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Efficient CORDIC-Based Sine and Cosine Implementation for a Dataflow Architecture

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Cyber Security Cryptography and Machine Learning (CSCML 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12161))

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Abstract

A program in a dataflow architecture is represented as a dataflow graph. The dataflow nodes in the graph represent operations to be executed on data. The edges represent a data value being transformed by a dataflow node. Such an architecture can allow exploitation of parallelism, code sharing, and out-of-order execution. The dataflow nodes include operations from a small set of operators: logical operations, switching, addition/subtraction, and multiplication. There is no arithmetic logic unit nor a floating-point unit. As a result, elementary operations for integer, and in particular floating-point, arithmetic are emulated in software. Therefore, when a more advanced functionality such as trigonometric functions is required, we find that the commonly used implementations are inefficient. The inefficiency results in an over-increased dataflow graph that directly translates to wasted area on the silicon, resulting in increased power consumption and lower throughput. Volder proposed the CORDIC algorithm for trigonometric functions, expressed in terms of basic rotations. In this work, we present a correctly-rounded and efficient implementation of the CORDIC algorithm for the dataflow architecture.

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Notes

  1. 1.

    The significand is sometimes called the mantissa, but the use of the term mantissa is discouraged and should be used in the context of logarithms.

  2. 2.

    Faithful rounding has a maximum error of one ulp, and is not defined by IEEE-754. It is mentioned for being a less precise rounding mode to emphasize the high precision requirement.

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Acknowledgments

We thank Shachar Lovett for his valuable input; John Gustafson for his comments. We thank Laura Ferguson for her assistance.

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  1. NextSilicon, Tel-Aviv, Israel

    Daniel Khankin, Elad Raz & Ilan Tayari

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  1. Daniel Khankin
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  2. Elad Raz
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  3. Ilan Tayari
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Correspondence to Daniel Khankin .

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Editors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, Be'er Sheva, Israel

    Shlomi Dolev

  2. School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

  3. Tata Consultancy Services, Chennai, Tamil Nadu, India

    Sachin Lodha

  4. Department of Computer Science, Ben-Gurion University of the Negev, Be'er Sheva, Israel

    Gera Weiss

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Khankin, D., Raz, E., Tayari, I. (2020). Efficient CORDIC-Based Sine and Cosine Implementation for a Dataflow Architecture. In: Dolev, S., Kolesnikov, V., Lodha, S., Weiss, G. (eds) Cyber Security Cryptography and Machine Learning. CSCML 2020. Lecture Notes in Computer Science(), vol 12161. Springer, Cham. https://doi.org/10.1007/978-3-030-49785-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-49785-9_9

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