An overview of C-XSC as a tool for interval arithmetic and its application in computing verified uncertain probabilistic models under Dempster–Shafer theory

Abstract

Interval arithmetic can be a useful tool in soft computing. However, working with intervals requires specialized algorithms and appropriate data structures. In this paper, we give an overview of the C++ library C-XSC, which provides many useful data types and functions for (verified) scientific computing, with a special focus on interval arithmetic. We describe its basic features and focus especially on some recent new features that significantly broaden the range of uses of C-XSC, such as dot products in K-fold double precision, sparse data types and BLAS support. In a second section, we describe an application of C-XSC in soft computing in the form of an interface between C-XSC and MATLAB for the DSI-Toolbox, which combines Dempster---Shafer theory to model uncertain data with verified interval arithmetic. For some applications, utilizing C-XSC in MATLAB (or as a standalone) can be more effective than the widely used INTLAB extension for MATLAB, due to the lack of interpretation overhead. As an example, we use C-XSC for the normalization function in the DSI-Toolbox and compare the results and performance to those provided by INTLAB. Using C-XSC in MATLAB also extends the functionality of MATLAB/INTLAB. As an example, the interval error function of C-XSC (this function is not provided by INTLAB) is utilized via a MEX-interface for the verified sampling of the cumulative normal distribution.