Non-uniform Segmentation for Hardware Function Evaluation

This paper presents a method for evaluating functions in hardware based on polynomial approximation with non-uniform segments. The novel use of non-uniform segments enables us to approximate non-linear regions of a function particularly well. The appropriate segment address for a given function can be rapidly calculated in run time by a simple combinational circuit. Scaling factors are used to deal with large polynomial coefficients and to trade precision with range. Our function evaluator is based on first-order polynomials, and is suitable for applications requiring high performance with small area, at the expense of accuracy. The proposed method is illustrated using two functions, \(\sqrt{-\ln(x)}\) and cos(2 πx), which have been used in Gaussian noise generation.