Fixed-point Accuracy Analysis of Datapaths with Mixed CORDIC and Polynomial Computations

Fixed-point accuracy analysis of imprecise datapaths in terms of Maximum-Mismatch (MM) [1], or Mean-Square-Error (MSE) [14], w.r.t. a reference model is a challenging task. Typically, arithmetic circuits are represented with polynomials; however, for a variety of functions, including trigonometric, hyperbolic, logarithm, exponential, square root and division, Coordinate Rotation Digital Computer (CORDIC) units can result in more efficient implementations with better accuracy. This paper presents a novel approach to robustly analyze the fixed-point accuracy of an imprecise datapath, which may consist of a combination of polynomials and CORDIC units. The approach builds a global polynomial for the error of the whole datapath by converting the CORDIC units and their errors into the lowest possible order Taylor series. The previous work for almost accurate analysis of MM [1] and MSE [14, 15] in large datapaths can only handle polynomial computations.