An Abstraction-guided Approach to Scalable and Rigorous Floating-Point Error Analysis

by   Arnab Das, et al.

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.



There are no comments yet.


page 1

page 2

page 3

page 4


A Verified Certificate Checker for Floating-Point Error Bounds

Being able to soundly estimate roundoff errors in floating-point computa...

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

We present a detailed study of roundoff errors in probabilistic floating...

Combining Tools for Optimization and Analysis of Floating-Point Computations

Recent renewed interest in optimizing and analyzing floating-point progr...

Solving systems of inequalities in two variables with floating point arithmetic

From a theoretical point of view, finding the solution set of a system o...

A Framework for Semi-Automatic Precision and Accuracy Analysis for Fast and Rigorous Deep Learning

Deep Neural Networks (DNN) represent a performance-hungry application. F...

Precision-aware Deterministic and Probabilistic Error Bounds for Floating Point Summation

We analyze the forward error in the floating point summation of real num...

FPDetect: Efficient Reasoning About Stencil Programs Using Selective Direct Evaluation

We present FPDetect, a low overhead approach for detecting logical error...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.