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On Parallel Addition and Multiplication via Symmetric Ternary Numeral System

  • Iurii V. StroganovEmail author
  • Liliya Volkova
  • Igor V. Rudakov
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)

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.

Keywords

Ternary computation Ternary logic Symmetric ternary numeral system Arithmetic operations implementation Parallel algorithms 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BMSTUMoscowRussia

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