Reliable Integration of Exact and Approximated Arithmetic with Three-Valued Logic in Python⋆

Abstract. The error-ranges of exact rational numbers and intervals can be guaranteed even during the arithmetic operations whereas we cannot rely on the error-ranges of floating-point numbers. In this paper, we propose a novel number system, where the exact rational numbers are strictly separated from inexact floating point numbers and carefully in-tegrated with the inexact numbers. A three-valued logic is also shipped with our number system to appropriately deal with uncertainties due to the inexactness. A prototype implementation of our number system in Python is demonstrated.