Abstract
The quasi-Monte Carlo algorithms utilize deterministic low-discrepancy sequences in order to increase the rate of convergence of stochastic simulation algorithms. Such kinds of algorithms are widely applicable and consume large share of the computational time on advanced HPC systems. The recent advances in HPC are increasingly rely on the use of accelerators and other similar devices that improve the energy efficiency and offer better performance for certain type of computations. The Xeon Phi coprocessors combine efficient vector floating point computations with familiar operational and development environment. One potentially difficult part of the conversion of a Monte Carlo algorithm into a quasi-Monte Carlo one is the generation of the low-discrepancy sequences. On such specialized equipment as the Xeon Phi, the value of memory increases due to the presence of a large number of computational cores. In order to allow quasi-Monte Carlo algorithms to make use of hybrid OpenMP+MPI programming, we implemented generation routines that save both memory space and memory bandwidth, with the aim to widen the applicability of quasi-Monte Carlo algorithms in environments with an extremely large number of computational elements. We present our implementation and compare it with regular Monte Carlo using a popular pseudorandom number generator, demonstrating the applicability and advantages of our approach.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Atanassov, E.I.: A new efficient algorithm for generating the scrambled Sobol’ sequence. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds.) NMA 2002. LNCS, vol. 2542, pp. 83–90. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36487-0_8
Atanassov, E., Dimitrov, D., Ivanovska, S.: Efficient implementation of the Heston model using GPGPU. Monte Carlo Methods and Applications, De Gruyter, pp. 21–28 (2012). ISBN: 978-3-11-029358-6, ISSN: 0929-9629
Atanassov, E., Gurov, T., Karaivanova, A., Ivanovska, S., Durchova, M., Georgiev, D., Dimitrov, D.: Tuning for Scalability on Hybrid HPC Cluster. Mathematics in Industry, pp. 64–77. Cambridge Scholar Publishing, Cambridge (2014)
Atanassov, E., Karaivanova, A., Ivanovska, S.: Tuning the generation of Sobol sequence with owen scrambling. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 459–466. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12535-5_54
Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)
Meswani, M., Carrington, L., Unat, D., Snavely, A., Baden, S., Poole, S.: Modeling and predicting application performance on hardware accelerators. Int. J. High Perform. Comput. (2012)
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. Society for Industrial and Applied Mathematics, Philadelphia (1992)
Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. Zh. Vych. Mat. Mat. Fiz. 16, 1332–1337 (1976, in Russian). U.S.S.R Comput. Maths. Math. Phys. 16, 236–242 (1976, in English)
Sobol, I., Asotsky, D., Kreinin, A., Kucherenko, S.: Construction and comparison of high-dimensional Sobol generators. Wilmott J. 56, 64–79 (2011)
Intel Math Kernel Library (MKL). http://software.intel.com/en-us/articles/intel-math-kernel-library-documentation
Acknowledgments
This work was supported by the National Science Fund of Bulgaria under Grant #DFNI-I02/8 and by the European Commission under H2020 project VI-SEEM (Contract Number 675121).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Atanassov, E., Gurov, T., Ivanovska, S., Karaivanova, A., Simchev, T. (2018). On the Parallel Implementation of Quasi-Monte Carlo Algorithms. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-73441-5_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73440-8
Online ISBN: 978-3-319-73441-5
eBook Packages: Computer ScienceComputer Science (R0)