Static analyses of the precision of floating-point operations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2126 LNCS, Issue , 2001, Pages 234-259

  Goubault, Eric ^a  

^a DIF   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTING; APPLICATION PROGRAMS; DIGITAL ARITHMETIC; PROGRAM DEBUGGING; SEMANTICS;

ABSTRACT INTERPRETATIONS; BASIC OPERATION; EXTRACT INFORMATIONS; FLOATING POINT NUMBERS; FLOATING POINT OPERATIONS; FLOATING POINT UNITS; ON-BOARD SYSTEMS; RELATED WORKS;

STATIC ANALYSIS;

EID: 84890027616     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-47764-0_14     Document Type: Conference Paper

References (62)

1. Y. Ameur, P. Cros, J-J. Falcon, and A. Gomez. An application of abstract interpretation to floating-point arithmetic. In Proceedings of the W orkshop on Static Analysis, 1992.
2. A. Arnold. Systèmes de transitions finis et sémantique des processus communicants. Masson, 1992.
3. G. A. Baker. Essentials of Padé approximants. Academic Press, New York, 1975.
4. J.-D. Boissonat, F. Cazals, F. Da, O. Devillers, S. Pion, F. Rebufat, M. Teillaud, and M. Yvinec. Programming with CGAL: The example of triangulations. In Proceedings of the Conference on Computational Geometry (SCG'99), pages 421-422, New York, N.Y., June 13-16 1999. ACM Press.
5. A. F. Beardon. Iteration of Rational Functions. Graduate Texts in Mathematics. Springer-Verlag, 1991.
6. J. C. Bajard, D. Michelucci, J. M. Moreau, and J. M. Muller, editors. Real Numbers and Computers - Les Nombres réels et l'Ordinateur, 1995.
7. F. Bourdoncle. Interprocedural abstract interpretation of block structured languages with nested procedures, aliasing and recursivity. In PLILP'90, Volume 456 of LNCS, pages 307-323. Springer-Verlag, 1990.
8. F. Bourdoncle. Abstract interpretation by dynamic partitioning. Journal of Functional Programming, 2(4): 407-435, 1992.
9. F. Bourdoncle. Efficient chaotic iteration strategies with widenings. Lecture Notes in Computer Science, 735, 1993.
10. P. Cousot and R. Cousot. Abstract interpretation frameworks. Journal of Logic and Computation, 2(4): 511-547, 1992.
11. P. Cousot and R. Cousot. Comparing the Galois connection and widening/narrowing approaches to abstract interpretation, invited paper. In M. Bruynooghe and M. Wirsing, editors, Proceedings of the International Workshop Programming Language Implementation and Logic Programming, PLILP '92, Leuven, Belgium, 13-17 August 1992, Lecture Notes in Computer Science 631, pages 269-295. Springer-Verlag, Berlin, Germany, 1992.
12. F. Chaitin-Chatelin. Le calcul sur ordinateur à précision finie, théorie et eat at de l'art. Technical Report TR/PA/94/05, CERFACS, 1994.
13. F. Chaitin-Chatelin and V. Frayss. Lectures on Finite Precision Computations. SIAM, 1996.
14. F. Chaitin-Chatelin and E. Traviesas. Precise, a toolbox for assessing the quality of numerical methods and software. In 16th IMACS World Congress, 2000.
15. P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of a program. In Conference Record of the Fifth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 84-97, Tucson, Arizona, 1978. ACM Press, New York, NY.
16. J. M. Chesneaux. L'Arithmétique Stochastique et le Logiciel CADNA. Habilitation diriger des recherches, Université Pierre et Marie Curie, Paris, France, November 1995.
17. C. W. Clenshaw. Rational approximations for special functions. In D. J. Evans, editor, Software for Numerical Mathematics. Academic Press, New York, 1974.
18. J. M. Chesneaux and J. Vignes. Sur la robustesse de la méthode CESTAC. Comptes Rendus de l'Académie des Sciences, Paris, 307(1): 855-860, 1988.
19. J. M. Chesneaux and J. Vignes. Les fondements de l'arithmétique stochastique. Comptes-Rendus de l'Académie des Sciences, Paris, 1(315): 1435-1440, 1992.
20. M. Daumas and J. M. Muller, editors. Qualité des Calculs sur Ordinateur. Masson, 1997.
21. A. Edalat. Domains for Computation in Mathematics, Physics and Exact Real Arithmetic. Bulletin of Symbolic Logic, 3(4): 401-452, 1997.
22. A. Edalat and P. J. Potts. Exact real computer arithmetic. Technical report, Department of Computing Technical Report DOC 97/9, Imperial College, 1997.
23. A. Edalat and P. Snderhauf. A Domain-theoretic Approach to Real Number Computation. Theoretical Computer Science, 210: 73-98, 1998.
24. E. Goubault, D. Guilbaud, A. Pacalet, B. Starynkévitch, and F. Védrine. A simple abstract interpreter for threat detection and test case generation. In Proceedings of WAPATV'01 (ICSE'01), May 2001.
25. D. I. Good and R. L. London. Computer interval arithmetic: Definition and proof of correct implementation. Journal of the Association for Computing Machinery, 17(4): 603-612, October 1970.
26. D. Goldberg. What every computer-scientist should know about computer arithmetic. Computing Surveys, 1991.
27. P. Granger. Improving the results of static analyses of programs by local decreasing iterations. Lecture Notes in Computer Science, 652, 1992.
28. A. Griewank. Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation. SIAM, 2000.
29. J. F. Hart, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. G. Thacher, and C. Witzgall. Computer Approximations. Wiley, New York, 1968.
30. N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 1996.
31. W. Kahan. The improbability of probabilistic error analyses for numerical computations. Technical report, University of Berkeley, 1991.
32. W. Kahan. Lecture notes on the status of IEEE standard 754 for binary floating-point arithmetic. Technical report, Berkeley University, 1996.
33. M. Karr. Affine relationships between variables of a program. Acta Informatica, (6): 133-151, 1976.
34. W. Krandick and J. R. Johnson. Efficient multiprecision floating point multiplication with optimal directional rounding. In E. E. Swartzlander, M.J. Irwin, and J. Jullien, editors, Proceedings of the 11th IEEE Symposium on Computer Arithmetic, pages 228-233, Windsor, Canada, June 1993. IEEE Computer Society Press, Los Alamitos, CA.
35. S. Kla. Calcul parallèle et en ligne des fonctions arithmétiques. PhD thesis, Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France, February 1993.
36. P. Kornerup and D. W. Matula. Finite-precision rational arithmetic: an arithmetic unit. IEEE Transactions on Computers, C-32: 378-388, 1983.
37. P. Kornerup and D. W. Matula. Finite precision lexicographic continued fraction number systems. In Proceedings of the 7th IEEE Symposium on Computer Arithmetic, Urbana, USA, 1985. IEEE Computer Society Press, Los Alamitos, CA.
38. Reprinted in E. E. Swartzlander, Computer Arithmetic, Vol. 2, IEEE Computer Society Press Tutorial, Los Alamitos, CA, 1990.
39. P. Kornerup and D. W. Matula. An on-line arithmetic unit for bit-pipelined rational arithmetic. Journal of Parallel and distributed Computing, Special Issue on Parallelism in Computer Arithmetic (5), 1988.
40. D. Knuth. The Art of Computer Programming, Volume 2. Addison Wesley, Reading, MA, 1973.
41. V. Lefevre, J.M. Muller, and A. Tisserand. Toward correctly rounded transcendentals. IEEE Transactions on Computers, 47(11), 1998.
42. P. Langlois and F. Nativel. Improving automatic reduction of round-off errors. In IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Volume 2, 1997.
43. M. Martel. Semantics of floating point operations with error understanding. Technical report, CEA, submitted, May 2001.
44. D. Monniaux. Abstract interpretation of probabilistic semantics. In Seventh International Static Analysis Symposium (SAS'00), number 1824 in Lecture Notes in Computer Science. Springer-Verlag, 2000.
45. D. Monniaux. An abstract Monte-Carlo method for the analysis of probabilistic programs (extended abstract). In 28th Symposium on Principles of Programming Languages (POPL '01). Association for Computer Machinery, 2001.
46. R. E. Moore. Methods and Applications of Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1979.
47. P. J. Potts and A. Edalat. A new representation of exact real numbers. Electronic Notes in Computer Science, 6, 1998.
48. P. J. Potts, A. Edalat, and H. M. Escardó. Semantics of exact real arithmetic. In Procs of Logic in Computer Science. IEEE Computer Society Press, 1997.
49. G. Plotkin. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus, 1981.
50. M. La Porte and J. Vignes. Error analysis in computing. In Information Processing 74. North-Holland, 1974.
51. N. Regal. Petite analyse en nombres flottants. Technical Report DTA/LETI/DEIN/SLA/99-055, CEA, 1999.
52. J. E. Robertson and K. S. Trivedi. The status of investigations into computer hardware design based on the use of continued fractions. IEEE Transactions on Computers, C-22: 555-560, 1973.
53. C. W. Schelin. Calculator function approximation. American Mathematical Monthly, 90(5), May 1983.
54. M. Scott. Fast rounding in multiprecision floating-slash arithmetic. IEEE Transactions on Computers, 38: 1049-1052, 1989.
55. R. B. Seidensticker. Continued fractions for high-speed and high-accuracy computer arithmetic. In Proceedings of the 6th IEEE Sym posium on Computer Arithmetic, Aarhus, Denmark, 1983. IEEE Computer Society Press, Los Alamitos, CA.
56. J. Vignes and R. Alt. An efficient stochastic method for round-off error analysis. In Miranker Willard and Toupin, editors, Accurate Scientific Computations, Lecture notes in Computer Science 235. Springer-Verlag, 1985.
57. M. Vincius, A. Andrade, J. L. D. Comba, and J. Stolfi. Affine arithmetic. In INTERVAL'94, March 1994.
58. J. Vignes. New methods for evaluating the validity of mathematical software. Math. Comp. Simul. IMACS, 20: 227-249, 1978.
59. J. Vignes. Contrôle et estimation stochastique des arrondis de calcul. AFCET Interfaces, 54: 3-10, 1987.
60. J. Vignes. A stochastic arithmetic for reliable scientific computation. Math. Comp. Simul., 35: 233-261, 1993.
61. J. Vignes. A survey of the CESTAC method. In Proceedings of Real Numbers and Computer Conference, 1996.
62. J. E. Vuillemin. Exact real computer arithmetic with continued fractions. IEEE Transactions on Computers, 39(8), 1990.