Design of table-based function evaluators with reduced memory size Using a bottom-up non-uniform segmentation method

Abstract

One category of table-based arithmetic function evaluators is to partition the input interval into uniform segments of equal width where each segment is approximated by a polynomial. This paper presents a non-uniform segmentation method in order to reduce table size that usually increases rapidly with respect to precision. Our approach employs a bottom-up approach that merges neighbouring uniform segments obtained in conventional piecewise polynomial interpolation. The proposed non-uniform segmentation scheme is applied to computing some elementary functions under different bit accuracies. Analytical comparison and experiential results show that the proposed method leads to smaller table size compared with other previous methods due to the efficient segmentation algorithm.