Analysis of range and precision for fixed-point linear arithmetic circuits with feedbacks

Analysis of range and precision is always an important task for high level synthesis and verification. Although several researches have been dedicated to these two problems, in the case of linear fixed-point arithmetic circuits with feedbacks such as an Infinite Impulse Response (IIR) filter, conventional approaches are either constituting major overestimations or cannot handle arbitrary order feedback circuits. In this paper we focus on this problem and propose two efficient heuristics for range and precision analysis of such circuits, when the input and error bounds are given. The methods can be used for efficient integer and fractional bit-width allocation in the optimization flow. Moreover, for the purpose of module reusability and matching, verification algorithms have been proposed. Experimental results prove robust computations of range and precision.