Radix-2<sup>r</sup> Arithmetic for Multiplication by a Constant: Further Results and Improvements

Abstract

In a previous brief, we proposed a new sublinear-runtime recoding heuristic for the multiplication by a constant, accompanied by its upper bound complexity. In this brief, further results are provided, namely, the analytic expressions of the average number of additions and the maximum adder depth. Improvements to the proposed heuristic are considered as well, using a redundant recoding followed by a common-digit-elimination step.