A Verified Certificate Checker for Floating-Point Error Bounds

07/07/2017
by   Heiko Becker, et al.
0

Being able to soundly estimate roundoff errors in floating-point computations is important for many applications in embedded systems and scientific computing. Due to the unintuitive nature of floating-point arithmetic, automated static analysis tools are highly valuable for this task. The results, however, are only as correct as the implementations of the static analysis tools. This paper presents a new modular framework for the analysis of finite-precision computations which computes sound roundoff error bounds fully automatically. The main focus of this paper are the correctness certificates generated by our framework. These can be checked independently by our checker functions, thus providing more confidence in the analysis results. We present implementations of certificate generation and checking for both Coq and HOL4 and evaluate it on a number of examples from the literature. The experiments use both in-logic evaluation of Coq and HOL4, and execution of extracted code outside of the logics: we benchmark Coq extracted unverified OCaml code and a CakeML-generated verified binary.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/06/2020

Exploiting Verified Neural Networks via Floating Point Numerical Error

We show how to construct adversarial examples for neural networks with e...
research
04/24/2020

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

Automated techniques for rigorous floating-point round-off error analysi...
research
07/07/2017

On Sound Relative Error Bounds for Floating-Point Arithmetic

State-of-the-art static analysis tools for verifying finite-precision co...
research
07/09/2018

Confidence Intervals for Stochastic Arithmetic

Quantifying errors and losses due to the use of Floating-Point (FP) calc...
research
10/17/2021

Correct Probabilistic Model Checking with Floating-Point Arithmetic

Probabilistic model checking computes probabilities and expected values ...
research
03/26/2020

Benchmarking Software Model Checkers on Automotive Code

This paper reports on our experiences with verifying automotive C code b...
research
07/19/2017

Secure SURF with Fully Homomorphic Encryption

Cloud computing is an important part of today's world because offloading...

Please sign up or login with your details

Forgot password? Click here to reset