IJPAM: Volume 45, No. 2 (2008)
ARBITRARY PRECISION COMPUTATIONS
FOR UNIVERSAL ALGORITHMS
Department of Mathematics
Independent University of Moscow
Bolshoi Vlasievskii Per., 11, Moscow, 119002, RUSSIA
e-mail: glitvinov@gmail.com
Research Institute for Nuclear Physics
Moscow State University
Vorobjevy Gory, Moscow, 119992, RUSSIA
e-mail: ayarodionov@yahoo.com
Department of Physics
Moscow State University
Vorobjevy Gory, Moscow, 119992, RUSSIA
e-mail: churandr@mail.ru
Abstract.We will describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments are given in order to compare efficiency and accuracy of different types of approximate arithmetics and rounding procedures. Relations with universal algorithms and generic programming are briefly discussed.
Received: February 12, 2008
AMS Subject Classification: 11Y65, 65G50, 68Q25, 68Q65
Key Words and Phrases: approximate rational arithmetic, continued fractions, round-off errors, multiple and arbitrary precision computations, universal algorithms
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 2