RN-codes : algorithmes d'addition, de multiplication et d'élévation au carré

Jean-Michel Muller 1 Jean-Luc Beuchat 1, 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : A property of the original Booth recoding is that the non-zero digit following --1 is necessarily -- 1 and vice versa.This allows to prove that truncating the Booth recoding of a number x is equivalent to rounding x to the nearest. P. Kornerup and J.-M. Mulleri nvestigated the positional,radix Beta, number systems sharing this rounding property and called them RN-codings.This research report is devoted to the study of addition,multiplication,and squaring algorithms for radix 2 RN-codings (i.e.Boothrecodings).We show tha tinteger arithmetic and logic units operations allow to add or multiply Booth recodings.We also describe algorithms taking advantage of the properties oft heoriginal Booth recoding to generate optimized hardware operators.
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Jean-Michel Muller, Jean-Luc Beuchat. RN-codes : algorithmes d'addition, de multiplication et d'élévation au carré. [Rapport de recherche] RR-5438, LIP RR-2004-60, INRIA, LIP. 2004, pp.17. ⟨inria-00070569⟩

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