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Optimization of the Hardware Costs of Interpolation Converters for Calculations in the Logarithmic Number 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

The logarithmic number system (LNS) is an advanced alternative to the widely known in a computer technology representation of floating-point numbers. It provides greater accuracy and speed of computation with a comparable range of representation of numbers. However, the widespread use of LNS is prevented by the need to apply interpolation to convert numbers from the traditional format and back, and to perform addition/subtraction operations. Known solutions are oriented to interpolation by a first-order polynomial, which does not allow the use of double or quadruple precision due to exponential growth of hardware costs. The work is devoted to minimizing hardware costs by optimizing the order of the interpolation polynomial and the interpolation step for computations over numbers of different width. The results of the work can be used to develop arithmetic devices that operate with numbers in the LNS and are optimized for the level of hardware costs.

The work was supported by the Russian Science Foundation, grant N 17-71-10043.

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Authors and Affiliations

  1. Scientific Production Association Real-Time Software Complexes, Krasnoproletarskaya Street, 16, 127473, Moscow, Russia

    Ilya Osinin

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  1. Ilya Osinin
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Correspondence to Ilya Osinin .

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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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Osinin, I. (2019). Optimization of the Hardware Costs of Interpolation Converters for Calculations in the Logarithmic Number 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_9

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