Abstract
The increased appreciation of interval analysis as a powerful tool for controlling roundoff errors and modelling
with uncertain data leads to a growing number of diverse interval software. Beside in some other aspects,
the available interval software differs with respect to the environment in which it operates and the provided
functionality. Some specific software tools are built on the top of other more general interval software but
there is no single environment supporting all (or most) of the available interval methods. On another side,
most recent interval applications require a combination of diverse methods. It is difficult for the endusers
to combine and manage the diversity of interval software tools, packages, and research codes, even the latter
being accessible. Two recent initiatives: [1], directed toward developing of a comprehensive fullfeatured library
of validated routines, and [3] intending to provide a general service framework for validated computing in
heterogeneous environment, reflect the realized necessity for an integration of the available methods and
software tools.
It is commonly understood that quality comprehensive libraries are not compiled by a single person or small
group of people over a short time [1]. Therefore, in this work we present an alternative approach based on
interval software interoperability.
While the simplest form of interoperability is the exchange of data files, we will focus on the ability to run
a particular routine executable in one environment from within another software environment, and viceversa,
via communication protocols. We discuss the motivation, advantages and some problems that may appear in
providing interoperability between the existing interval software.
Since the generalpurpose environments for scientific/technical computing like Matlab, Mathematica, Maple, etc.
have several features not attributable to the compiled languages from one side and on another side most problem
solving tools are developed in some compiled language for efficiency reasons, it is interesting to study
the possibilities for interoperability between these two kinds of interval supporting environments.
More specifically, we base our presentation on the interoperability between Mathematica [5] and external
CXSC programs [2] via MathLink communication protocol [4]. First, we discuss the portability and reliability
of interval arithmetic in Mathematica. Then, we present MathLink technology for building external
MathLinkcompatible programs. On the example of a CXSC function for solving parametric linear systems,
called from within a Mathematica session, we demonstrate some advantages of interval software interoperability.
Namely, expanded functionality for both environments, exchanging data without using intermediate files and
without any conversion but under dynamics and interactivity in the communication, symbolic manipulation interfaces
for the compiled language software that often make access to the external functionality from within Mathematica
more convenient even than from its own native environment. Once established, MathLink connection to external
interval libraries or problemsolving software opens up an array on new possibilities for the latter.
References:
[1] G. Corliss, R. B. Kearfott, N. Nedialkov, S. Smith: Towards an Interval Subroutine Library,
Workshop on Reliable Engineering Computing, Svannah, Georgia, USA, Feb. 2224, 2006.
[2] W. Hofschuster: CXSC: Highlights and new developments. In: Numerical Validation in Current Hardware
Architectures. Number 08021 Dagstuhl Seminar, Internationales Begegnungs und Forschungszentrum f"ur
Informatik, Schloss Dagstuhl, Germany, 2008.
[3] W. Luther, W. Kramer: Accurate Grid Computing, 12th GAMMIMACS Int. Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics (SCAN 2006), Duisburg, Sept. 2629, 2006.
[4] Ch. Miyaji, P. Abbot eds.: Mathlink: Network Programming with Mathematica, Cambridge Univ. Press, Cambridge, 2001.
[5] Wolfram Research Inc.: Mathematica, Version 5.2, Champaign, IL, 2005.
BibTeX  Entry
@InProceedings{popova:DSP:2008:1450,
author = {Evgenija D. Popova},
title = {On the Interoperability between Interval Software},
booktitle = {Numerical Validation in Current Hardware Architectures},
year = {2008},
editor = {Annie Cuyt and Walter Kr{\"a}mer and Wolfram Luther and Peter Markstein},
number = {08021},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1450},
annote = {Keywords: Software interoperability, interfacing, interval software, CXSC, MathLink, Mathematica}
}
Keywords: 

Software interoperability, interfacing, interval software, CXSC, MathLink, Mathematica 
Seminar: 

08021  Numerical Validation in Current Hardware Architectures 
Issue Date: 

2008 
Date of publication: 

22.04.2008 