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.

Retiming, algebraic and redundancy manipulation transformations are widely used in both the high level synthesis and the compilers fields. We present a new approach on how these powerful transformations can be applied to improve the performance of embedded systems, by optimizing their latency and throughput. A simple modification is sufficient to adapt both the Leiserson-Saxe retiming algorithm and the recently introduced ERB algorithm for the new task. We introduce a new negative retiming technique and the algorithm which coordinates this technique with both algebraic and redundancy manipulation techniques for latency optimization. The effectiveness of all discussed techniques is demonstrated on a set of "real-life" examples. Latency and throughput are improved by factors of 7.06 and 2.83 respectively, often with minimal or no additional hardware overhead.>