Automatically improving accuracy for floating point expressions

Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)

Volumn 2015-June, Issue , 2015, Pages 1-11

  Panchekha, Pavel ^a   Sachez Stern, Alex ^a   Wilcox, James R ^a   Tatlock, Zachary ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Floating point; Numerical accuracy; Program rewriting

Indexed keywords

ARTIFICIAL INTELLIGENCE; CLUSTERING ALGORITHMS; COMPUTATIONAL LINGUISTICS; COMPUTER PROGRAMMING LANGUAGES; ERRORS; HEURISTIC ALGORITHMS; LEARNING SYSTEMS; NUMERICAL METHODS;

FLOATING POINTS; HEURISTIC SEARCH; MATHEMATICAL LIBRARY; NUMERICAL ACCURACY; PROGRAM REWRITING; REAL ARITHMETIC; SCIENTIFIC AND ENGINEERING APPLICATIONS; SERIES EXPANSION;

DIGITAL ARITHMETIC;

EID: 84951777639     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2737924.2737959     Document Type: Conference Paper

References (38)

1. M. Altman and M. McDonald. The robustness of statistical abstractions. Political Methodology, 1999.
2. M. Altman and M. P. McDonald. Replication with attention to numerical accuracy. Political Analysis, 11(3):302-307, 2003. URL http://pan.oxfordjournals.org/content/11/3/302.abstract.
3. M. Altman, J. Gill, and M. P. McDonald. Numerical Issues in Statistical Computing for the Social Scientist. Springer-Verlag, 2003.
4. E. T. Barr, T. Vo, V. Le, and Z. Su. Automatic detection of floating-point exceptions. POPL'13, 2013.
5. F. Benz, A. Hildebrandt, and S. Hack. A dynamic program analysis to find floating-point accuracy problems. PLDI'12, pages 453-462, New York, NY, USA, 2012. ACM. ISBN 978-1-4503-1205-9. URL http://doi.acm.org/10.1145/2254064.2254118.
6. S. Boldo. Kahan's algorithm for a correct discriminant computation at last formally proven. IEEE Transactions on Computers, 58(2):220-225, Feb. 2009. URL http://hal.inria.fr/inria-00171497/.
7. S. Boldo, F. Clément, J.-C. Filliâtre, M. Mayero, G. Melquiond, and P. Weis. Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program. Journal of Automated Reasoning, 50(4):423-456, Apr. 2013. URL http://hal.inria.fr/hal-00649240/en/.
8. W.-F. Chiang, G. Gopalakrishnan, Z. Rakamarić, and A. Solovyev. Efficient search for inputs causing high floating-point errors. pages 43-52. ACM, 2014.
9. V. Chvatal. A greedy heuristic for the set-covering problem. Mathematics of Operations Research, 4(3): pp. 233-235, 1979. URL http://www.jstor.org/stable/3689577.
10. E. Darulova and V. Kuncak. Sound compilation of reals. POPL'14, pages 235-248, New York, NY, USA, 2014. ACM. ISBN 978-1-4503-2544-8. URL http://doi.acm.org/10.1145/2535838. 2535874.
11. E. Darulova, V. Kuncak, R. Majumdar, and I. Saha. Synthesis of fixed-point programs. EMSOFT'13, pages 22:1-22:10, Piscataway, NJ, USA, 2013. IEEE Press. ISBN 978-1-4799-1443-2. URL http://dl.acm.org/citation. cfm?id=2555754.2555776.
12. M. Daumas and G. Melquiond. Certification of bounds on expressions involving rounded operators. ACM Trans. Math. Softw., 37(1):2:1-2:20, Jan. 2010. http://gappa.gforge.inria.fr/.
13. J. de Jong. math.js: An extensive math library for JavaScript and Node.js, 2013. URL http://mathjs.org/.
14. H. Eldib and C. Wang. An SMT based method for optimizing arithmetic computations in embedded software code. FMCAD'13, 2013.
15. European Commission. The introduction of the euro and the rounding of currency amounts. Euro papers. European Commission, Directorate General II Economic and Financial Affairs, 1998.
16. L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Transactions on Mathematical Software, 33(2):13:1-13:15, June 2007. URL http://doi.acm.org/10.1145/1236463. 1236468.
17. D. Goldberg. What every computer scientist should know about floating-point arithmetic. ACM Comput. Surv., 23(1):5-48, Mar. 1991. URL http://doi.acm.org/10.1145/103162.103163.
18. E. Goubault and S. Putot. Static analysis of finite precision computations. VMCAI'11, pages 232-247, Berlin, Heidelberg, 2011. Springer-Verlag. ISBN 978-3-642-18274-7. URL http://dl.acm.org/citation. cfm?id=1946284.1946301.
19. R. Hamming. Numerical Methods for Scientists and Engineers. Dover Publications, 2nd edition, 1987.
20. N. J. Higham. Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2nd edition, 2002. ISBN 0898715210.
21. IEEE. IEEE standard for binary floating-point arithmetic. IEEE Std. 754-2008, 2008.
22. A. Ioualalen and M. Martel. Synthesizing accurate floating-point formulas. ASAP'13, pages 113-116, June 2013.
23. W. Kahan. A Survey of Error Analysis. Defense Technical Information Center, 1971. URL http://books.google.com/books?id=dkW7tgAACAAJ.
24. W. Kahan. Miscalculating area and angles of a needle-like triangle. Technical report, University of California, Berkeley, Mar. 2000. URL http://www.cs.berkeley.edu/~wkahan/Triangle.pdf.
25. W. Kahan and J. D. Darcy. How Java's floating-point hurts everyone everywhere. Technical report, University of California, Berkeley, June 1998. URL http://www.cs.berkeley.edu/~wkahan/JAVAhurt. pdf.
26. J. Kleinberg and E. Tardos. Algorithm Design. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 2005. ISBN 0321295358.
27. V. Lefévre and J.-M. Muller. The table maker's dilemma: our search for worst cases. Technical report, Ecole Normale Supérieure de Lyon, Oct. 2003. URL http://perso.ens-lyon. fr/jean-michel. muller/Intro-to-TMD.htm.
28. M. Martel. Program transformation for numerical precision. PEPM'09, pages 101-110, New York, NY, USA, 2009. ACM. ISBN 978-1-60558-327-3. URL http://doi.acm.org/10.1145/1480945.1480960.
29. B. D. McCullough and H. D. Vinod. The numerical reliability of econometric software. Journal of Economic Literature, 37(2):633-665, 1999.
30. D. Monniaux. The pitfalls of verifying floating-point computations. ACM Trans. Program. Lang. Syst., 30(3):12:1-12:41, May 2008. URL http://doi.acm.org/10.1145/1353445.1353446.
31. C. G. Nelson. Techniques for Program Verification. PhD thesis, Stanford University, 1979.
32. P. Panchekha. Numerical imprecision in complex square root, 2014. URL https://github.com/josdejong/mathjs/pull/208.
33. P. Panchekha. Accuracy of sinh and complex cos/sin, 2014. URL https://github.com/josdejong/mathjs/pull/247.
34. K. Quinn. Ever had problems rounding off figures? This stock exchange has. The Wall Street Journal, page 37, November 8, 1983.
35. C. Rubio-González, 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. SC'13, 2013.
36. E. Schkufza, R. Sharma, and A. Aiken. Stochastic optimization of floating point programs using tunable precision. PLDI'14, 2014.
37. A. Solovyev, C. Jacobsen, Z. Rakamaric, and G. Gopalakrishnan. Rigorous estimation of floating-point round-off errors with symbolic taylor expansions. FM'15. Springer, June 2015.
38. N. Toronto and J. McCarthy. Practically accurate floating-point math. Computing in Science Engineering, 16(4):80-95, July 2014.