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On Parallel Addition and Multiplication via Symmetric Ternary Numeral System

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Recent Research in Control Engineering and Decision Making (ICIT 2019)

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 199))

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Abstract

This article is concerned with ternary logic application. Usage of ternary numeral system is recommended, particularly of symmetric ternary numeral system, as implementing arithmetic operations in ternary allows reducing roundoff errors, accumulated during finite-precision computation. A shift is suggested towards ternary computational machines. Ternary computations basis is given; addition and multiplication algorithms are discussed in classic and adapted versions, the latter is suggested as to develop a parallel implementation. Particular effects are highlighted which allow computing these operations in parallel mode, several examples illustrate the algorithms suggested. The resulting time and acceleration gain is discussed basing on data aggregated by means of an implementation in Haskell. Basing on experimental data, multithreaded implementation is recommended in order to accelerate addition and multiplication operations modelling. This research justifies the prospect of application of ternary co-processors for more precise computation.

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Author information

Authors and Affiliations

  1. BMSTU, 2-ya Baumanskaya ul. 5/1, 105005, Moscow, Russia

    Iurii V. Stroganov, Liliya Volkova & Igor V. Rudakov

Authors
  1. Iurii V. Stroganov
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  2. Liliya Volkova
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  3. Igor V. Rudakov
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Corresponding author

Correspondence to Iurii V. Stroganov .

Editor information

Editors and Affiliations

  1. Institute of Applied Information Technologies and Communication, Yuri Gagarin State Technical University of Saratov, Saratov, Russia

    Olga Dolinina

  2. Institute of Applied Information Technologies and Communication, Yuri Gagarin State Technical University of Saratov, Saratov, Russia

    Alexander Brovko

  3. Institute of Applied Information Technologies and Communication, Yuri Gagarin State Technical University of Saratov, Saratov, Russia

    Vitaly Pechenkin

  4. Institute of Applied Information Technologies and Communication, Yuri Gagarin State Technical University of Saratov, Saratov, Russia

    Alexey Lvov

  5. Department of Automation, Novosibirsk State Technical University, Novosibirsk, Russia

    Vadim Zhmud

  6. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Stroganov, I.V., Volkova, L., Rudakov, I.V. (2019). On Parallel Addition and Multiplication via Symmetric Ternary Numeral System. In: Dolinina, O., Brovko, A., Pechenkin, V., Lvov, A., Zhmud, V., Kreinovich, V. (eds) Recent Research in Control Engineering and Decision Making. ICIT 2019. Studies in Systems, Decision and Control, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-030-12072-6_39

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