Multiple Constant Multiplication Algorithm for High-Speed and Low-Power Design

In this brief, Radix-2
^r
arithmetic is applied to the multiple constant multiplication (MCM) problem. Given a number M of nonnegative constants with a bit length N, we determine the analytic formulas for the maximum number of additions, the average number of additions, and the maximum number of cascaded additions forming the critical path. We get the first proven bounds known so far for MCM. In addition to being fully predictable with respect to the problem size (M, N), the RADIX-2
^r
MCM heuristic exhibits sublinear runtime complexity O(M × N/r), where r is a function of (M, N). For high-complexity problems, it is most likely the only one that is even feasible to run. Another merit is that it has the shortest adder depth in comparison with the best published MCM algorithms.