A Formal Method for Optimal High-Level Casting of Heterogeneous Fixed-Point Adders and Subtractors

Fixed-point arithmetic datapaths with heterogeneous scaling and wordlengths are commonplace in resource, latency, or power constrained designs. This paper describes and proves correct a formal method for accurate high-level casting of optimal adders and subtractors. The proposed approach allows for an early accurate estimation of resource usage which is then available for high-level decision-taking in the design flow. As a result, decoupling between high-level and low-level synthesis is achieved. Results concerning the impact of the approach on resource estimates and a discussion on the wide applicability of the method are presented.