Multiplication by a Constant is Sublinear
Vassil S. Dimitrov, Laurent Imbert, Andrew Zakaluzny · Proceedings/Proceedings - Symposium on Computer Arithmetic · 2007
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 Lefevre'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.