Efficient search for inputs causing high floating-point errors

Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP

Volumn , Issue , 2014, Pages 43-52

  Chiang, Wei Fan ^a   Gopalakrishnan, Ganesh ^a   Rakamarić, Zvonimir ^a   Solovyev, Alexey ^a  

^a University of Utah   (United States)

Author keywords

Floating point error estimation methods; Guided search; Sequential and parallel programming

Indexed keywords

ESTIMATION METHODS; GUIDED SEARCH; HEURISTIC SEARCH; HEURISTIC SEARCH ALGORITHMS; HEURISTIC SEARCH METHODS; PERFORMANCE OPTIMIZATIONS; PRECISION ANALYSIS; PROGRAM UNDERSTANDING;

COMPUTER PROGRAMMING LANGUAGES; CONCRETE TESTING; ERRORS; ESTIMATION; HEURISTIC ALGORITHMS; MATHEMATICAL OPERATORS; MODULAR ROBOTS; OPTIMIZATION; PARALLEL PROGRAMMING; TOOLS;

DIGITAL ARITHMETIC;

EID: 84896808432     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2555243.2555265     Document Type: Conference Paper

References (39)

1. E. Anderson, Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. J. Dongarra, J. Du Croz, S. Hammarling, A. Greenbaum, A. McKenney, and D. Sorensen. LAPACK Users? Guide (3rd Ed.). SIAM: Society for Industrial and Applied Mathematics, 1999.
2. J. Ansel, C. Chan, Y. L. Wong, M. Olszewski, Q. Zhao, A. Edelman, and S. Amarasinghe. Petabricks: a language and compiler for algorithmic choice. In ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), pages 38-49, 2009.
3. D. H. Bailey and J. M. Borwein. Highly parallel, high-precision numerical integration, 2005.
4. E. T. Barr, T. Vo, V. Le, and Z. Su. Automatic detection of floatingpoint exceptions. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), pages 549-560, 2013.
5. F. Benz, A. Hildebrandt, and S. Hack. A dynamic program analysis to find floating-point accuracy problems. In ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), pages 453-462, 2012.
6. S. Boldo and G. Melquiond. Flocq: A unified library for proving floating-point algorithms in Coq. In IEEE Symposium on Computer Arithmetic, pages 243-252, 2011.
7. S. Boldo, J.-C. Filliâtre, and G. Melquiond. Combining Coq and Gappa for certifying floating-point programs. In Intelligent Computer Mathematics, pages 59-74. Springer-Verlag, 2009.
8. C. Cadar and K. Sen. Symbolic execution for software testing: three decades later. Communications of the ACM, 56(2):82-90, Feb. 2013.
9. W.-F. Chiang, G. Gopalakrishnan, Z. Rakamarić, D. H. Ahn, and G. L. Lee. Determinism and reproducibility in large-scale HPC systems. In Workshop on Determinism and Correctness in Parallel Programming (WoDet), 2013.
10. Coq. The Coq proof assistant. http://coq.inria.fr/.
11. E. Darulova and V. Kuncak. Trustworthy numerical computation in Scala. In Conference on Object-Oriented Programming Systems (OOPSLA), pages 325-344, 2011.
12. F. de Dinechin, C. Q. Lauter, and G. Melquiond. Assised verification of elementary functions using Gappa. In ACM Symposium on Applied computing (SAC), pages 1318-1322, 2006.
13. L. De Moura and N. Bjørner. Z3: An efficient SMT solver. In International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS), pages 337-340, 2008.
14. D. Delmas, E. Goubault, S. Putot, J. Souyris, K. Tekkal, and F. Védrine. Towards an industrial use of FLUCTUAT on safety-critical avionics software. In Workshop on Formal Methods for Industrial Critical Systems (FMICS), pages 53-69, 2009.
15. J. Demmel and H. D. Nguyen. Numerical reproducibility and accuracy at exascale. In IEEE Symposium on Computer Arithmetic, pages 235-237, 2013.
16. J. W. Demmel. Trading off parallelism and numerical stability. Technical Report UCB/CSD-92-702, EECS Department, University of California, Berkeley, 1992.
17. A. Goodloe, C. Muñoz, F. Kirchner, and L. Correnson. Verification of numerical programs: From real numbers to floating point numbers. In NASA Formal Methods Symposium (NFM), pages 441-446, 2013.
18. M. Harris. Optimizing parallel reduction in CUDA. NVIDIA Developer Technology, 2007.
19. M. Heideman, D. Johnson, and C. Burrus. Gauss and the history of the fast Fourier transform. ASSP Magazine, IEEE, 1(4):14-21, 1984.
20. N. J. Higham. Accuracy and Stability of Numerical Algorithms (2nd Ed.). SIAM: Society for Industrial and Applied Mathematics, 2002.
21. C. A. R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12(10):576-580, 1969.
22. F. Hutter, H. H. Hoos, and T. Stutzle. Automatic algorithm configuration based on local search. In National Conference on Artificial Intelligence, pages 1152-1157, 2007.
23. IEEE Task P754. ANSI/IEEE 754-1985, Standard for Binary Floating-Point Arithmetic. IEEE, 1985.
24. F. Ivancic, M. K. Ganai, S. Sankaranarayanan, and A. Gupta. Numerical stability analysis of floating-point computations using software model checking. In IEEE/ACM Intl. Conference on Formal Methods and Models for Codesign (MEMOCODE), pages 49-58, 2010.
25. W. Kahan. Pracniques: Further remarks on reducing truncation errors. Communications of the ACM, 8(1):40-, Jan. 1965.
26. J. Kennedy. Particle swarm optimization. In Encyclopedia of Machine Learning, pages 760-766. Springer-Verlag, 2010.
27. A. B. Kinsman and N. Nicolici. Finite precision bit-width allocation using SAT-modulo theory. In Conference on Design, Automation and Test in Europe (DATE), pages 1106-1111, 2009.
28. M. O. Lam, J. K. Hollingsworth, B. R. de Supinski, and M. P. LeGendre. Automatically adapting programs for mixed-precision floatingpoint computation. In International Conference on Supercomputing (ICS), pages 369-378, 2013.
29. M. O. Lam, J. K. Hollingsworth, and G.W. Stewart. Dynamic floatingpoint cancellation detection. Parallel Computing, 39(3):146-155, 2013.
30. P. Li, G. Li, and G. Gopalakrishnan. Parametric flows: automated behavior equivalencing for symbolic analysis of races in CUDA programs. In International Conference on High Performance Computing, Networking, Storage and Analysis (SC), pages 29:1-29:10, 2012.
31. M. D. Linderman, M. Ho, D. L. Dill, T. H. Y. Meng, and G. P. Nolan. Towards program optimization through automated analysis of numerical precision. In IEEE/ACM International Symposium on Code Generation and Optimization (CGO), pages 230-237, 2010.
32. H. R. Lourenço, O. C. Martin, and T. Stutzle. Iterated local search. arXiv preprint math/0102188, 2001.
33. J. Luitjens, B. Worthen, M. Berzins, and T. C. Henderson. Petascale Computing Algorithms and Applications, chapter Scalable parallel AMR for the Uintah multiphysics code, pages 67-82. Chapman and Hall/CRC, 2007.
34. MAGMA. The MAGMA library. http://icl.cs.utk.edu/ magma/index.html.
35. NPB. The NAS parallel benchmarks (NPB). http://www.nas. nasa.gov/publications/npb.html.
36. C. Rubio-Gonzalez, C. Nguyen, H. D. Nguyen, J. Demmel,W. Kahan, K. Sen, D. H. Bailey, C. Iancu, and D. Hough. Precimonious: Tuning assistant for floating-point precision. In International Conference on High Performance Computing, Networking, Storage and Analysis (SC), pages 27:1-27:12, 2013.
37. S3FP. Guided random testing for floating-point error estimation. https://sites.google.com/site/grt4fperror/.
38. M. Souza, M. Borges, M. d'Amorim, and C. S. P?as?areanu. CORAL: Solving complex constraints for symbolic Pathfinder. In NASA Formal Methods Symposium (NFM), pages 359-374, 2011.
39. J. A. Stratton, C. Rodrigues, I.-J. Sung, N. Obeid, L.-W. Chang, N. Anssari, G. D. Liu, and W.-m. W. Hwu. Parboil: A revised benchmark suite for scientific and commercial throughput computing. Center for Reliable and High-Performance Computing, 2012.