IJPAM: Volume 45, No. 2 (2008)

APPROXIMATE RATIONAL ARITHMETICS AND
ARBITRARY PRECISION COMPUTATIONS
FOR UNIVERSAL ALGORITHMS

G.L. Litvinov$^1$, A.Ya. Rodionov$^2$, A.V. Tchourkin$^3$
$^1$Department of Mathematics
Independent University of Moscow
Bolshoi Vlasievskii Per., 11, Moscow, 119002, RUSSIA
e-mail: glitvinov@gmail.com
$^2$Research Institute for Nuclear Physics
Moscow State University
Vorobjevy Gory, Moscow, 119992, RUSSIA
e-mail: ayarodionov@yahoo.com
$^3$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