A detailed complexity model for multiple constant multiplication and an algorithm to minimize the complexity

Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work, we consider the number of full and half adder cells required to realize those additions, and a novel complexity measure is proposed. The proposed complexity measure can be utilized for all types of constant operations based on shifts, additions and subtractions. Based on the proposed complexity measure a novel MCM algorithm is presented. Simulations show that compared with previous algorithms, the proposed MCM algorithm have a similar number of additions while the number of full adder cells are significantly reduced.