Numerical stability analysis of floating-point computations using software model checking

8th ACM/IEEE International Conference on Formal Methods and Models for Codesign, MEMOCODE 2010

Volumn , Issue , 2010, Pages 49-58

  Ivančić, Franjo ^a   Ganai, Malay K ^a   Sankaranarayanan, Sriram ^b   Gupta, Aarti ^a  

^a NEC LABORATORIES AMERICA   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACT INTERPRETATIONS; BOUNDED MODEL CHECKING; EMBEDDED CONTROLLERS; FLOATING POINTS; FLOATING-POINT COMPUTATION; MIXED INTEGER; MODEL SIMPLIFICATION; NUMERIC INSTABILITY; NUMERICAL PRECISION; NUMERICAL PROGRAMS; NUMERICAL STABILITY ANALYSIS; PRODUCTION SOFTWARE; SATISFIABILITY MODULO THEORIES; SOFTWARE MODEL CHECKING; SOFTWARE VERIFICATION;

ABSTRACTING; COMPUTER SOFTWARE SELECTION AND EVALUATION; DIGITAL ARITHMETIC; EMBEDDED SOFTWARE; FORMAL METHODS; PROGRAM DEBUGGING; PROGRAM INTERPRETERS;

MODEL CHECKING;

EID: 77957796073     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MEMCOD.2010.5558622     Document Type: Conference Paper

References (28)

1. M.V.A. Andrade, J.L.D. Comba, and J. Stolfi. Affine arithmetic. In INTERVAL'94, March 1994.
2. A. Armando, J. Mantovan, and L. Platania. Bounded model checking of software using SMT solvers instead of SAT solvers. J. Softw. Tools Technol. Transf., 11(1):69-83, 2009.
3. G. Balakrishnan, S. Sankaranarayanan, F. Ivančić, O. Wei, and A. Gupta. SLR: Path-sensitive analysis through infeasible-path detection and syntactic language refinement. In SAS, pages 238-254. Springer, 2008.
4. T. Ball and S. Rajamani. The SLAM toolkit. In CAV, 2001.
5. B. Blanchet, P. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné, D. Monniaux, and X. Rival. A static analyzer for large safety-critical software. In PLDI. ACM, 2003.
6. A. Brillout, D. Kroening, and T. Wahl. Mixed abstractions for floating-point arithmetic. In FMCAD, 2009.
7. E.M. Clarke, A. Biere, R. Raimi, and Y. Zhu. Bounded model checking using satisfiability solving. Formal Methods in Systems Design, 19(1):7-34, 2001.
8. E.M. Clarke, O. Grumberg, S. Jha, Y. Lu, and H. Veith. Counterexample-guided abstraction refinement. In CAV, pages 154-169, 2000.
9. E.M. Clarke, D. Kroening, and F. Lerda. A tool for checking ANSI-C programs. In Tools and Algorithms for the Construction and Analysis of Systems, 2004.
10. B. Cook, A. Podelski, and A. Rybalchenko. Terminator: Beyond safety. In Computer Aided Verification (CAV), pages 415-418. Springer, 2006.
11. P. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné, D. Monniaux, and X. Rival. The ASTREÉ analyzer. In ESOP. Springer, 2005.
12. M. Davis, G. Logemann, and D. Loveland. A machine program for theorem proving. Communications of the ACM, (5):394-397, 1962.
13. M. Davis and H. Putnam. A computing procedure for quantification theory. Journal of the ACM, (7):7-201, 1960.
14. B. Dutertre and L.M. de Moura. A fast linear-arithmetic solver for DPLL(T). In Computer Aided Verification (CAV), pages 81-94. Springer, 2006.
15. G.E. Fainekos, S. Sankaranarayanan, F. Ivančić, and A. Gupta. Robustness of model-based simulations. In 30th IEEE Real-Time Systems Symposium, 2009.
16. M. Fränzle, C. Herde, T. Teige, S. Ratschan, and T. Schubert. Efficient solving of large non-linear arithmetic constraint systems with complex boolean structure. JSAT, 1(3-4):209-236, 2007.
17. M.K. Ganai and F. Ivančíc. Efficient decision procedure for non-linear arithmetic constraints using CORDIC. In FMCAD, November 2009.
18. E. Goubault. Static analyses of the precision of floating-point operations. In Symposium on Static Analysis (SAS), pages 234-259. Springer, 2001.
19. E. Goubault, S. Putot, P. Baufreton, and J. Gassino. Static analysis of the accuracy in control systems: Principles and experiments. In FMICS. Springer, 2007.
20. K. Havelund and T. Pressburger. Model checking Java programs using Java PathFinder. Software Tools for Technology Transfer, 2(4), April 2000.
21. T.A. Henzinger, R. Jhala, R. Majumdar, and G. Sutre. Lazy abstraction. In POPL, pages 58-70, 2002.
22. IEEE. 754-2008: IEEE standard for floating-point arithmetic, August 2008. http://ieeexplore.ieee.org/servlet/opac?punumber=4610933.
23. F. Ivančić, I. Shlyakhter, A. Gupta, M.K. Ganai, V. Kahlon, C. Wang, and Z. Yang. Model checking C programs using F-SOFT. In ICCD. IEEE Computer Society, 2005.
24. MathWorks. PolySpace program analysis tool. http://www.polyspace.com.
25. R. E. Moore. Interval Analysis. Prentice-Hall, 1966.
26. NEC Laboratories America. NECLA verification benchmarks. www.nec-labs.com/research/system/systems SAVwebsite/benchmarks.php.
27. J.E. Volder. The CORDIC trigonometric computing technique. IRE Trans. on Electronic Computers, EC-8(3):330-334, 1959.
28. J.S. Walther. A unified algorithm for elementary functions. In AFIPS Spring Joint Computer Conference, 1975.