performance with both parallel_for and task/futures on traditional x86 multicores. However, the choice of which high-level abstraction to use on many-core systems depends on both the architectures and input matrices.