Abstract
The Sparse Matrix-Vector Multiplication (SpMV) is fundamental to a broad spectrum of scientific and engineering applications, such as many iterative numerical methods. The widely used Compressed Sparse Row (CSR) sparse matrix storage format was chosen to carry on this study for sustainability and reusability reasons.
We parallelized for Intel Many Integrated Core (MIC) architecture a vectorized SpMV kernel using MPI and OpenMP, both pure and hybrid versions of them. In comparison to pure models and vendor-supplied BLAS libraries across different mainstream architectures (CPU, GPU), the hybrid model exhibits a substantial improvement.
To further assess the behavior of hybrid model, we attribute the inadequacy of performances to vectorization rate, irregularity of non-zeros, and load balancing issue. A mathematical relationship between the first two factors and the performance is then proposed based on the experimental data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The average number of nonzero elements is defined as the quotient of total number of nonzero elements over the row dimension.
References
Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page (2013). http://www.mcs.anl.gov/petsc
Berrendorf, R., Nieken, G.: Performance characteristics for OpenMP constructs on different parallel computer architectures. Concurrency Pract. Exp. 12(12), 1261–1273 (2000)
Bull, J.M.: Measuring synchronisation and scheduling overheads in OpenMP. In: Proceedings of First European Workshop on OpenMP, pp. 99–105 (1999)
Cappello, F., Etiemble, D.: MPI versus MPI+OpenMP on IBM SP for the NAS benchmarks. In: Proceedings of the 2000 ACM/IEEE Conference on Supercomputing, Supercomputing 2000. IEEE Computer Society, Washington, DC (2000). http://dl.acm.org/citation.cfm?id=370049.370071
Chow, E., Hysom, D.: Assessing performance of hybrid MPI/OpenMP programs on SMP clusters. Technical report, Lawrence Livermore National Laboratory (2001)
Davis, T.A., Hu, Y.: The university of florida sparse matrix collection. ACM Trans. Math. Softw 38(1), 1:1–1:25 (2011). http://doi.acm.org/10.1145/2049662.2049663
Heroux, M., Bartlett, R., Hoekstra, V.H.R., Hu, J., Kolda, T., Lehoucq, R., Long, K., Pawlowski, R., Phipps, E., Salinger, A., Thornquist, H., Tuminaro, R., Willenbring, J., Williams, A.: An overview of trilinos. Technical report, SAND2003-2927, Sandia National Laboratories (2003)
Intel: Intel Xeon Phi Coprocessor System Software Developers Guide. Technical report (2012)
Kourtis, K., Goumas, G., Koziris, N.: Exploiting compression opportunities to improve SpMxV performance on shared memory systems. ACM Trans. Architec. Code Optim. 7(3), 16:1–16:31 (2010)
Liu, X., Smelyanskiy, M., Chow, E., Dubey, P.: Efficient sparse matrix-vector multiplication on x86-based many-core processors. In: Proceedings of the 27th International ACM Conference on International Conference on Supercomputing, ICS 2013, pp. 273–282. ACM, New York (2013). http://doi.acm.org/10.1145/2464996.2465013
Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)
Williams, S., Oliker, L., Vuduc, R., Shalf, J., Yelick, K., Demmel, J.: Optimization of sparse matrix-vector multiplication on emerging multicore platforms. In: Proceedings of the 2007 ACM/IEEE Conference on Supercomputing, SC 2007, pp. 38:1–38:12. ACM, New York (2007). http://doi.acm.org/10.1145/1362622.1362674
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ye, F., Calvin, C., Petiton, S.G. (2015). A Study of SpMV Implementation Using MPI and OpenMP on Intel Many-Core Architecture. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science -- VECPAR 2014. VECPAR 2014. Lecture Notes in Computer Science(), vol 8969. Springer, Cham. https://doi.org/10.1007/978-3-319-17353-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-17353-5_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17352-8
Online ISBN: 978-3-319-17353-5
eBook Packages: Computer ScienceComputer Science (R0)