Abstract
This paper introduces a new framework for tackling constraints over the floating-point numbers. An important application area where such solvers are required is program analysis (e.g., structural test case generation, correctness proof of numeric operations). Albeit the floating-point numbers are a finite subset of the real numbers, classical CSP techniques are ineffective due to the huge size of the domains. Relations that hold over the real numbers may not hold over the floating-point numbers. Moreover, constraints that have no solutions over the reals may hold over the floats. Thus, interval-narrowing techniques, which are used in numeric CSP, cannot safely solve constraints systems over the floats. We analyse here the specific properties of the relations over the floats. A CSP over the floats is formally defined. We show how local-consistency filtering algorithms used in interval solvers can be adapted to achieve a safe pruning of such CSP. Finally, we illustrate the capabilities of a CSP over the floats for the generation of test data.
This work was partially supported by the RNTL project INKA
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
ANSI/IEEE, New York. IEEE Standard for Binary Floating Point Arithmetic, Std 754–1985 edition, 1985.
F. Benhamou, D. McAllester, and P. Van-Hentenryck. Clp(intervals) revisited. In Proceedings of the International Symposium on Logic Programming, pages 124–138, 1994.
H. Collavizza, F. Delobel, and M. Rueher. A note on partial consistencies over continuous domains solving techniques. In Proc. CP98 (Fourth International Conference on Principles and Practice of Constraint Programming), Pisa, Italy, October 26-30, 1998.
A. Colmerauer. Spécifications de prolog iv. Technical report, GIA, Faculté des Sciences de Luminy,163, Avenue de Luminy 13288 Marseille cedex 9 (France), 1994.
E. Davis. Constraint propagation with interval labels. Journal of Artificial Intelligence, pages 32:281–331, 1987.
A. Gotlieb, B. Botella, and Rueher K. A clp framework for computing structural test data. In Proc. ISSTA 98 (Symposium on Software Testing and Analysis),. ACM SIGSOFT, vol. 2, pp. 53–62, 1998.
David Goldberg. What every computer scientist should know about floatingpoint arithmetic. ACM Computing Surveys, 23(1):5–48, March 1991.
A. Gotlieb. Automatic Test Data Generation using Constraint Logic Programming. PhD thesis, Université de Nice — Sophia Antipolis, France, 2000.
F. Gualard. Langages et environnements en programmation par contraintes d’intervalles. PhD thesis, Université de Nantes— 2, rue de la Houssiniére, F-44322 NANTES CEDEX 3, France, 2000.
E. Hansen, editor. Global optimization using interval analysis. Marcel Dekker, 1992.
H. Hong and V. Stahl. Safe starting regions by fixed points and tightening. Computing, pages 53:323–335, 1994.
R. Baker Kearfott. Rigorous Global Search: Continuous Problems. Number 13 in Nonconvex optimization and its applications. Kluwer Academic Publishers Group, Norwell, MA, USA, and Dordrecht, The Netherlands, 1996.
Bogdan Korel. Automated Software Test Data Generation. IEEE Transactions on Software Engineering, 16(8):870–879, august 1990.
O. Lhomme. Consistency techniques for numeric csps. In Proceedings of IJCAI’ 93, pages 232–238, 1993.
A. Mackworth. Consistency in networks of relations. Journal of Artificial Intelligence, pages 8(1):99–118, 1977.
R. Moore. Interval Analysis. Prentice Hall, 1966.
J.F. Puget and P. Van-Hentenryck. A constraints satisfaction approach to a circuit design problem. Journal of global optimization, pages 13(1):75–93, 1998.
P. Van-Hentenryck, L. Michel, and Y. Deville. Numerica: a Modeling Languge for Global Optimization. MIT press, 1997.
P. Van Hentenryck, D. McAllester, and D. Kapur. Solving polynomial systems using a branch and prune aprroach. SIAM Journal, 34(2), 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Michel, C., Rueher, M., Lebbah, Y. (2001). Solving Constraints over Floating-Point Numbers. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_36
Download citation
DOI: https://doi.org/10.1007/3-540-45578-7_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42863-3
Online ISBN: 978-3-540-45578-3
eBook Packages: Springer Book Archive