Modular Range Reduction

Marc Daumas (Lab. LIP, Ecole Normale Superieure de Lyon, France)

Christophe Mazenc (Lab. LIP, Ecole Normale Superieure de Lyon, France)

Xavier Merrheim (Lab. LIP, Ecole Normale Superieure de Lyon, France)

Jean-Michel Muller (CNRS, Lab. LIP, Ecole Normale Superieure de Lyon, France)

Abstract: A new range reduction algorithm, called ModularRange Reduction (MRR), briefly 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 (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. Web propose two possible architectures implementing this algorithm.

Keywords: Computer Arithmetic, Elementary Functions, Range Reduction

Categories: B.2, G.1.0