New evaluation scheme for software function approximation with non-uniform segmentation

Abstract

Modern applications embed complex mathematical processing based on composition of elementary functions. A good balance between approximation accuracy, and implementation cost, i.e. memory space requirement and computation time, is needed to design an efficient implementation. From this point of view, approaches working with polynomial approximation obtain results of a monitored accuracy with a moderate implementation cost. For software implementation in fixed-point processors, accurate results can be obtained if the segment on which the function is computed I is segmented accurately enough, to have an approximating polynomial on each segment. Non-uniform segmentation is required to limit the number of segments and then the implementation cost. The proposed recursive scheme exploits the trade-off between memory requirement and evaluation time. The method is illustrated with the function exp(−√(x)) on the segment [2−6; 25] and showed a mean speed-up ratio of 98.7 compared to the mathematical C standard library on the Digital Signal Processor C55x.