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Short Division of Long Integers

David Harvey Paul Zimmermann 1 
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We consider the problem of short division --- division without remainder --- of multiple-precision integers. We present ready-to-be-implemented algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.
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Contributor : Paul Zimmermann Connect in order to contact the contributor
Submitted on : Thursday, July 28, 2011 - 1:16:13 PM
Last modification on : Saturday, June 25, 2022 - 7:42:28 PM

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David Harvey, Paul Zimmermann. Short Division of Long Integers. 20th IEEE Symposium on Computer Arithmetic (ARITH-20), Jul 2011, Tuebingen, Germany. pp.7-14, ⟨10.1109/ARITH.2011.11⟩. ⟨inria-00612232⟩



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