Implementation and Evaluation of Algorithmic Skeletons: Parallelisation of Computer Algebra Algorithms

This thesis presents design and implementation approaches for the parallel algorithms of computer algebra. We use algorithmic skeletons and also further approaches, like data parallel arithmetic and actors. We have implemented skeletons for divide and conquer algorithms and some special parallel loops, that we call ‘repeated computation with a possibility of premature termination’. We introduce in this thesis a rational data parallel arithmetic. We focus on parallel symbolic computation algorithms, for these algorithms our arithmetic provides a generic parallelisation approach. The implementation is carried out in Eden, a parallel functional programming language based on Haskell. This choice enables us to encode both the skeletons and the programs in the same language. Moreover, it allows us to refrain from using two different languages—one for the implementation and one for the interface—for our implementation of computer algebra algorithms. Further, this thesis presents methods for evaluation and estimation of parallel execution times. We partition the parallel execution time into two components. One of them accounts for the quality of the parallelisation, we call it the ‘parallel penalty’. The other is the sequential execution time. For the estimation, we predict both components separately, using statistical methods. This enables very confident estimations, although using drastically less measurement points than other methods. We have applied both our evaluation and estimation approaches to the parallel programs presented in this thesis. We haven also used existing estimation methods. We developed divide and conquer skeletons for the implementation of fast parallel multiplication. We have implemented the Karatsuba algorithm, Strassen’s matrix multiplication algorithm and the fast Fourier transform. The latter was used to implement polynomial convolution that leads to a further fast multiplication algorithm. Specially for our implementation of Strassen algorithm we have designed and implemented a divide and conquer skeleton basing on actors. We have implemented the parallel fast Fourier transform, and not only did we use new divide and conquer skeletons, but also developed a map-and-transpose skeleton. It enables good parallelisation of the Fourier transform. The parallelisation of Karatsuba multiplication shows a very good performance. We have analysed the parallel penalty of our programs and compared it to the serial fraction—an approach, known from literature. We also performed execution time estimations of our divide and conquer programs. This thesis presents a parallel map+reduce skeleton scheme. It allows us to combine the usual parallel map skeletons, like parMap, farm, workpool, with a premature termination property. We use this to implement the so-called ‘parallel repeated computation’, a special form of a speculative parallel loop. We have implemented two probabilistic primality tests: the Rabin–Miller test and the Jacobi sum test. We parallelised both with our approach. We analysed the task distribution and stated the fitting configurations of the Jacobi sum test. We have shown formally that the Jacobi sum test can be implemented in parallel. Subsequently, we parallelised it, analysed the load balancing issues, and produced an optimisation. The latter enabled a good implementation, as verified using the parallel penalty. We have also estimated the performance of the tests for further input sizes and numbers of processing elements. Parallelisation of the Jacobi sum test and our generic parallelisation scheme for the repeated computation is our original contribution. The data parallel arithmetic was defined not only for integers, which is already known, but also for rationals. We handled the common factors of the numerator or denominator of the fraction with the modulus in a novel manner. This is required to obtain a true multiple-residue arithmetic, a novel result of our research. Using these mathematical advances, we have parallelised the determinant computation using the Gauß elimination. As always, we have performed task distribution analysis and estimation of the parallel execution time of our implementation. A similar computation in Maple emphasised the potential of our approach. Data parallel arithmetic enables parallelisation of entire classes of computer algebra algorithms. Summarising, this thesis presents and thoroughly evaluates new and existing design decisions for high-level parallelisations of computer algebra algorithms

Überblick zur Softwareentwicklung in Wissenschaftlichen Anwendungen

Viele wissenschaftliche Disziplinen müssen heute immer komplexer werdende numerische Probleme lösen. Die Komplexität der benutzten wissenschaftlichen Software steigt dabei kontinuierlich an. Diese Komplexitätssteigerung wird durch eine ganze Reihe sich ändernder Anforderungen verursacht: Die Betrachtung gekoppelter Phänomene gewinnt Aufmerksamkeit und gleichzeitig müssen neue Technologien wie das Grid-Computing oder neue Multiprozessorarchitekturen genutzt werden, um weiterhin in angemessener Zeit zu Berechnungsergebnissen zu kommen. Diese Fülle an neuen Anforderungen kann nicht mehr von kleinen spezialisierten Wissenschaftlergruppen in Isolation bewältigt werden. Die Entwicklung wissenschaftlicher Software muss vielmehr in interdisziplinären Gruppen geschehen, was neue Herausforderungen in der Softwareentwicklung induziert. Ein Paradigmenwechsel zu einer stärkeren Separation von Verantwortlichkeiten innerhalb interdisziplinärer Entwicklergruppen ist bis jetzt in vielen Fällen nur in Ansätzen erkennbar. Die Kopplung partitioniert durchgeführter Simulationen physikalischer Phänomene ist ein wichtiges Beispiel für softwaretechnisch herausfordernde Aufgaben im Gebiet des wissenschaftlichen Rechnens. In diesem Kontext modellieren verschiedene Simulationsprogramme unterschiedliche Teile eines komplexeren gekoppelten Systems. Die vorliegende Arbeit gibt einen Überblick über Paradigmen, die darauf abzielen Softwareentwicklung für Berechnungsprogramme verlässlicher und weniger abhängig voneinander zu machen. Ein spezielles Augenmerk liegt auf der Entwicklung gekoppelter Simulationen.Fields of modern science and engineering are in need of solving more and more complex numerical problems. The complexity of scientific software thereby rises continuously. This growth is caused by a number of changing requirements. Coupled phenomena gain importance and new technologies like the computational Grid, graphical and heterogeneous multi-core processors have to be used to achieve high-performance. The amount of additional complexity can not be handled by small groups of specialised scientists. The interdiciplinary nature of scientific software thereby presents new challanges for software engineering. A paradigm shift towards a stronger separation of concerns becomes necessary in the development of future scientific software. The coupling of independently simulated physical phenomena is an important example for a software-engineering concern in the domain of computational science. In this context, different simulation-programs model only a part of a more complex coupled system. The present work gives overview on paradigms which aim at making software-development in computational sciences more reliable and less interdependent. A special focus is put on the development of coupled simulations

Model-Based Performance Prediction for Concurrent Software on Multicore Architectures

Model-based performance prediction is a well-known concept to ensure the quality of software.Current approaches are based on a single-metric model, which leads to inaccurate predictions for modern architectures. This thesis presents a multi-strategies approach to extend performance prediction models to support multicore architectures.We implemented the strategies into Palladio and significantly increased the performance prediction power

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Parallel and Distributed Execution of Model Management Programs

The engineering process of complex systems involves many stakeholders and development artefacts. Model-Driven Engineering (MDE) is an approach to development which aims to help curtail and better manage this complexity by raising the level of abstraction. In MDE, models are first-class artefacts in the development process. Such models can be used to describe artefacts of arbitrary complexity at various levels of abstraction according to the requirements of their prospective stakeholders. These models come in various sizes and formats and can be thought of more broadly as structured data. Since models are the primary artefacts in MDE, and the goal is to enhance the efficiency of the development process, powerful tools are required to work with such models at an appropriate level of abstraction. Model management tasks – such as querying, validation, comparison, transformation and text generation – are often performed using dedicated languages, with declarative constructs used to improve expressiveness. Despite their semantically constrained nature, the execution engines of these languages rarely capitalize on the optimization opportunities afforded to them. Therefore, working with very large models often leads to poor performance when using MDE tools compared to general-purpose programming languages, which has a detrimental effect on productivity. Given the stagnant single-threaded performance of modern CPUs along with the ubiquity of distributed computing, parallelization of these model management program is a necessity to address some of the scalability concerns surrounding MDE. This thesis demonstrates efficient parallel and distributed execution algorithms for model validation, querying and text generation and evaluates their effectiveness. By fully utilizing the CPUs on 26 hexa-core systems, we were able to improve performance of a complex model validation language by 122x compared to its existing sequential implementation. Up to 11x speedup was achieved with 16 cores for model query and model-to-text transformation tasks

XXV Congreso Argentino de Ciencias de la Computación - CACIC 2019: libro de actas

Trabajos presentados en el XXV Congreso Argentino de Ciencias de la Computación (CACIC), celebrado en la ciudad de Río Cuarto los días 14 al 18 de octubre de 2019 organizado por la Red de Universidades con Carreras en Informática (RedUNCI) y Facultad de Ciencias Exactas, Físico-Químicas y Naturales - Universidad Nacional de Río CuartoRed de Universidades con Carreras en Informátic

XXV Congreso Argentino de Ciencias de la Computación - CACIC 2019: libro de actas

Trabajos presentados en el XXV Congreso Argentino de Ciencias de la Computación (CACIC), celebrado en la ciudad de Río Cuarto los días 14 al 18 de octubre de 2019 organizado por la Red de Universidades con Carreras en Informática (RedUNCI) y Facultad de Ciencias Exactas, Físico-Químicas y Naturales - Universidad Nacional de Río CuartoRed de Universidades con Carreras en Informátic