Abstract
In this brief, $\mbox{Radix}\mbox{-}2^r$ 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 $\mbox{RADIX}\mbox{-}2^r$ MCM heuristic exhibits sublinear runtime complexity $O(M \times N/r)$ , 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IEEE Transactions on Circuits and Systems II: Express Briefs
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
