Multiplicative square root algorithms for FPGAs

Florent de Dinechin 1, 2 Mioara Joldes 1, 2 Bogdan Pasca 1, 2 Guillaume Revy 1, 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Most current square root implementations for FPGAs use a digit recurrence algorithm which is well suited to their LUT structure. However, recent computing-oriented FPGAs include embedded multipliers and RAM blocks which can also be used to implement quadratic convergence algorithms, very high radix digit recurrences, or polynomial approximation algorithms. The cost of these solutions is evaluated and compared, and a complete implementation of a polynomial approach is presented within the open-source FloPoCo framework. It allows a much shorter latency and a higher frequency than the classical approach. The cost of IEEE-compliant correct rounding using such approximation algorithms is shown to be very high, and faithful (last-bit accurate) operators are advocated in this case.
Mots-clés : Square-root FPGA
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Preprints, Working Papers, ...
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00475779
Contributor : Bogdan Pasca <>
Submitted on : Thursday, April 22, 2010 - 9:42:39 PM
Last modification on : Thursday, January 17, 2019 - 3:16:03 PM
Long-term archiving on : Monday, October 22, 2012 - 3:21:10 PM

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Florent de Dinechin, Mioara Joldes, Bogdan Pasca, Guillaume Revy. Multiplicative square root algorithms for FPGAs. 2010. ⟨ensl-00475779v1⟩

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