Development of quadruple precision arithmetic toolbox QuPAT on Scilab

Abstract

When floating point arithmetic is used in numerical computation, cancellation of significant digits, round-off errors and information loss cannot be avoided. In some cases it becomes necessary to use multiple precision arithmetic; however some operations of this arithmetic are difficult to implement within conventional computing environments. In this paper we consider implementation of a quadruple precision arithmetic environment QuPAT (Quadruple Precision Arithmetic Toolbox) using the interactive numerical software package Scilab as a toolbox. Based on Double-Double (DD) arithmetic, QuPAT uses only a combination of double precision arithmetic operations. QuPAT has three main characteristics: (1) the same operator is used for both double and quadruple precision arithmetic; (2) both double and quadruple precision arithmetic can be used at the same time, and also mixed precision arithmetic is available; (3) QuPAT is independent of which hardware and operating systems are used. Finally we show the effectiveness of QuPAT in the case of analyzing a convergence property of the GCR(m) method for a system of linear equations. © 2010 Springer-Verlag Berlin Heidelberg.