libieeep1788: A C#x002B;#x002B; Implementation of the IEEE interval standard P1788

摘要

In 2008 the IEEE interval standard working group P1788 has been founded to enlarge the acceptance of interval arithmetic. One of the main challenges for the working group was to cope with different approaches of interval arithmetic. Such as set based interval arithmetic or modal interval arithmetic, which have been developed during the last 50 years. For this reason a concept called flavors is defined by the standard. The concept specifies the behavior of the operations. Additionally, a so called decoration system is introduced to treat mathematical events like discontinuity or undefinedness of an expression for a given interval box. The C++ library libieeep1788 tries to implement all features of the tentative interval standard in a clear and straightforward manner. The main goal is to have a faithful reference implementation of the standard and not to use dubious optimizations and “hacks”. The main design concept of the library is to map the flavors concept one-to-one onto the implementation. To achieve this requirement the so called policy based class design is used. In this paper we will present the key concepts of the faithful C++ library libieeep1788 which will be accompanied by an overview of the preliminary IEEE P1788 interval standard.