A Mixed Real and Floating-Point Solver

Reasoning about mixed real and floating-point constraints is essential for developing accurate analysis tools for floating-point pro- grams. This paper presents FPRoCK, a prototype tool for solving mixed real and floating-point formulas. FPRoCK transforms a mixed formula into an equisatisfiable one over the reals. This formula is then solved using an off-the-shelf SMT solver. FPRoCK is also integrated with the PRECiSA static analyzer, which computes a sound estimation of the round-off error of a floating-point program. It is used to detect infeasible computational paths, thereby improving the accuracy of PRECiSA

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

On Sound Relative Error Bounds for Floating-Point Arithmetic

State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the magnitude of the computed values. Relative errors, which compute errors relative to the value's magnitude, are thus preferable. While today's tools do report relative error bounds, these are merely computed via absolute errors and thus not necessarily tight or more informative. Furthermore, whenever the computed value is close to zero on part of the domain, the tools do not report any relative error estimate at all. Surprisingly, the quality of relative error bounds computed by today's tools has not been systematically studied or reported to date. In this paper, we investigate how state-of-the-art static techniques for computing sound absolute error bounds can be used, extended and combined for the computation of relative errors. Our experiments on a standard benchmark set show that computing relative errors directly, as opposed to via absolute errors, is often beneficial and can provide error estimates up to six orders of magnitude tighter, i.e. more accurate. We also show that interval subdivision, another commonly used technique to reduce over-approximations, has less benefit when computing relative errors directly, but it can help to alleviate the effects of the inherent issue of relative error estimates close to zero

Mira: A Framework for Static Performance Analysis

The performance model of an application can pro- vide understanding about its runtime behavior on particular hardware. Such information can be analyzed by developers for performance tuning. However, model building and analyzing is frequently ignored during software development until perfor- mance problems arise because they require significant expertise and can involve many time-consuming application runs. In this paper, we propose a fast, accurate, flexible and user-friendly tool, Mira, for generating performance models by applying static program analysis, targeting scientific applications running on supercomputers. We parse both the source code and binary to estimate performance attributes with better accuracy than considering just source or just binary code. Because our analysis is static, the target program does not need to be executed on the target architecture, which enables users to perform analysis on available machines instead of conducting expensive exper- iments on potentially expensive resources. Moreover, statically generated models enable performance prediction on non-existent or unavailable architectures. In addition to flexibility, because model generation time is significantly reduced compared to dynamic analysis approaches, our method is suitable for rapid application performance analysis and improvement. We present several scientific application validation results to demonstrate the current capabilities of our approach on small benchmarks and a mini application