article

FILIB++, a fast interval library supporting containment computations

Authors:

German Tischler,

Jürgen Wolff Von Gudenberg,

Werner Hofschuster,

Walter KrämerAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 32, Issue 2

Pages 299 - 324

https://doi.org/10.1145/1141885.1141893

Published: 01 June 2006 Publication History

Abstract

filib++ is an extension of the interval library filib originally developed at the University of Karlsruhe. The most important aim of filib is the fast computation of guaranteed bounds for interval versions of a comprehensive set of elementary functions. filib++ extends this library in two aspects. First, it adds a second mode, the extended mode, that extends the exception-free computation mode (using special values to represent infinities and NaNs known from the IEEE floating-point standard 754) to intervals. In this mode, the so-called containment sets are computed to enclose the topological closure of a range of a function over an interval. Second, our new design uses templates and traits classes to obtain an efficient, easily extendable, and portable C++ library.

References

[1]

Alefeld, G. and Herzberger, J. 1983. Introduction to Interval Computations. Academic Press, New York, NY.

[2]

Chiriaev, D. and Walster, G. 1999. Interval arithmetic specification. www.mscs.mu.edu/&tilde;globsol/walster-papers.html.

[3]

Hammer, R., Hocks, M., Kulisch, U., and Ratz, D. 1995. C++ Toolbox for Verified Computing---Basic Numerical Problems. Springer-Verlag, Berlin, Germany.

[4]

Hofschuster, W. and Krämer, W. 1998a. FI_LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format. Preprint 98/7, Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Universität Karlsruhe. http://www.math.uni-wuppertal.de/wrswt/preprints/prep987.ps.

[5]

Hofschuster, W. and Krämer, W. 1998b. fi_lib sources. http://www.math.uni-wuppertal.de/WRSWT/software.html.

[6]

Hofschuster, W. and Krämer, W. 2004. C-XSC 2.0---a C++ class library for extended scientific computing. In Numerical Software with Result Verification, R. Alt, A. Frommer, B. Kearfott, and W. Luther, Eds. Springer Lecture Notes in Computer Science, Vol. 2991, 15--35.

[7]

Hofschuster, W., Krämer, W., Wedner, S., and Wiethoff, A. 2001. C-XSC 2.0---a C++ class library for extended scientific computing. Preprint 01/1, Wissenschaftliches Rechnen/Software Technologie, Universität Wuppertal. http://www.math.uni-wuppertal.de/wrswt/preprints/prep_01_1.ps.

[8]

Kearfott, R. B. 1996. Algorithm 763: Interval arithmetic, A fortran 90 module for an interval data type. ACM Trans. Math. Soft. 22, 4, 385--392.

[9]

Kearfott, R. B., Dawande, M., Du, K., and Hu, C. 1994. Algorithm 737: Intlib, a portable fortran-77 elementary function library. ACM Trans. Math. Soft. 20, 4 (Dec.) 447--459.

[10]

Kearfott, R. B. and Novoa, M. 1990. Algorithm 681: Intbis, a portable interval newton/bisection package. ACM Trans. Math. Soft. 16, 2 (June) 152--157.

[11]

Klatte, R., Kulisch, U., Lawo, C., Rauch, M., and Wiethoff, A. 1993. C-XSC---A C++ Class Library for Scientific Computing. Springer-Verlag, Berlin, Germany.

[12]

Knüppel, O. 1994. Profil/bias---a fast interval library. Computing 53, 277--287.

[13]

Krämer, W. 2002. Advanced software tools for validated computing. In Proceedings of the 31st Spring Conference of the Union of Bulgarian Mathematicians. Union of Bulgarian Mathematicians, Borovets, Bulgaria, 344--355.

[14]

Krämer, W. and Wolff von Gudenberg, J. 2001. Scientific Computing, Validated Numerics, Interval Methods. Kluwer Academic/Plenum Publishers, New York, NY.

[15]

Kulisch, U., Lohner, R., and Facius, A. 2001. Perspectives on Enclosure Methods. Springer-Verlag, Berlin, Germany.

[16]

Lerch, M., Tischler, G., Wolff von Gudenberg, J., Hofschuster, W., and Krämer, W. 2001. The interval library filib++ 2.0 - design, features and sample programs. Preprint BUGHW-WRSWT 2001/4, Universität Wuppertal.

[17]

Lerch, M. and Wolff von Gudenberg, J. 2000. fi_lib++ : Specification, implementation and test of a library for extended interval arithmetic. In RNC4 Proceedings. 111--123.

[18]

Myers, N. 1995. Traits: a new and useful template technique. C++ Report.

[19]

Rump, S., M. 1998. Intlab--interval laboratory. In Developments in Reliable Computing, T. Csendes, Ed. KluwerAcademic Publisher, New York, NY.

[20]

Rump, S. M. 1999. Fast and parallel interval arithmetic. Bit 39, 3 (Sept.) 534--554.

[21]

Stroustrup, B. 2000. The C++ Programming Language, Special Ed. Addison-Wesley, Reading, MA.

[22]

Sun Microsystems 2001. C++ Interval Arithmetic Programming Reference (Forte Developer 6 update 2). Sun Microsystems. http://www.sun.com/forte/cplusplus/interval/index.html.

[23]

Walster, G. et al. 2000a. The “simpl” closed interval system. Tech. rep., Sun Microsystems.

[24]

Walster, G. W. et al. 2000b. Extended real intervals and the topological closure of extended real numbers. Tech. rep., Sun Microsystems.

[25]

Walster, W. G., Hansen, E. R., and D. P. J. 2000. Extended real intervals and the topological closure of extended real relations. Tech. rep., Sun Microsystems.

[26]

Wolff von Gudenberg, J. 2000. Interval arithmetic and multimedia architectures. Tech. Rep. 265, Informatik, Universität Würzburg.

Cited By

Auer EAhrens A(2024)Verified Bit and Power Allocation for MIMO Systems: A Comparison of SVD Based Techniques With GMDActa Cybernetica10.14232/actacyb.30132326:4(775-798)Online publication date: 21-Mar-2024
https://doi.org/10.14232/actacyb.301323
Revol NBenet LFerranti LZhilin S(2023)Testing Interval Arithmetic Libraries, Including Their IEEE-1788 ComplianceParallel Processing and Applied Mathematics10.1007/978-3-031-30445-3_36(428-440)Online publication date: 27-Apr-2023
https://doi.org/10.1007/978-3-031-30445-3_36
Tang XFerguson ZSchneider TZorin DKamil SPanozzo D(2023)A Cross-Platform Benchmark for Interval Computation LibrariesParallel Processing and Applied Mathematics10.1007/978-3-031-30445-3_35(415-427)Online publication date: 27-Apr-2023
https://doi.org/10.1007/978-3-031-30445-3_35
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Index Terms

FILIB++, a fast interval library supporting containment computations
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Interval arithmetic
  2. Mathematical software

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Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 32, Issue 2

June 2006

205 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1141885

Issue’s Table of Contents

Copyright © 2006 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 2006

Published in TOMS Volume 32, Issue 2

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Cited By

Auer EAhrens A(2024)Verified Bit and Power Allocation for MIMO Systems: A Comparison of SVD Based Techniques With GMDActa Cybernetica10.14232/actacyb.30132326:4(775-798)Online publication date: 21-Mar-2024
https://doi.org/10.14232/actacyb.301323
Revol NBenet LFerranti LZhilin S(2023)Testing Interval Arithmetic Libraries, Including Their IEEE-1788 ComplianceParallel Processing and Applied Mathematics10.1007/978-3-031-30445-3_36(428-440)Online publication date: 27-Apr-2023
https://doi.org/10.1007/978-3-031-30445-3_36
Tang XFerguson ZSchneider TZorin DKamil SPanozzo D(2023)A Cross-Platform Benchmark for Interval Computation LibrariesParallel Processing and Applied Mathematics10.1007/978-3-031-30445-3_35(415-427)Online publication date: 27-Apr-2023
https://doi.org/10.1007/978-3-031-30445-3_35
Benet LFerranti LRevol N(2023)A framework to test interval arithmetic libraries and their IEEE 1788‐2015 complianceConcurrency and Computation: Practice and Experience10.1002/cpe.785636:1Online publication date: 31-Aug-2023
https://doi.org/10.1002/cpe.7856
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Fernández JG.-Tóth B(2022)Interval Tools in Branch-and-Bound Methods for Global OptimizationThe Palgrave Handbook of Operations Research10.1007/978-3-030-96935-6_8(237-267)Online publication date: 8-Jul-2022
https://doi.org/10.1007/978-3-030-96935-6_8
Ferguson ZLi MSchneider TGil-Ureta FLanglois TJiang CZorin DKaufman DPanozzo D(2021)Intersection-free rigid body dynamicsACM Transactions on Graphics10.1145/3450626.345980240:4(1-16)Online publication date: 19-Jul-2021
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Rivera JFranchetti FPüschel MLee J(2021)An interval compiler for sound floating-point computationsProceedings of the 2021 IEEE/ACM International Symposium on Code Generation and Optimization10.1109/CGO51591.2021.9370307(52-64)Online publication date: 27-Feb-2021
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Schmitteckert P(2019)Towards verified numerical renormalization group calculationsThe European Physical Journal Special Topics10.1140/epjst/e2018-800058-3Online publication date: 24-Jan-2019
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