1 research outputs found
An Abstraction-guided Approach to Scalable and Rigorous Floating-Point Error Analysis
Automated techniques for rigorous floating-point round-off error analysis are
important in areas including formal verification of correctness and precision
tuning. Existing tools and techniques, while providing tight bounds, fail to
analyze expressions with more than a few hundred operators, thus unable to
cover important practical problems. In this work, we present Satire, a new tool
that sheds light on how scalability and bound-tightness can be attained through
a combination of incremental analysis, abstraction, and judicious use of
concrete and symbolic evaluation. Satire has handled problems exceeding 200K
operators. We present Satire's underlying error analysis approach,
information-theoretic abstraction heuristics, and a wide range of case studies,
with evaluation covering FFT, Lorenz system of equations, and various PDE
stencil types. Our results demonstrate the tightness of Satire's bounds, its
acceptable runtime, and valuable insights provided.Comment: A more informative and updated version of this paper has been
accepted for publication at SuperComputing 202