Lower Bound Analysis and Perturbation of Critical Path for Area-Time Efficient Multiple Constant Multiplications

Abstract

In this paper, a precise systematic delay model is proposed for the analysis and estimation of critical path delay of multiple constant multiplication (MCM) blocks. For the first time in literature, the mathematical derivation of lower bound of critical path delay of MCM blocks is presented and necessary conditions for achieving the lower bound of critical path delay are discussed. It is shown that the lower bound of critical path delay of MCMs is significantly smaller than that achieved by existing MCM algorithms. An improved genetic algorithm-based approach, with a heuristic algorithm to generate the initial population, is proposed to search for low complexity MCM solutions with the lower bound of critical path delay. This is the first time that design algorithms with gate-level delay control is proposed. Moreover, it is shown that using the information of lower bound of critical path delay, perturbation of timing can be applied to tradeoff the lower bound critical path delay against hardware complexity. It is shown that area-time efficient design of MCM blocks can be obtained by using the proposed techniques.