Multiplication by a Constant is Sublinear

Vassil Dimitrov Laurent Imbert 1 Andrew Zakaluzny
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This paper explores the use of the double-base number system (DBNS) for constant integer multiplication. The DBNS recoding scheme represents integers – in this case constants – in a multiple-radix way in the hope of minimizing the number of additions to be performed during constant multiplication. On the theoretical side, we propose a formal proof which shows that our recoding technique diminishes the number of additions in a sublinear way. Therefore, we prove Lefèvre's conjecture that the multiplication by an integer constant is achievable in sublinear time. In a second part, we investigate various strategies and we provide numerical data showcasing the potential interest of our approach.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00158322
Contributor : Laurent Imbert <>
Submitted on : Thursday, June 28, 2007 - 3:09:22 PM
Last modification on : Tuesday, December 11, 2018 - 5:16:02 PM

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  • HAL Id : lirmm-00158322, version 1

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Vassil Dimitrov, Laurent Imbert, Andrew Zakaluzny. Multiplication by a Constant is Sublinear. ARITH-18: 18th IEEE Symposium on Computer Arithmetic, Jun 2007, Montpellier, France, pp.261-268. ⟨lirmm-00158322⟩

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