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Complex Square Root with Operand Prescaling

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Abstract

We propose a radix-r digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation of digit selection. Moreover, the use of digit recurrence approach allows correct rounding of the result if needed. The algorithm, compatible with the complex division presented in Ercegovac and Muller (“Complex Division with Prescaling of the Operands,” in Proc. Application-Specific Systems, Architectures, and Processors (ASAP’03), The Hague, The Netherlands, June 24–26, 2003), and its design are described. We also give rough estimates of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.

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Authors and Affiliations

  1. Computer Science Department, University of California at Los Angeles, 4732 Boelter Hall, Los Angeles, CA, 90095, USA

    Miloš D. Ercegovac

  2. CNRS-Laboratoire CNRS-ENSL-INRIA-UCBL LIP Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    Jean-Michel Muller

Authors
  1. Miloš D. Ercegovac
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  2. Jean-Michel Muller
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Correspondence to Miloš D. Ercegovac.

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Ercegovac, M.D., Muller, JM. Complex Square Root with Operand Prescaling. J VLSI Sign Process Syst Sign Im 49, 19–30 (2007). https://doi.org/10.1007/s11265-006-0029-2

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  • DOI: https://doi.org/10.1007/s11265-006-0029-2

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