Automatically adapting programs for mixed-precision floating-point computation

Proceedings of the International Conference on Supercomputing

Volumn , Issue , 2013, Pages 369-378

  Lam, Michael O ^a   Hollingsworth, Jeffrey K ^a   De Supinski, Bronis R ^b   Legendre, Matthew P ^b  

^a Institute of Advanced Computer Science   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

binary instrumentation; floating point; mixed precision

Indexed keywords

BINARY INSTRUMENTATIONS; FLOATING-POINT; FLOATING-POINT ARITHMETIC; FLOATING-POINT COMPUTATION; MIXED PRECISION; SCIENTIFIC COMPUTATION; SIMPLE SEARCH ALGORITHM; STREAMING ARCHITECTURE;

SUPERCOMPUTERS;

DIGITAL ARITHMETIC;

EID: 84879807319     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2464996.2465018     Document Type: Conference Paper

References (44)

1. ASC Sequoia Benchmark Codes. https://asc.llnl.gov/sequoia/benchmarks/. Accessed 21 September 2011.
2. M. V. A. Andrade, J. a. L. D. Comba, and J. Stolfi. Affine Arithmetic, 1994.
3. H. Anzt, B. Rocker, and V. Heuveline. Energy efficiency of mixed precision iterative refinement methods using hybrid hardware platforms. Computer Science Research and Development, 25(3-4):141-148, 2010.
4. M. Baboulin, A. Buttari, J. Dongarra, J. Kurzak, J. Langou, J. Langou, P. Luszczek, and S. Tomov. Accelerating Scientific Computations with Mixed Precision Algorithms. Computer Physics Communications, 180(12):2526-2533, 2008.
5. D. Bailey, T. Harris, W. Saphir, R. V. D. Wijngaart, A. Woo, and M. Yarrow. The NAS Parallel Benchmarks 2.0, 1995.
6. F. Benz, S. Hack, and A. Hildebrandt. A Dynamic Program Analysis to find Floating-Point Accuracy Problems. In ACM SIGPLAN Conference on Programming Language Design and Implementation, 2012.
7. R. F. Boisvert, R. Pozo, K. Remington, R. Barrett, and J. J. Dongarra. The Matrix Market: A web resource for test matrix collections. In R. F. Boisvert, editor, Quality of Numerical Software, Assessment and Enhancement, pages 125-137. Chapman & Hall, London, 1997.
8. B. Buck and J. K. Hollingsworth. An API for runtime code patching. The International Journal of High Performance Computing Applications, 14:317-329, 2000.
9. A. Buttari, J. Dongarra, J. Kurzak, J. Langou, P. Luszczek, and S. Tomov. Exploiting Mixed Precision Floating Point Hardware for Scientific Computation. In High Performance Computing and Grids in Action. IOS Press, 2008.
10. A. Buttari, J. Dongarra, J. Kurzak, P. Luszczek, and S. Tomov. Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy. 2007.
11. J. W. Carr. Error analysis in floating point arithmetic. Communications of the ACM, 2(5):10-16, May 1959.
12. M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi. Solving Lattice QCD systems of equations using mixed precision solvers on GPUs. Computer Physics Communications, 181(9):30, 2010.
13. F. De Dinechin, C. Q. Lauter, and G. Melquiond. Assisted verification of elementary functions using Gappa. Proceedings of the 2006 ACM symposium on Applied computing SAC 06, page 1318, 2006.
14. J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, and J. W. H. Liu. A Supernodal Approach to Sparse Partial Pivoting. SIAM Journal on Matrix Analysis and Applications, 20(3):720-755, 1999.
15. J. Dongarra, P. Beckman, T. Moore, P. Aerts, G. Aloisio, J. C. Andre, D. Barkai, J. Y. Berthou, T. Boku, B. Braunschweig, F. Cappello, B. Chapman, A. Choudhary, S. Dosanjh, T. Dunning, S. Fiore, A. Geist, B. Gropp, R. Harrison, M. Hereld, M. Heroux, A. Hoisie, K. Hotta, Y. Ishikawa, F. Johnson, S. Kale, R. Kenway, D. Keyes, B. Kramer, J. Labarta, A. Lichnewsky, T. Lippert, B. Lucas, B. Maccabe, S. Matsuoka, P. Messina, P. Michielse, B. Mohr, M. S. Mueller, W. E. Nagel, H. Nakashima, M. E. Papka, D. Reed, M. Sato, E. Seidel, J. Shalf, D. Skinner, M. Snir, T. Sterling, R. Stevens, F. Streitz, B. Sugar, S. Sumimoto, W. Tang, J. Taylor, R. Thakur, A. Trefethen, M. Valero, A. Van Der Steen, J. Vetter, P. Williams, R. Wisniewski, and K. Yelick. The International Exascale Software Project roadmap. International Journal of High Performance Computing Applications, 25(1):3-60, 2011.
16. S. P. Eric Goubault Matthieu Martel. Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter. Programming Languages and Systems, pages 287-306, 2002.
17. C. F. Fang, R. A. Rutenbar, M. Püschel, and T. Chen. Toward efficient static analysis of finite-precision effects in DSP applications via affine arithmetic modeling. Proceedings of the 40th conference on Design automation DAC 03, page 496, 2003.
18. M. Furuichi, D. a. May, and P. J. Tackley. Development of a Stokes flow solver robust to large viscosity jumps using a Schur complement approach with mixed precision arithmetic. Journal of Computational Physics, 230(24):8835-8851, Oct. 2011.
19. D. Göddeke and R. Strzodka. Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed Precision Multigrid. IEEE Transactions on Parallel and Distributed Systems, 22(1):22-32, 2011.
20. D. Göddeke, R. Strzodka, and S. Turek. Performance and accuracy of hardware-oriented native-, emulated-and mixed-precision solvers in FEM simulations. International Journal of Parallel, Emergent and Distributed Systems, 22(4):221-256, Aug. 2007. (Pubitemid 46925816)
21. D. Goldberg. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, 23(1):5-48, Mar. 1991. (Pubitemid 21723680)
22. E. Goubault. Static Analyses of the Precision of Floating-Point Operations. Static Analysis, pages 234-259, 2001.
23. X. Hao and A. Varshney. Variable-precision rendering. Proceedings of the 2001 symposium on Interactive 3D graphics SI3D 01, http:149-158, 2001.
24. N. J. Higham. Accuracy and Stability of Numerical Algorithms, Second Edition. SIAM Philadelphia, 2002.
25. J. D. Hogg and J. A. Scott. A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems. ACM Transactions on Mathematical Software, 37(2):1-24, 2010.
26. IEEE. IEEE 754-2008, Standard for Floating-Point Arithmetic. IEEE, New York, Aug. 2008.
27. J. Jenkins, E. R. Schendel, S. Lakshminarasimhan, D. A. Boyuka II, T. Rogers, S. Ethier, R. Ross, S. Klasky, and N. F. Samatova. Byte-precision level of detail processing for variable precision analytics. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, SC '12, pages 48:1-48:11, Los Alamitos, CA, USA, 2012. IEEE Computer Society Press.
28. T. Kaneko and B. Liu. On Local Roundoff Errors in Floating-Point Arithmetic. J. ACM, 20(3):391-398, 1973.
29. W. Kraemer. A Priori Worst Case Error Bounds for Floating-Point Computations. IEEE transactions on computers, 47(7):750-756, 1998.
30. W. Krämer and A. Bantle. Automatic Forward Error Analysis for Floating Point Algorithms. Reliable Computing, 7(4):321-340, Aug. 2001. (Pubitemid 32659085)
31. T. I. Laakso and L. B. Jackson. Bounds for floating-point roundoff noise. IEEE transactions on circuits and systems, 41(6):424-426, 1994.
32. M. O. Lam, J. K. Hollingsworth, and G. W. Stewart. Dynamic Floating-Point Cancellation Detection. In WHIST '11, 2011.
33. J. L. Larson, M. E. Pasternak, and J. A. Wisniewski. Algorithm 594: Software for Relative Error Analysis. ACM Transactions on Mathematical Software, 9(1):125-130, Mar. 1983.
34. X. S. Li, M. C. Martin, B. J. Thompson, T. Tung, D. J. Yoo, J. W. Demmel, D. H. Bailey, G. Henry, Y. Hida, J. Iskandar, W. Kahan, S. Y. Kang, and A. Kapur. Design, implementation and testing of extended and mixed precision BLAS. ACM Transactions on Mathematical Software, 28(2):152-205, June 2002. (Pubitemid 135701674)
35. M. D. Linderman, M. Ho, D. L. Dill, T. H. Meng, and G. P. Nolan. Towards program optimization through automated analysis of numerical precision. Proceedings of the 8th annual IEEE ACM international symposium on Code generation and optimization CGO 10, page 230, 2010.
36. B. Liu and T. Kaneko. Error analysis of digital filters realized with floating-point arithmetic. Proceedings of the IEEE, 57(10):1735-1747, 1969.
37. C.-K. Luk, R. Cohn, R. Muth, H. Patil, A. Klauser, G. Lowney, S. Wallace, V. J. Reddi, and K. Hazelwood. Pin: building customized program analysis tools with dynamic instrumentation. In PLDI '05: Proceedings of the 2005 ACM SIGPLAN conference on Programming language design and implementation, pages 190-200, New York, NY, USA, 2005. ACM.
38. M. Martel. Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach. Programming Languages and Systems, pages 159-186, 2002.
39. M. Martel. Semantics-Based Transformation of Arithmetic Expressions. Static Analysis, pages 298-314, 2007.
40. M. Martel. Program transformation for numerical precision. In PEPM '09: Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation, pages 101-110, New York, NY, USA, Jan. 2009. ACM Press.
41. P. L. Richman. Automatic error analysis for determining precision. Communications of the ACM, 15(9):813-820, Sept. 1972.
42. Robert Strzodka and Dominik Goddeke. Mixed Precision Methods for Convergent Iterative Schemes. In Proceedings of the 2006 Workshop on Edge Computing Using New Commodity Architectures, May 2006, 2006.
43. Robert Strzodka and Dominik Goddeke. Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components. IEEE Proceedings on Field-Programmable Custom Computing, 2006.
44. J. H. Wilkinson. Rounding Errors in Algebraic Processes. Prentice-Hall, Inc., 1964.