Related papers: Towards a Compiler for Reals
Large scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in…
This technical report presents the work done as part of the AutoSeer project. Our work in this project was to develop a source-to-source compiler, MANET, for the C language that could be used for instrumentation of critical parts of…
Data generation and analysis is a fundamental aspect of many industries and disciplines, from strategic decision making in business to research in the physical and social sciences. However, data generated using software and algorithms can…
We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method…
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…
Reverse engineering of binary executables is a critical problem in the computer security domain. On the one hand, malicious parties may recover interpretable source codes from the software products to gain commercial advantages. On the…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
We introduce a framework for repurposing error estimators for source problems to compute an estimator for the gap between eigenspaces and their discretizations. Of interest are eigenspaces of finite clusters of eigenvalues of unbounded…
The proliferation of low-precision units in modern high-performance architectures increasingly burdens domain scientists. Historically, the choice in HPC was easy: can we get away with 32 bit floating-point operations and lower bandwidth…
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…
We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…
The error function of real argument can be uniformly approximated to a given accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or…
Floating-point arithmetic is error-prone and unintuitive. Floating-point debuggers instrument programs to monitor floating-point arithmetic at run time and flag numerical issues. They estimate residues, i.e., the difference between actual…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
We develop a tool that enables domain experts to quickly generate numerical solvers for emerging multi-physics phenomena starting from a high-level description based on ordinary/partial differential equations and their initial and boundary…
Fault tolerance is a critical aspect of modern computing systems, ensuring correct functionality in the presence of faults. This paper presents a comprehensive survey of fault tolerance methods and software-based mitigation techniques in…
With the proliferation of embedded systems requiring intelligent behavior, custom number systems to optimize performance per Watt of the entire system become essential components for successful commercial products. We present the Universal…
Radio-Stereometric-Analysis and x-ray fluoroscopy are radiological techniques that require dedicated software to process data. The accurate calibration of these software is therefore critical. The aim of this work is to produce a protocol…
Correctness in scientific computing (SC) is gaining increasing attention in the formal methods (FM) and programming languages (PL) community. Existing PL/FM verification techniques struggle with the complexities of realistic SC…