A variable RADIX-2ralgorithm for single constant multiplication
Ahmed Liacha, Abdelkrim K. Oudjida, Farid Ferguene, Jose Carlos Monteiro, Paulo F. Flores · 2017
In previous work, a fully predictable sub-linear runtime heuristic for the multiplication by a constant based on Radix-2rarithmetic using a fixed radix was developed, called RADIX-2r. In this paper, we introduce a new constant multiplication algorithm based also on Radix-2rarithmetic but considering a variable radix. The new version is named RADIX-2r-VAR. Using a variable radix allows to optimize the average number of additions in the constant multiplication since a larger search space is explored. The new RADIX-2r-VAR recoding requires an average of 4.4% and 2.2% less additions than RADIX-2rfor 24 and 32 bits, respectively. The RADIX-2r-VAR algorithm is combined with RADIX-2rfor more improvements of the average number of additions. An overall saving of 6.7% and 5.5% is obtained over RADIX-2rfor 24 and 32 bits, respectively.