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Accurate Floating Point Arithmetic through Hardware Error-Free Transformations

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Reconfigurable Computing: Architectures, Tools and Applications (ARC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6578))

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Abstract

This paper presents a hardware approach to performing accurate floating point addition and multiplication using the idea of error-free transformations. Specialized iterative algorithms are implemented for computing arbitrarily accurate sums and dot products. The results of a Xilinx Virtex 6 implementation are given, area and performance are compared against standard floating point units and it is shown that the time×area product can be improved by a factor of 4 and 6 over software error-free addition and multiplication. Furthermore, it is illustrated that a number of area and performance trade-offs can be made when calculating vector sums and dot products.

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References

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Author information

Authors and Affiliations

  1. Imperial College, London, UK

    Manouk V. Manoukian & George A. Constantinides

Authors
  1. Manouk V. Manoukian
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  2. George A. Constantinides
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Editor information

Editors and Affiliations

  1. FB 20 Informatik, Technische Universität Darmstadt, Hochschulstraße 10, 64289, Darmstadt, Germany

    Andreas Koch

  2. Intel Corp., 97006, Hillsboro, OR, USA

    Ram Krishnamurthy

  3. School of Electronics, Electrical Engineering and Computer Science, Institute of Electronics, Communications and Information Technology, Queen’s University of Belfast, Queen’s Road, BT3 9DT, Belfast, UK

    John McAllister  & Roger Woods  & 

  4. Department of Electrical and Computer Engineering, George Washington University, 801, 22nd Street NW, 20052, Washington, DC, USA

    Tarek El-Ghazawi

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© 2011 Springer-Verlag Berlin Heidelberg

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Manoukian, M.V., Constantinides, G.A. (2011). Accurate Floating Point Arithmetic through Hardware Error-Free Transformations. In: Koch, A., Krishnamurthy, R., McAllister, J., Woods, R., El-Ghazawi, T. (eds) Reconfigurable Computing: Architectures, Tools and Applications. ARC 2011. Lecture Notes in Computer Science, vol 6578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19475-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-19475-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19474-0

  • Online ISBN: 978-3-642-19475-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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