Multiplication by a Constant is Sublinear

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.