Multiplication by a Constant is Sublinear

Abstract— 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 Lef`evre’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.

• Type: Conference
• Year: 2007
• Where: ARITH
• Authors: Vassil S. Dimitrov, Laurent Imbert, Andrew Zakaluzny
• Keywords: Applied Computing, ARITH 2007, Constant Integer Multiplication, Constant Multiplication, DBNS Recoding Scheme