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A Modular-Positional Computation Technique for Multiple-Precision Floating-Point Arithmetic

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Parallel Computing Technologies (PaCT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9251))

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Abstract

Floating-point machine precision is often not sufficient to correctly solve large scientific and engineering problems. Moreover, computation time is a critical parameter here. Therefore, any research aimed at developing high-speed methods for multiple-precision arithmetic is of great immediate interest. This paper deals with a new technique of multiple-precision computations, based on the use of modular-positional floating-point format for representation of numbers. In this format, the significands are represented in residue number system (RNS), thus enabling high-speed processing of the significands with possible parallelization by RNS modules. Number exponents and signs are represented in the binary number system. The interval-positional characteristic method is used to increase the speed of executing complex non-modular operations in RNS. Algorithms for rounding off and aligning the exponents of numbers in modular-positional format are presented. The structure and features of a new multiple-precision library are given. Some results of an experimental study on the efficiency of this library are also presented.

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Acknowledgement

The reported study was supported by RFBR, research project No. 14-07-31075 mol_a.

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Authors and Affiliations

  1. Department of Electronic Computing Machines, Vyatka State University, Kirov, 610000, Russia

    Konstantin Isupov & Vladimir Knyazkov

Authors
  1. Konstantin Isupov
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  2. Vladimir Knyazkov
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Correspondence to Konstantin Isupov .

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Editors and Affiliations

  1. Russian Academy of Sciences, Novosibirsk, Russia

    Victor Malyshkin

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Isupov, K., Knyazkov, V. (2015). A Modular-Positional Computation Technique for Multiple-Precision Floating-Point Arithmetic. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_5

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  • DOI: https://doi.org/10.1007/978-3-319-21909-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21908-0

  • Online ISBN: 978-3-319-21909-7

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