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.
Fri 30 OctDisplayed time zone: Eastern Time (US & Canada) change
10:30 - 12:00 | 9. Compilation & Dynamic AnalysisOOPSLA at Grand Station 1 Chair(s): Frank Tip Samsung Research America | ||
10:30 22mTalk | Runtime Pointer Disambiguation OOPSLA Pericles Rafael Alves Federal University of Minas Gerais, Brazil, Fabian Gruber INRIA, France, Johannes Doerfert Saarland University, Alexandros Labrineas INRIA, France, Tobias Grosser ETH Zurich, Switzerland, Fabrice Rastello INRIA, France, Fernando Magno Quintão Pereira Federal University of Minas Gerais, Brazil Link to publication | ||
10:52 22mTalk | Performance Problems You Can Fix: A Dynamic Analysis of Memoization Opportunities OOPSLA Luca Della Toffola ETH Zurich, Switzerland, Michael Pradel TU Darmstadt, Germany, Thomas Gross ETH Zurich, Switzerland DOI | ||
11:15 22mTalk | RAIVE: Runtime Assessment of Floating-Point Instability by Vectorization OOPSLA Wen-Chuan Lee Purdue University, USA, Tao Bao Purdue University, USA, Yunhui Zheng IBM Research, Xiangyu Zhang Purdue University, USA, Keval Vora University of California at Riverside, USA, Rajiv Gupta University of California at Riverside, USA DOI | ||
11:37 22mTalk | Automated Backward Error Analysis for Numerical Code OOPSLA Zhoulai Fu University of California at Davis, USA, Zhaojun Bai University of California at Davis, USA, Zhendong Su University of California at Davis, USA DOI | ||