Mixed abstractions for floating-point arithmetic

9th International Conference Formal Methods in Computer Aided Design, FMCAD 2009

Volumn , Issue , 2009, Pages 69-76

  Brillout, Angelo ^a   Kroening, Daniel ^b   Wahl, Thomas ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTION PROCESS; CONTROL FLOWS; DECISION PROCEDURE; FLOATING-POINT ARITHMETIC; FLOATING-POINT CALCULATIONS; FORMAL ANALYSIS; SAFETY CRITICAL SYSTEMS;

ABSTRACTING; COMPUTER AIDED DESIGN; DIGITAL ARITHMETIC; EMBEDDED SYSTEMS;

FORMAL METHODS;

EID: 76549105713     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FMCAD.2009.5351141     Document Type: Conference Paper

References (27)

1. Gander, W.: Heisenberg effects in computer-arithmetic (2005) http://www.inf.ethz.ch/news/focus/res-focus/april-2005.
2. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, New York, USA, ACM (1977) 238-252
3. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: CAV. (2000) 154-169
4. Bryant, R.E., Kroening, D., Ouaknine, J., Seshia, S.A., Strichman, O., Brady, B.A.: Deciding bit-vector arithmetic with abstraction. In: TACAS. (2007) 358-372
5. Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58 (2003) 118-149
6. Eén, N., Sörensson, N.: An extensible sat-solver. In: SAT. Number 2919 in LNCS, Springer (2003) 502-518
7. SNU Computer Architecture and Network Laboratory: (SNU Real-Time Benchmarks) http://archi.snu.ac.kr/realtime/benchmark.
8. Lee, C., Potkonjak, M., Mangione-Smith, W.H.: Mediabench: A tool for evaluating and synthesizing multimedia and communicatons systems. In: MICRO. (1997) 330-335
9. Clarke, E.M., Kroening, D., Lerda, F.: A tool for checking ANSI-C programs. In: TACAS. (2004) 168-176
10. Carreno, V.A.: Interpretation of IEEE-854 floating-point standard and definition in the HOL system. Technical report, NASA Langley Research Center (1995)
11. Harrison, J.: Formal verification of square root algorithms. Form. Methods Syst. Des. 22 (2003) 143-153
12. Harrison, J.: Formal verification of floating point trigonometric functions. In: FMCAD. (2000) 217-233
13. Harrison, J.: Floating point verification in HOL light: The exponential function. In: AMAST. (1997) 246-260
14. Russinoff, D.M.: A mechanically checked proof of correctness of the AMD K5 floating point square root microcode. Form. Methods Syst. Des. 14 (1999) 75-125
15. Russinoff, D.M.: A case study in fomal verification of register-transfer logic with ACL2: The floating point adder of the AMD AthlonTM processor. In: FMCAD '00: Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design, London, UK, Springer-Verlag (2000) 3-36
16. Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: A static analyzer for large safety-critical software. In: PLDI, ACM (2003) 196-207
17. Miné, A.: Relational abstract domains for the detection of floating-point run-time errors. In: ESOP. Volume 2986 of Lecture Notes in Computer Science., Springer (2004) 3-17
18. Chen, L., Miné, A., Cousot, P.: A sound floating-point polyhedra abstract domain. In: APLAS. Volume 5356 of Lecture Notes in Computer Science., Springer (2008) 3-18
19. Jeannet, B., Miné, A.: APRON: A library of numerical abstract domains for static analysis. In: CAV. (2009, to appear)
20. Goubault, E.: Static analyses of the precision of floating-point operations. In: SAS. (2001) 234-259
21. Goubault, E., Martel, M., Putot, S.: Asserting the precision of floatingpoint computations: A simple abstract interpreter. In: ESOP. Volume 2305 of Lecture Notes in Computer Science., Springer (2002) 209-212
22. Martel, M.: Static analysis of the numerical stability of loops. In: SAS. Volume 2477 of Lecture Notes in Computer Science., Springer (2002) 133-150
23. Putot, S., Goubault, E., Martel, M.: Static analysis-based validation of floating-point computations. In: Numerical Software with Result Verification. Volume 2991 of Lecture Notes in Computer Science., Springer (2003) 306-313
24. Michel, C., Rueher, M., Lebbah, Y.: Solving constraints over floatingpoint numbers. In: CP. Volume 2239 of Lecture Notes in Computer Science., Springer (2001) 524-538
25. Botella, B., Gotlieb, A., Michel, C.: Symbolic execution of floatingpoint computations. Softw. Test., Verif. Reliab. 16 (2006) 97-121
26. Jacobi, C., Berg, C.: Formal verification of the VAMP floating point unit. Formal Methods in System Design 26 (2005) 227-266
27. Monniaux, D.: On using floating-point computations to help an exact linear arithmetic decision procedure. In: CAV. (2009, to appear)