Taylor approximation for symmetric level-index arithmetic processing
Xunyang Shen, PETER R. TURNER · IMA Journal of Numerical Analysis · 2006
Symmetric level-index arithmetic was introduced to overcome the problems of overflow and underflow in the floating-point system. The purpose of this paper is to improve the algorithm performance of SLI arithmetic by introducing an approximation scheme using Taylor's expansion. Following a brief summary of the SLI system and its algorithm for addition/subtraction, the deduction and analysis of Taylor approximation are presented. Also some results from numerical experiments and timing comparisons on possible implementations show the advantage of the approximation method.