Modular range reduction: A new algorithm for fast and accurate computation of the elementary functions

Abstract: A new range reduction algorithm, called Modular Range Reduction (MRR), brie y introduced by the authors in [Daumas et al. 1994] is deeply analyzed. It is used to reduce the arguments to exponential and trigonometric function algorithms to be within the small range for which the algorithms are valid. MRR reduces the arguments quickly and accurately. A fast hardwired implementation of MRR operates in time O(log ( n)), where n is the number of bits of the binary input value. For example, with MRR it becomes possible to compute the sine and cosine of a very large number accurately. We propose two possible architectures implementing this algorithm