Abstract
In this paper a new software library for multiple-precision (integer and floating-point) and extended-range computations is considered. The library is targeted at heterogeneous CPU-GPU architectures. The use of residue number system (RNS), enabling effective parallelization of arithmetic operations, lies in the basis of library multiple-precision modules. The paper deals with the supported number formats and the library features. An algorithm for the selection of an RNS moduli set for a given precision of computations are also presented.
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References
Albicocco, P., Cardarilli, G., Nannarelli, A., Re, M.: Twenty years of research on RNS for DSP: lessons learned and future perspectives. In: Proceedings of 14th International Symposium on Integrated Circuits (ISIC), Singapore, pp. 436–439, December 2014
Brent, R., Zimmermann, P.: Modern Computer Arithmetic. Cambridge University Press, New York (2010)
Brzeziński, D.W., Ostalczyk, P.: Numerical calculations accuracy comparison of the inverse Laplace transform algorithms for solutions of fractional order differential equations. Nonlinear Dyn. 84(1), 65–77 (2016)
Chang, C.H., Low, J.Y.S.: Simple, fast, and exact RNS scaler for the three-moduli set \(\{2^{n} - 1, 2^{n}, 2^{n} + 1\}\). IEEE Trans. Circ. Syst. I Regul. Pap. 58(11), 2686–2697 (2011)
Defour, D., de Dinechin, F.: Software carry-safe for fast multiple-precision algorithms. In: Proceedings of 1st International Congress of Mathematical Software, Beijing, China, pp. 29–39, August 2002
Esmaeildoust, M., Schinianakis, D., Javashi, H., Stouraitis, T., Navi, K.: Efficient RNS implementation of elliptic curve point multiplication over \(\rm {GF}(p)\). IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 21(8), 1545–1549 (2013)
Hauser, J.R.: Handling floating-point exceptions in numeric programs. ACM Trans. Program. Lang. Syst. 18(2), 139–174 (1996)
He, K., Zhou, X., Lin, Q.: High accuracy complete elliptic integrals for solving the Hertzian elliptical contact problems. Comput. Math. Appl. 73(1), 122–128 (2017)
Hemenway, B., Lu, S., Ostrovsky, R., Welser IV, W.: High-precision secure computation of satellite collision probabilities. In: Zikas, V., De Prisco, R. (eds.) SCN 2016. LNCS, vol. 9841, pp. 169–187. Springer, Cham (2016). doi:10.1007/978-3-319-44618-9_9
Isupov, K., Knyazkov, V.: Non-modular Computations in Residue Number Systems Using Interval Floating-Point Characteristics. Deposited in VINITI, No. 61-B2015 (2015). (in Russian)
Isupov, K., Knyazkov, V.: Parallel multiple-precision arithmetic based on residue number system. Program Syst. Theor. Appl. 7(1), 61–97 (2016). (in Russian)
Isupov, K., Knyazkov, V.: RNS-based data representation for handling multiple-precision integers on parallel architectures. In: Proceedings of the 2016 International Conference on Engineering and Telecommunication (EnT 2016), Moscow, pp. 76–79, November 2016
Isupov, K., Knyazkov, V., Kuvaev, A., Popov, M.: Development of high-precision arithmetic package for supercomputers with graphics processing units. Programmnaya Ingeneria 7(9), 387–394 (2016). (in Russian)
Isupov, K., Knyazkov, V., Kuvaev, A., Popov, M.: Parallel computation of normalized legendre polynomials using graphics processors. In: Voevodin, V. (ed.) Russian Supercomputing Days 2016. CCIS, vol. 687. Springer International Publishing, Cham (2017)
Mohan, P.V.A.: Residue Number Systems: Theory and Applications. Birkhäuser, Basel (2016)
Szabo, N.S., Tanaka, R.I.: Residue Arithmetic and its Application to Computer Technology. McGraw-Hill, New York (1967)
Tomczak, T.: Fast sign detection for RNS \(\{2^{n} - 1, 2^{n}, 2^{n} + 1\}\). IEEE Trans. Circ. Syst. I Regul. Pap. 55(6), 1502–1511 (2008)
Acknowledgement
This work is supported by the Russian Foundation for Basic Research (project no. 16-37-60003 mol_a_dk) and FASIE UMNIK grant.
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Isupov, K., Kuvaev, A., Popov, M., Zaviyalov, A. (2017). Multiple-Precision Residue-Based Arithmetic Library for Parallel CPU-GPU Architectures: Data Types and Features. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2017. Lecture Notes in Computer Science(), vol 10421. Springer, Cham. https://doi.org/10.1007/978-3-319-62932-2_18
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DOI: https://doi.org/10.1007/978-3-319-62932-2_18
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