Numerical code uses floating-point arithmetic and necessarily suffers from roundoff and truncation errors. Error analysis is the process to quantify such uncertainty in the solution to a problem. Forward error analysis and backward error analysis are two popular paradigms of error analysis. Forward error analysis is more intuitive and has been explored and automated by the programming languages (PL) community. In contrast, although backward error analysis is more preferred by numerical analysts and the foundation for numerical stability, it is less known and unexplored by the PL community. To fill the gap, this paper presents an automated backward error analysis for numerical code to empower both numerical analysts and application developers. In addition, we use the computed backward error results to also compute the condition number, an important quantity recognized by numerical analysts for measuring how sensitive a function is to changes or errors in the input. Experimental results on Intel X87 FPU functions and widely-used GNU C Library functions demonstrate that our analysis is effective at analyzing the accuracy of floating-point programs.
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10:30 - 12:00: OOPSLA - 9. Compilation & Dynamic Analysis at Grand Station 1 Chair(s): Frank TipSamsung Research America | ||||||||||||||||||||||||||||||||||||||||||
| 10:30 - 10:52 Talk | Pericles Rafael AlvesFederal University of Minas Gerais, Brazil, Fabian GruberINRIA, France, Johannes DoerfertSaarland University, Alexandros LabrineasINRIA, France, Tobias GrosserETH Zurich, Switzerland, Fabrice RastelloINRIA, France, Fernando Magno Quintão PereiraFederal University of Minas Gerais, Brazil Link to publication | |||||||||||||||||||||||||||||||||||||||||
| 10:52 - 11:15 Talk | Luca Della ToffolaETH Zurich, Switzerland, Michael PradelTU Darmstadt, Germany, Thomas GrossETH Zurich, Switzerland DOI | |||||||||||||||||||||||||||||||||||||||||
| 11:15 - 11:37 Talk | Wen-Chuan LeePurdue University, USA, Tao BaoPurdue University, USA, Yunhui ZhengPurdue University, USA, Xiangyu ZhangPurdue University, USA, Keval VoraUniversity of California at Riverside, USA, Rajiv GuptaUniversity of California at Riverside, USA DOI | |||||||||||||||||||||||||||||||||||||||||
| 11:37 - 12:00 Talk | Zhoulai FuUniversity of California at Davis, USA, Zhaojun BaiUniversity of California at Davis, USA, Zhendong SuUniversity of California at Davis, USA DOI | |||||||||||||||||||||||||||||||||||||||||