Division of floating point expansions with an application to the computation of a determinant

Journal of Universal Computer Science

Volumn 5, Issue 6, 1999, Pages 323-338

  Daumas, Marc ^a   Finot, Claire ^a  

^a NONE

Author keywords

Computational geometry; Division; Exact arithmetic; Expansion; Floating point; Library; Multiple precision

Indexed keywords

EID: 0001453394     PISSN: 0958695X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. D. Berthelot and M. Daumas. A library for real numbers using Cauchy's embedded interval sequences. In International Conference on Interval Methods and Computer Aided Proofs in Science and Engineering, pages 23-24, Würzburg, Germany, 1996.
2. D. Berthelot and M. Daumas. Computing on sequences of embedded intervals. Reliable Computing, 3(3):219-227, 1997.
3. 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.
4. M. Daumas. Multiplications of floating point expansions. Research report 98-39, Laboratoire de l'Informatique du Parallélisme, Lyon, France, 1998.
5. M. Daumas. Multiplications of floating point expansions. In Proceedings of the 14th Symposium on Computer Arithmetic, Adelaide, Australia, 1999.
6. T. J. Dekker. A floating point technique for extending the available precision. Numerische Mathematik, 18(3):224-242, 1971.
7. D. Goldberg. What every computer scientist should know about floating point arithmetic. ACM Computing Surveys, 23(1):5-47, 1991.
8. D. Goldberg. Computer Architecture: A Quantitative Approach, chapter Computer Arithmetic, pages A1-A77. Morgan Kaufmann, 1996.
9. J. L. Hennessy and D. A. Patterson. Computer architecture: A quantitative approach. Morgan Kaufmann, 1996.
10. D. E. Knuth. The Art of Computer Programming: Seminumerical Algorithms. Addison-Wesley, 1981.
11. I. Koren. Computer Arithmetic Algorithms. Prentice Hall, 1993.
12. J.-M. Muller. Arithmétique des Ordinateurs. Masson, 1989.
13. D. M. Priest. Algorithms for arbitrary precision floating point arithmetic. In P. Kornerup and D. Matula, editors, Proceedings of the 10th Symposium on Computer Arithmetic, pages 132-144, Grenoble, France, 1991. IEEE Computer Society Press.
14. J. R. Shewchuk. Robust adaptative floating point geometric predicates. In Proceedings of the 12th Annual ACM Symposium on Computational Geometry, pages 141-150, Philadelphia, Pensylvania, 1996.
15. J. R. Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. In Discrete and Computational Geometry, volume 18, pages 305-363, 1997.
16. B. Shriver and B. Smith. The Anatomy of a High Performance Microprocessor, A Systems Perspective. IEEE Computer Society, 1998.
17. D. Stevenson et al. A proposed standard for binary floating point arithmetic. IEEE Computer, 14(3):51-62, 1981.
18. D. Stevenson et al. An american national standard: IEEE standard for binary floating point arithmetic. ACM SIGPLAN Notices, 22(2):9-25, 1987.