Approximate rational arithmetics and arbitrary precision computations
Grigori Litvinov, Anatoli Rodionov, Andrei Chourkin
TL;DR
An approximate rational arithmetic with round-off errors controlled by the user with results to compare efficiency and accuracy of different types of approximate arithmetics and rounding procedures.
Abstract
We 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.