Revisiting bitwidth optimizations

This paper revisits the classical bitwidth optimization problem for fixed-point designs. Our approach also starts from static analysis (range analysis and precision analysis) techniques. We first point out that AA-based precision analysis, which is widely used in many previous works, are not correctly applied for some corner cases. We propose to use interval coefficients to model the sensitivity (the mathematic form is similar to classical generalized interval arithmetic) to correct those issues. Based on the analysis, we use a convex optimization problem to optimize the area costs. In the formulation, we also allow different bitwidths for the multiple uses of the same signal. We get an additional 2% to 3% area reduction compared with previous AA-based analysis and optimizations. We also conduct some optimality study to see how much the gap between the current methods and the possible optimal point is.