Representable correcting terms for possibly underflowing floating point operations

Proceedings - Symposium on Computer Arithmetic

Volumn , Issue , 2003, Pages 79-86

  Boldo, Sylvie ^a   Daumas, Marc ^a  

^a UNIV LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SYSTEMS; SET THEORY; THEOREM PROVING;

PROOF CHECKERS;

DIGITAL ARITHMETIC;

EID: 0042134525     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. R. L. Ashenhurst and N. Metropolis. Unnormalized floating point arithmetic. Journal of the ACM, 6(3):415-428, 1959.
2. G. Bohlender, W. Walter, P. Kornerup, and D. W. Matula. Semantics for exact floating point operations. In P. Kornerup and D. Matula, editors, Proceedings of the 10th Symposium on Computer Arithmetic, pages 22-26, Grenoble, France, 1991.
3. V. A. Carreño. Interpretation of IEEE-854 floating-point standard and definition in the HOL system. Technical Report Technical Memorandum 110189, NASA Langley Research Center, 1995.
4. W. J. Cody, R. Karpinski, et al. A proposed radix and word-length independent standard for floating point arithmetic. IEEE Micro, 4(4):86-100, 1984.
5. M. Daumas, L. Rideau, and L. Théry. A generic library of floating-point numbers and its application to exact computing. In 14th International Conference on Theorem Proving in Higher Order Logics, pages 169-184, Edinburgh, Scotland, 2001.
6. T. J. Dekker. A floating point technique for extending the available precision. Numerische Mathematik, 18(3):224-242, 1971.
7. J. Demmel. Underflow and the reliability of numerical software. SIAM Journal on Scientific and Statistical Computing, 5(4):887-919, 1984.
8. J. Harrison. A machine-checked theory of floating point arithmetic. In Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Théry, editors, 12th International Conference on Theorem Proving in Higher Order Logics, pages 113-130, Nice, France, 1999.
9. G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq proof assistant: a tutorial: version 7.2. Technical Report 256, Institut National de Recherche en Informatique et en Automatique, Le Chesnay, France, 2002.
10. C. Jacobi. Formal verification of a theory of IEEE founding. In 14th International Conference on Theorem Proving in Higher Order Logics, pages 239-254, Edinburgh, Scotland, 2001. supplemental proceedings.
11. W. Kahan. Further remarks on reducing truncation errors. Communications of the ACM, 8(1):40, 1965.
12. A. H. Karp and P. Markstein. High precision division and square root. ACM Transactions on Mathematical Software, 23(4)561-589, 1997.
13. S. Linnainmaa. Software for doubled precision floating point computations. ACM Transactions on Mathematical Software, 7(3):272-283, 1981.
14. P. Markstein, IA-64 and elementary functions: speed and precision. Prentice Hall, 2000.
15. P. S. Miner. Defining the IEEE-854 floating-point standard in PVS. Technical Report Technical Memorandum 110167, NASA Langley Research Center, 1995.
16. O. Møller. Quasi double-precision in floating point addition. BIT, 5(1):37-50, 1965.
17. J. Rushby and F. von Henke. Formal verification of algorithms for critical systems. In Proceedings of the Conference on Software for Critical Systems, pages 1-15, New Orleans, Louisiana, 1991.
18. D. M. Russinoff. A mechanically checked proof of IEEE compliance of the floating point multiplication, division and square root algorithms of the AMD-K7 processor. LMS Journal of Computation and Mathematics, 1:148-200, 1998.
19. J. R. Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. In Discrete and Computational Geometry, volume 18, pages 305-363, 1997.
20. P. H. Sterbenz. Floating point computation. Prentice Hall, 1974.
21. D. Stevenson et al. An American national standard: IEEE standard for binary floating point arithmetic. ACM SIGPLAN Notices, 22(2):9-25, 1987.