×

Interval arithmetic using expression templates, template meta programming and the upcoming C++ standard. (English) Zbl 1238.65040

Summary: We discuss different realizations for an efficient interval arithmetic implementation using expression templates and template meta programming in C++. We improve the handling of the rounding mode switches using expression templates and show how the constructed expression trees can be combined with other features like automatic differentiation. For a further improvement of the run time performance we try to move as many functionality as possible to the compile time using template meta programming techniques. In addition we illustrate how an interval arithmetic implementation will profit from new features and keywords defined in the upcoming C++ standard.

MSC:

65G30 Interval and finite arithmetic
65Y04 Numerical algorithms for computer arithmetic, etc.
68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)
68W30 Symbolic computation and algebraic computation
65D25 Numerical differentiation
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Alexandrescu A (2001) Modern C++ design: generic programming and design patterns applied. Addison-Wesley Longman Publishing Co. Inc., Boston
[2] Aubert P, Di Césaré N, Pironneau O (2001) Automatic differentiation in C++ using expression templates and application to a flow control problem. Comput Vis. Sci. 3: 197–208 · Zbl 0966.68029
[3] Becker P (2011) Working Draft, Standard for Programming Language C++. Tech. Rep. N3242=11-0012, ISO/IEC JTC1/SC22/WG21
[4] Bendtsen C, Stauning O (1996) FADBAD, a flexible C++ package for automatic differentiation. Technical Report IMM–REP–1996–17, Department of Mathematical Modelling. Technical University of Denmark, Lyngby, Denmark
[5] Bischof CH, Bücker HM (2000) Computing derivatives of computer programs. In: Grotendorst J (ed) Modern methods and algorithms of quantum chemistry: proceedings, 2nd edn. NIC Series, vol 3, pp 315–327. NIC-Directors, Jülich
[6] Bischof CH, Roh L, Mauer A (1997) ADIC–An extensible automatic differentiation tool for ANSI-C. Softw Pract Exp 27(12): 1427–1456 · Zbl 05471765
[7] Boost Interval Arithmetic Library (2011). http://www.boost.org/doc/libs/1_46_1/libs/numeric/interval/doc/interval.htm
[8] Corliss GF, Griewank A (1993) Operator Overloading as an Enabling Technology for Automatic Differentiation. Tech. Rep. CRPC-TR93431, Center for Research on Parallel Computation. Rice University, Houston
[9] CRlibm-Correctly Rounded mathematical library (2011). http://lipforge.ens-lyon.fr/www/crlibm/
[10] Daramy-Loirat C, Defour D, de Dinechin F, Gallet M, Gast N, Quirin Lauter C, Muller JM (2009) CR-LIBM A library of correctly rounded elementary functions in double-precision. http://lipforge.ens-lyon.fr/frs/download.php/153/crlibm-1.0beta3.pdf
[11] Gil J, Gutterman Z (1998) Compile time symbolic derivation with C++ templates. In: Proceedings of the 4th conference on USENIX conference on object-oriented technologies and systems, vol 4, COOTS’98, pp 18–18. USENIX Association, Berkeley
[12] Gregor D, Järvi J, Powell G (2006) Variadic templates (revision 3). Tech. Rep. N2080=06-0150, ISO/IEC JTC1/SC22/WG21
[13] Griewank A, Juedes D, Utke J (1996) Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++. ACM Trans Math Softw 22(2): 131–167 · Zbl 0884.65015
[14] Hammer R, Ratz D, Kulisch U, Hocks M (1997) C++ Toolbox for Verified Computing I: Basic Numerical Problems. Springer-Verlag New York Inc., Secaucus · Zbl 0828.68041
[15] Hascoët L, Pascual V (2004) TAPENADE 2.1 user’s guide. Rapport technique 300, INRIA, Sophia Antipolis
[16] Järvi J, Stroustrup B, Reis GD (2004) Decltype and auto (revision 4). Tech. Rep. N1705=04-0145, ISO/IEC JTC1/SC22/WG21
[17] Lambov B (2008) Interval arithmetic using SSE-2. Lecture Notes in Computer Science, vol 5045, pp 102–113 · Zbl 1165.65339
[18] Lerch M, Tischler G, Wolff von Gudenberg J, Hofschuster W, Krämer W (2006) Filib++, a fast interval library supporting containment computations. ACM Trans Math Softw 32(2): 299–324 · Zbl 1365.65140
[19] Myers N (1995) A new and useful template technique: traits. C++ Report 7(5):32–35. Reprinted in Lippman SB (ed) 1996 C++ Gems. SIGS publications, Inc., New York, NY, USA
[20] Nehmeier M, Wolff von Gudenberg J (2011) filib++, Expression Templates and the Coming Interval Standard. Reliab Comput 15(4): 312–320
[21] Rall LB (1981) Automatic differentiation: techniques and applications. Lecture Notes in Computer Science, vol 120. Springer, Berlin · Zbl 0473.68025
[22] Veldhuizen T (1995) Expression templates. C++ Report 7(5):26–31. Reprinted in Lippman SB (ed) 1996 C++ Gems. SIGS publications, Inc., New York, NY, USA
[23] Veldhuizen T (1995) Using C++ template metaprograms. C++ Report 7(4):36–43. Reprinted in Lippman SB (ed) 1996 C++ Gems. SIGS publications, Inc., New York, NY, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.