Optimisations arithmétiques et synthèse de haut niveau

High-level synthesis (HLS) tools offer increased productivity regarding FPGA programming.However, due to their relatively young nature, they still lack many arithmetic optimizations.This thesis proposes safe arithmetic optimizations that should always be applied.These optimizations are simple operator specializations, following the C semantic.Other require to a lift the semantic embedded in high-level input program languages, which are inherited from software programming, for an improved accuracy/cost/performance ratio.To demonstrate this claim, the sum-of-product of floating-point numbers is used as a case study. The sum is performed on a fixed-point format, which is tailored to the application, according to the context in which the operator is instantiated.In some cases, there is not enough information about the input data to tailor the fixed-point accumulator.The fall-back strategy used in this thesis is to generate an accumulator covering the entire floating-point range.This thesis explores different strategies for implementing such a large accumulator, including new ones.The use of a 2's complement representation instead of a sign+magnitude is demonstrated to save resources and to reduce the accumulation loop delay.Based on a tapered precision scheme and an exact accumulator, the posit number systems claims to be a candidate to replace the IEEE floating-point format.A throughout analysis of posit operators is performed, using the same level of hardware optimization as state-of-the-art floating-point operators.Their cost remains much higher that their floating-point counterparts in terms of resource usage and performance. Finally, this thesis presents a compatibility layer for HLS tools that allows one code to be deployed on multiple tools.This library implements a strongly typed custom size integer type along side a set of optimized custom operators.À cause de la nature relativement jeune des outils de synthèse de haut-niveau (HLS), de nombreuses optimisations arithmétiques n'y sont pas encore implémentées. Cette thèse propose des optimisations arithmétiques se servant du contexte spécifique dans lequel les opérateurs sont instanciés.Certaines optimisations sont de simples spécialisations d'opérateurs, respectant la sémantique du C.D'autres nécéssitent de s'éloigner de cette sémantique pour améliorer le compromis précision/coût/performance.Cette proposition est démontré sur des sommes de produits de nombres flottants.La somme est réalisée dans un format en virgule-fixe défini par son contexte.Quand trop peu d’informations sont disponibles pour définir ce format en virgule-fixe, une stratégie est de générer un accumulateur couvrant l'intégralité du format flottant.Cette thèse explore plusieurs implémentations d'un tel accumulateur.L'utilisation d'une représentation en complément à deux permet de réduire le chemin critique de la boucle d'accumulation, ainsi que la quantité de ressources utilisées. Un format alternatif aux nombres flottants, appelé posit, propose d'utiliser un encodage à précision variable.De plus, ce format est augmenté par un accumulateur exact.Pour évaluer précisément le coût matériel de ce format, cette thèse présente des architectures d'opérateurs posits, implémentés avec le même degré d'optimisation que celui de l'état de l'art des opérateurs flottants.Une analyse détaillée montre que le coût des opérateurs posits est malgré tout bien plus élevé que celui de leurs équivalents flottants.Enfin, cette thèse présente une couche de compatibilité entre outils de HLS, permettant de viser plusieurs outils avec un seul code. Cette bibliothèque implémente un type d'entiers de taille variable, avec de plus une sémantique strictement typée, ainsi qu'un ensemble d'opérateurs ad-hoc optimisés

Implementation and Synthesis of Math Library Functions

Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.Comment: 25 pages, 12 figure

Finding apparent horizons in numerical relativity

This paper presents a detailed discussion of the ``Newton's method'' algorithm for finding apparent horizons in 3+1 numerical relativity. We describe a method for computing the Jacobian matrix of the finite differenced H(h) function \H(\h) by symbolically differentiating the finite difference equations, giving the Jacobian elements directly in terms of the finite difference molecule coefficients used in computing \H(\h). Assuming the finite differencing scheme commutes with linearization, we show how the Jacobian elements may be computed by first linearizing the continuum H(h) equations, then finite differencing the linearized (continuum) equations. We find this symbolic differentiation method of computing the \H(\h) Jacobian to be {\em much\/} more efficient than the usual numerical-perturbation method, and also much easier to implement than is commonly thought. When solving the (discrete) \H(\h) = 0 equations, we find that Newton's method generally converges very rapidly, although there are difficulties when the initial guess contains high-spatial-frequency errors. Using 4th~order finite differencing, we find typical accuracies for the horizon position in the 10^{-5} range for \Delta \theta = \frac{\pi/2}{50}

Communication framework for distributed computer vision on stationary and mobile platforms

Recent advances in the complexity and manufacturability of digital video cameras coupled with the ubiquity of high speed computers and communication networks have led to burgeoning research in the fields of computer vision and image understanding. As the generated vision algorithms become increasingly complex, a need arises for robust communication between remote cameras on mobile units and their associated distributed vision algorithms. A communication framework would provide a basis for modularization and abstraction of a collection of computer vision algorithms; the resulting system would allow for straightforward image capture, simplified communication between algorithms, and easy replacement or upgrade of existing component algorithms. The objective of this thesis is to create such a communication framework and demonstrate its viability and applicability by implementing a relatively complex system of distributed computer vision algorithms. These multi-camera algorithms include body tracking, pose estimation and face recognition. Although a plethora of research exists documenting individual algorithms which may utilize multiple networked cameras, this thesis aims to develop a novel way of sharing information between cameras and algorithms in a distributed computation system. In addition, this thesis strives to extend such an approach to using both stationary and mobile cameras. For this application, a mobile computer vision platform was developed that integrates seamlessly with the aforementioned communication framework, extending both its functionality and robustness

Information-Theoretic Model Diagnostics (InfoMoD)

Model validation is a critical step in the development, deployment, and governance of machine learning models. During the validation process, the predictive power of a model is measured on unseen datasets with a variety of metrics such as Accuracy and F1-Scores for classification tasks. Although the most used metrics are easy to implement and understand, they are aggregate measures over all the segments of heterogeneous datasets, and therefore, they do not identify the performance variation of a model among different data segments. The lack of insight into how the model performs over segments of unseen datasets has raised significant challenges in deploying machine learning models into production environments. The unstable performance is especially concerning for critical applications such as credit risk models, cancer detection, and self-driving cars, which have significant impacts on users.In this dissertation, we leverage the notion of information-theoretic explanations to measure the performance of binary classifiers over various segments of data. We provide the following contributions: 1) A distributed implementation of the explanation framework that outperforms a single-node baseline. 2) An application of the framework to summarize the model’s performance over various segments of training and testing data in terms of overall accuracy as well as providing false-positive and false-negative patterns. 3) A further application of the framework to annotate test instances with expected performance indicators at the inference time. In addition to assisting machine learning engineers with model tuning and data augmentation decisions, the proposed tools can also identify potential model bias and unfairness with respect to protected attributes and data segments

FCAIR 2012 Formal Concept Analysis Meets Information Retrieval Workshop co-located with the 35th European Conference on Information Retrieval (ECIR 2013) March 24, 2013, Moscow, Russia

International audienceFormal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classifiation. The area came into being in the early 1980s and has since then spawned over 10000 scientific publications and a variety of practically deployed tools. FCA allows one to build from a data table with objects in rows and attributes in columns a taxonomic data structure called concept lattice, which can be used for many purposes, especially for Knowledge Discovery and Information Retrieval. The Formal Concept Analysis Meets Information Retrieval (FCAIR) workshop collocated with the 35th European Conference on Information Retrieval (ECIR 2013) was intended, on the one hand, to attract researchers from FCA community to a broad discussion of FCA-based research on information retrieval, and, on the other hand, to promote ideas, models, and methods of FCA in the community of Information Retrieval

Methodology of Algorithm Engineering

Research on algorithms has drastically increased in recent years. Various sub-disciplines of computer science investigate algorithms according to different objectives and standards. This plurality of the field has led to various methodological advances that have not yet been transferred to neighboring sub-disciplines. The central roadblock for a better knowledge exchange is the lack of a common methodological framework integrating the perspectives of these sub-disciplines. It is the objective of this paper to develop a research framework for algorithm engineering. Our framework builds on three areas discussed in the philosophy of science: ontology, epistemology and methodology. In essence, ontology describes algorithm engineering as being concerned with algorithmic problems, algorithmic tasks, algorithm designs and algorithm implementations. Epistemology describes the body of knowledge of algorithm engineering as a collection of prescriptive and descriptive knowledge, residing in World 3 of Popper's Three Worlds model. Methodology refers to the steps how we can systematically enhance our knowledge of specific algorithms. The framework helps us to identify and discuss various validity concerns relevant to any algorithm engineering contribution. In this way, our framework has important implications for researching algorithms in various areas of computer science