C-XSC - A C++ Class Library for Extended Scientific Computing Documentation

2.5.1

• Overview
• Simple programming examples
• C++ Toolbox for Verified Computing
• Using C-XSC in a Multi-Threaded Environment
• Credits

Overview

The speed of digital Computers is ever increasing. While the emphasis in computing was traditionally on speed, more emphasis can now be put on accuracy and reliability of results. Numerical mathematics has devised algorithms which deliver highly accurate and automatically verified results by applying mathematical fixed-point theorems. This means that these computation carry their own accuracy control. However, their implementation requires suitable arithmetic support and powerful programming tools which are not generally available.

Different hardware solutions are available for Personal Computers, Workstations, Mainframes and Super Computers. In particular a vector arithmetic coprocessor for the PC has been developed in VLSI-technology. Language support is available on the basis of FORTRAN, PASCAL, and C (ACRITH-XSC, Fortran-XSC, PASCAL-XSC, and C- XSC). Problem-solving routines with automatic result verification have been developed for many standard problems of numerical analysis as for linear or nonlinear systems of equations, for differential and integral equations, etc. as well as for a large number of applications in the engineering and natural sciences.

Language eXtensions for Scientific Computation provide all features indispensable for modern numerical software development, such as

• Operator concept (user-defined operators)
• Overloading concept
• Module concept
• Dynamic arrays
• Controlled rounding
• Predefined arithmetic data types real, (extended real), complex, interval, complex interval, and corresponding vector and matrix types
• Predefined arithmetic operators of highest accuracy for the arithmetic data types
• Predefined elementary functions of highest accuracy for the arithmetic data types
• Data type dotprecision for the exact representation of dot products
• Library of mathematical problem-solving routines with automatic result verification and high accuracy

Simple programming examples

To learn how to use the C-XSC class library you can read the page Simple programming examples and follow the examples described there.

For more experienced users the C++ Toolbox for Verified Computing is the more interesting place. There you find much more sophisticated examples on how to use the C-XSC class library.

C++ Toolbox for Verified Computing

The C++ Toolbox for Verified Computing is the C++ edition of the Numerical Toolbox for Verified Computing. The programs of the original edition were written in PASCAL-XSC, a PASCAL eXtension for Scientific Computation.

The methods presented here are practical, reliable, and elegant. They are provided in theory, algorithmic descriptions, and implementations to solve a number of basic numerical problems in a reliable way.

Using C-XSC in a Multi-Threaded Environment

Since C-XSC is now nearly twenty years old, thread-safety has not been a focus in its development for a long time. In recent years, a lot of work has been invested into making C-XSC fit for high performance computing and the threadsafety of C-XSC has been vastly improved in the process.

More information can be found in:

Zimmer, M.: "Using C-XSC in a Multi-Threaded Environment" Preprint BUW-WRSWT 2011/2, Universität Wuppertal, 2011, http://www2.math.uni-wuppertal.de/wrswt/preprints/prep_11_2.pdf

Credits

The work on C-XSC started in 1990 at the Institute for Applied Mathematics (Prof. Kulisch), University of Karlsruhe. Many colleagues and scientists have directly and indirectly contributed to the realization of C-XSC. The authors would like to thank each of them for his or her cooperation. Special thanks go to U. Allendörfer, C. Baumhof, H. Berlejung, H. Bleher, H. Böhm, B. Bohl, G. Bohlender, F. Blomquist, K. Braune, H.H. Chen, D. Cordes, A. Davidenkoff, H.-C. Fischer, M. Grimmer, K. Grüner, R. Hammer, M. Hinz, M. Hocks, B. Höffgen, W. Hofschuster, P. Januscke, E. Kaucher, R. Kelch, R. Kirchner, R. Klatte, W. Klein, W. Krämer, U. Kulisch, C. Lawo, M. Metzger, W.L. Miranker, M. Neaga, M. Neher, D. Ratz, M. Rauch, S. Ritterbusch, S.M. Rump, R. Saier, D. Schiriaev, L. Schmidt, G. Schumacher, U. Storck, J. Suckfüll, F. Toussaint, C. Ullrich, W. Walter, S. Wedner, G. Werheit, A. Wiethoff, H.W. Wippermann, J. Wolff von Gudenberg and M. Zimmer.

C-XSC is an outcome of an ongoing collaboration of the Institute for Applied Mathematics (Prof. Kulisch), University of Karlsruhe and the Institute for Scientific Computing/Software Engineering (Prof. Krämer), University of Wuppertal. For the latest news and up to date software contact http://www.math.uni-wuppertal.de/~xsc/ .

Thanks to the referees for valuable comments and suggestions.

Date:

June 2011

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