Critical Path Minimization Using Retiming and Algebraic Speed-Up

The power of retiming is often limited by the underlying topology of a computational structure. We combine the power of retiming with a complete set of algebraic transformations in an iterative improvement framework, where retiming and algebraic speed-up algorithms are successively applied, so that the latter enables the former. The key part of the approach is a new algebraic speed-up algorithm being used for the first time in high-level synthesis for transformations of algebraic expressions so that an arbitrary set of input arrival times and output required times are satisfied. Since the new method moves delays forward only and retiming is done locally and very infrequently, it also always calculates the new initial state efficiently. The proposed approach has yielded results better or equal to the best previously published on all benchmark examples and on several novel real-life examples.