Radix-2r Arithmetic for Multiplication by a Constant.

Abdelkrim K. Oudjida (1) , Nicolas Chaillet (2)

1 CDTA - Centre de Développement des Technologies Avancées
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

In this paper, radix-2r arithmetic is explored to minimize the number of additions in the multiplication by a constant. We provide the formal proof that for an N-bit constant, the maximum number of additions using radix-2r is lower than Dimitrov's estimated upper-bound (2.N/log(N)) using double base number system (DBNS). In comparison to canonical signed digit (CSD) and DBNS, the new radix-2r recoding requires an average of 23.12% and 3.07% less additions for 64-bit constant, respectively.

Domaines: Automatique / Robotique

Abdelkrim K. Oudjida, Nicolas Chaillet. Radix-2r Arithmetic for Multiplication by a Constant.. IEEE Transactions on Circuits and Systems II: Express Briefs, 2014, 61, pp.349-353. ⟨10.1109/TCSII.2014.2312799⟩. ⟨hal-01002468⟩