Detecting Floating-Point Errors via Atomic Conditions

This paper tackles the important, difficult problem of detecting program inputs that trigger large floating-point errors in numerical code. It introduces a novel, principled dynamic analysis that leverages the mathematically rigorously analyzed condition numbers for atomic numerical operations, which we call atomic conditions, to effectively guide the search for large floating-point errors. Compared with existing approaches, our work based on atomic conditions has several distinctive benefits: (1) it does not rely on high-precision implementations to act as approximate oracles, which are difficult to obtain in general and computationally costly; and (2) atomic conditions provide accurate, modular search guidance. These benefits in combination lead to a highly effective approach that detects more significant errors in real-world code (e.g., widely-used numerical library functions) and achieves several orders of speedups over the state-of-the-art, thus making error analysis significantly more practical. We expect the methodology and principles behind our approach to benefit other floating-point program analysis tasks such as debugging, repair and synthesis. To facilitate the reproduction of our work, we have made our implementation, evaluation data and results publicly available on GitHub at https://github.com/FP-Analysis/atomic-condition.ISSN:2475-142

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision values, automated static analysis tools are highly valuable to estimate roundoff errors. The results, however, are only as correct as the implementations of the static analysis tools. This paper presents a formally verified and modular tool which fully automatically checks the correctness of finite-precision roundoff error bounds encoded in a certificate. 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

Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic

Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation

Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring specific accuracy issues due to their massive use of floating-point computations. Yet, it is uncommon to guarantee their correctness. Indeed, we had to extend existing methods and tools for proving the correct behavior of programs to verify an existing numerical analysis program. This C program implements the second-order centered finite difference explicit scheme for solving the 1D wave equation. In fact, we have gone much further as we have mechanically verified the convergence of the numerical scheme in order to get a complete formal proof covering all aspects from partial differential equations to actual numerical results. To the best of our knowledge, this is the first time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with arXiv:1112.179

A study of systems implementation languages for the POCCNET system

The results are presented of a study of systems implementation languages for the Payload Operations Control Center Network (POCCNET). Criteria are developed for evaluating the languages, and fifteen existing languages are evaluated on the basis of these criteria

A Domain-Specific Language and Editor for Parallel Particle Methods

Domain-specific languages (DSLs) are of increasing importance in scientific high-performance computing to reduce development costs, raise the level of abstraction and, thus, ease scientific programming. However, designing and implementing DSLs is not an easy task, as it requires knowledge of the application domain and experience in language engineering and compilers. Consequently, many DSLs follow a weak approach using macros or text generators, which lack many of the features that make a DSL a comfortable for programmers. Some of these features---e.g., syntax highlighting, type inference, error reporting, and code completion---are easily provided by language workbenches, which combine language engineering techniques and tools in a common ecosystem. In this paper, we present the Parallel Particle-Mesh Environment (PPME), a DSL and development environment for numerical simulations based on particle methods and hybrid particle-mesh methods. PPME uses the meta programming system (MPS), a projectional language workbench. PPME is the successor of the Parallel Particle-Mesh Language (PPML), a Fortran-based DSL that used conventional implementation strategies. We analyze and compare both languages and demonstrate how the programmer's experience can be improved using static analyses and projectional editing. Furthermore, we present an explicit domain model for particle abstractions and the first formal type system for particle methods.Comment: Submitted to ACM Transactions on Mathematical Software on Dec. 25, 201