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A Novel Cotransformation for LNS Subtraction

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Abstract

The Logarithmic Number System (LNS) can be considered a simplification of the Floating Point (FP) Number System that assumes the mantissa is always equal to one, and has a binary fixed-point exponent. LNS converts multiplication/division to a single addition/subtraction, which make LNS a very attractive choice for applications where these operations predominate, such as in some signal-processing algorithms. However, for wordlengths greater than 20 bits LNS becomes expensive because of the hardware-demanding LNS operations of addition and subtraction, which are typically important for most signal-processing algorithms. This paper gives an overview of the family of LNS subtraction algorithms called “Cotransformations,” and proposes a “Novel Cotransformation Combination” that offers improvements in terms of area and speed without sacrificing accuracy compared to previous methods. The hardware requirements of the proposed method are analyzed mathematically, and the results are verified by using synthesis and simulations.

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Acknowledgements

The authors would like to thank Nicolas Frantzen and Jesus Garcia for their contributions in the early stages of this work.

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Author notes

  1. Panagiotis D. Vouzis

    Present address: Department of Chemical Enginering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

Authors and Affiliations

  1. Department of Computer Science & Engineering, Lehigh University, Bethlehem, PA, 18015, USA

    Panagiotis D. Vouzis & Mark G. Arnold

  2. Université de Perpignan Via Domitia, 52 avenue Paul Alduy, F-66860, Perpignan Cedex, France

    Caroline Collange

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  1. Panagiotis D. Vouzis
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  2. Caroline Collange
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Correspondence to Panagiotis D. Vouzis.

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Vouzis, P.D., Collange, C. & Arnold, M.G. A Novel Cotransformation for LNS Subtraction. J Sign Process Syst 58, 29–40 (2010). https://doi.org/10.1007/s11265-008-0282-7

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  • DOI: https://doi.org/10.1007/s11265-008-0282-7

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