Skip to main content
SpringerLink
Log in

Floating point verification in HOL

  • Conference paper
  • First Online:
Higher Order Logic Theorem Proving and Its Applications (TPHOLs 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 971))

Included in the following conference series:

Abstract

Floating-point verification is a very interesting application area for theorem provers. HOL is a general-purpose prover which is equipped with an extensive and rigorous theory of real analysis. We explain how it can be used in floating point verification, illustrating our remarks with complete verifications of simple square-root and (natural) logarithm algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alan Baker. Transcendental Number Theory. Cambridge University Press, 1975.

    Google Scholar 

  2. C. T. Fike. Computer Evaluation of Mathematical Functions. Series in Automatic Computation. Prentice-Hall, 1968.

    Google Scholar 

  3. David Goldberg. What every computer scientist should know about floating point arithmetic. ACM Computing Surveys, 23:5–48, 1991.

    Google Scholar 

  4. John Harrison. Constructing the real numbers in HOL. Formal Methods in System Design, 5:35–59, 1994.

    Google Scholar 

  5. IEEE. Standard for binary floating point arithmetic. ANSI/IEEE Standard 754-1985, The Institute of Electrical and Electronic Engineers, Inc., 345 East 47th Street, New York, NY 10017, USA, 1985.

    Google Scholar 

  6. Tim Leonard. The HOL numeral library. Distributed with HOL system, 1993.

    Google Scholar 

  7. F. Lindemann. über die Zahl π. Mathematische Annalen, 120:213–225, 1882.

    Google Scholar 

  8. Valérie Ménissier-Morain. Arithmétique exacte, conception, algorithmique et performances d'une implémentation informatique en précision arbitraire. Thèse, Université Paris 7, December 1994.

    Google Scholar 

  9. John O'Leary, Miriam Leeser, Jason Hickey, and Mark Aagaard. Non-restoring integer square root: A case study in design by principled optimization. In T. Kropf and R. Kumar, editors, Proceedings of the Second International Conference on Theorem Provers in Circuit Design (TPCD94): Theory, Practice and Experience, volume 901 of Lecture Notes in Computer Science, pages 52–71, Bad Herrenalb (Black Forest), Germany, 1994. Springer-Verlag.

    Google Scholar 

  10. Vaughan R. Pratt. Anatomy of the pentium bug. In ?, editor, Proceedings of the 5th International Joint Conference on the theory and practice of software development (TAPSOFT'95), volume 915 of Lecture Notes in Computer Science, pages 97–107, Aarhus, Denmark, 1995. Springer-Verlag.

    Google Scholar 

  11. E. Ya. Remez. Sur le calcul effectif des polynomes d'approximation. Comptes Rendus de l'Académie des Sciences, pages 337–340, 1934.

    Google Scholar 

  12. A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society (2), 42:230–265, 1936.

    Google Scholar 

  13. J. Volder. The CORDIC trigonometric computing technique. IRE Transactions on Electronic Computers, 8:330–334, 1959.

    Google Scholar 

  14. J. S. Walther. A unified algorithm for elementary functions. In Proceedings of the AFIPS Spring Joint Computer Conference, pages 379–385, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, New Museums Site Pembroke Street, CB2 3QG, Cambridge, England

    John Harrison

Authors
  1. John Harrison
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

E. Thomas Schubert Philip J. Windley James Alves-Foss

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Harrison, J. (1995). Floating point verification in HOL. In: Thomas Schubert, E., Windley, P.J., Alves-Foss, J. (eds) Higher Order Logic Theorem Proving and Its Applications. TPHOLs 1995. Lecture Notes in Computer Science, vol 971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60275-5_65

Download citation

  • DOI: https://doi.org/10.1007/3-540-60275-5_65

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60275-0

  • Online ISBN: 978-3-540-44784-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation