Some Steps into Verification of Exact Real Arithmetic

  • Norbert Th. Müller
  • Christian Uhrhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7226)

Abstract

The mathematical concept of real numbers is much richer than the double precision numbers widely used as their implementation on a computer. The field of ‘exact real arithmetic’ tries to combine the elegance and correctness of the mathematical theories with the speed of double precision hardware, as far as possible. In this paper, we describe an ongoing approach using the specification language ACSL, the tool suite Frama-C (with why and jessie) and the proof assistant Coq to verify central aspects of the iRRAM software package, which is known to be a fast C++ implementation of ‘exact’ reals numbers.

Keywords

Real Number Double Precision Interval Arithmetic Runtime Environment Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Bau08]
    Bauer, A.: Efficient computation with Dedekind reals. In: 5th International Conference on Computability and Complexity in Analysis, CCA 2008, Hagen, Germany, August 21-24 (2008)Google Scholar
  2. [BK08]
    Bauer, A., Kavkler, I.: Implementing real numbers with rz. Electron. Notes Theor. Comput. Sci. 202, 365–384 (2008)MathSciNetCrossRefGoogle Scholar
  3. [BHW07]
    Brattka, V., Hertling, P., Weihrauch, K.: A Tutorial on Computable Analysis. In: Barry Cooper, S., Löwe, B., Sorbi, A. (eds.) New Computational Paradigms: Changing Conceptions of What is Computable, pp. 425–491. Springer, New York (2008)Google Scholar
  4. [Lam07]
    Lambov, B.: Reallib: An efficient implementation of exact real arithmetic. Mathematical Structures in Computer Science 17(1), 81–98 (2007)MathSciNetMATHCrossRefGoogle Scholar
  5. [Les08]
    Lester, D.R.: The world’s shortest correct exact real arithmetic program? In: Proc. 8th Conference on Real Numbers and Computers, pp. 103–112 (2008)Google Scholar
  6. [MPMU04]
    Marché, C., Paulin-Mohring, C., Urbain, X.: The krakatoa tool for certification of java/javacard programs annotated in jml. J. Log. Algebr. Program. 58(1-2), 89–106 (2004)MATHCrossRefGoogle Scholar
  7. [Mue01]
    Müller, N.T.: The iRRAM: Exact Arithmetic in C++. In: Blank, J., Brattka, V., Hertling, P. (eds.) CCA 2000. LNCS, vol. 2064, pp. 222–252. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. [OS10]
    O’Connor, R., Spitters, B.: A computer-verified monadic functional implementation of the integral. Theor. Comput. Sci. 411(37), 3386–3402 (2010)MathSciNetMATHCrossRefGoogle Scholar
  9. [We00]
    Weihrauch, K.: Computable analysis: An introduction. Springer-Verlag New York, Inc. (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Norbert Th. Müller
    • 1
  • Christian Uhrhan
    • 2
  1. 1.Abteilung Informatik, FB IVUniversität TrierGermany
  2. 2.Faculty IVUniversität SiegenGermany

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