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Development of Quadruple Precision Arithmetic Toolbox QuPAT on Scilab

  • Tsubasa Saito
  • Emiko Ishiwata
  • Hidehiko Hasegawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6017)

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.

Keywords

quadruple precision arithmetic mixed precision Scilab 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tsubasa Saito
    • 1
  • Emiko Ishiwata
    • 2
  • Hidehiko Hasegawa
    • 3
  1. 1.Graduate School of ScienceTokyo University of ScienceJapan
  2. 2.Tokyo University of ScienceJapan
  3. 3.University of TsukubaJapan

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