Towards efficient exploitation of GPUs : a methodology for mapping index-digit algorithms

[Resumen]La computación de propósito general en GPUs supuso un gran paso, llevando la computación de alto rendimiento a los equipos domésticos. Lenguajes de programación de alto nivel como OpenCL y CUDA redujeron en gran medida la complejidad de programación. Sin embargo, para poder explotar totalmente el poder computacional de las GPUs, se requieren algoritmos paralelos especializados. La complejidad en la jerarquía de memoria y su arquitectura masivamente paralela hace que la programación de GPUs sea una tarea compleja incluso para programadores experimentados. Debido a la novedad, las librerías de propósito general son escasas y las versiones paralelas de los algoritmos no siempre están disponibles. En lugar de centrarnos en la paralelización de algoritmos concretos, en esta tesis proponemos una metodología general aplicable a la mayoría de los problemas de tipo divide y vencerás con una estructura de mariposa que puedan formularse a través de la representación Indice-Dígito. En primer lugar, se analizan los diferentes factores que afectan al rendimiento de la arquitectura de las GPUs. A continuación, estudiamos varias técnicas de optimización y diseñamos una serie de bloques constructivos modulares y reutilizables, que se emplean para crear los diferentes algoritmos. Por último, estudiamos el equilibrio óptimo de los recursos, y usando vectores de mapeo y operadores algebraicos ajustamos los algoritmos para las configuraciones deseadas. A pesar del enfoque centrado en la exibilidad y la facilidad de programación, las implementaciones resultantes ofrecen un rendimiento muy competitivo, que llega a superar conocidas librerías recientes.[Resumo] A computación de propósito xeral en GPUs supuxo un gran paso, levando a computación de alto rendemento aos equipos domésticos. Linguaxes de programación de alto nivel como OpenCL e CUDA reduciron en boa medida a complexidade da programación. Con todo, para poder aproveitar totalmente o poder computacional das GPUs, requírense algoritmos paralelos especializados. A complexidade na xerarquía de memoria e a súa arquitectura masivamente paralela fai que a programación de GPUs sexa unha tarefa complexa mesmo para programadores experimentados. Debido á novidade, as librarías de propósito xeral son escasas e as versións paralelas dos algoritmos non sempre están dispoñibles. En lugar de centrarnos na paralelización de algoritmos concretos, nesta tese propoñemos unha metodoloxía xeral aplicable á maioría dos problemas de tipo divide e vencerás cunha estrutura de bolboreta que poidan formularse a través da representación Índice-Díxito. En primeiro lugar, analízanse os diferentes factores que afectan ao rendemento da arquitectura das GPUs. A continuación, estudamos varias técnicas de optimización e deseñamos unha serie de bloques construtivos modulares e reutilizables, que se empregan para crear os diferentes algoritmos. Por último, estudamos o equilibrio óptimo dos recursos, e usando vectores de mapeo e operadores alxbricos axustamos os algoritmos para as configuracións desexadas. A pesar do enfoque centrado na exibilidade e a facilidade de programación, as implementacións resultantes ofrecen un rendemento moi competitivo, que chega a superar coñecidas librarías recentes.[Abstract]GPU computing supposed a major step forward, bringing high performance computing to commodity hardware. Feature-rich parallel languages like CUDA and OpenCL reduced the programming complexity. However, to fully take advantage of their computing power, specialized parallel algorithms are required. Moreover, the complex GPU memory hierarchy and highly threaded architecture makes programming a difficult task even for experienced programmers. Due to the novelty of GPU programming, common general purpose libraries are scarce and parallel versions of the algorithms are not always readily available. Instead of focusing in the parallelization of particular algorithms, in this thesis we propose a general methodology applicable to most divide-and-conquer problems with a buttery structure which can be formulated through the Index-Digit representation. First, we analyze the different performance factors of the GPU architecture. Next, we study several optimization techniques and design a series of modular and reusable building blocks, which will be used to create the different algorithms. Finally, we study the optimal resource balance, and through a mapping vector representation and operator algebra, we tune the algorithms for the desired configurations. Despite the focus on programmability and exibility, the resulting implementations offer very competitive performance, being able to surpass other well-known state of the art libraries

Solving Large Problem Sizes of Index-Digit Algorithms on GPU: FFT and Tridiagonal System Solvers

[Abstract] Current Graphics Processing Units (GPUs) are capable of obtaining high computational performance in scientific applications. Nevertheless, programmers have to use suitable parallel algorithms for these architectures and usually have to consider optimization techniques in the implementation in order to achieve said performance. There are many efficient proposals for limited-size problems which fit directly in the shared memory of CUDA GPUs, however, there are few GPU proposals that tackle the design of efficient algorithms for large problem sizes that exceed shared memory storage capacity. In this work, we present a tuning strategy that addresses this problem for some parallel prefix algorithms that can be represented according to a set of common permutations of the digits of each of its element indices [1], denoted as Index-Digit (ID) algorithms. Specifically, our strategy has been applied to develop flexible Multi-Stage (MS) algorithms for the Fast Fourier Transform (FFT) algorithm (MS-ID-FFT) and a tridiagonal system solver (MS-ID-TS) on the GPU. The resulting implementation is compact and outperforms other well-known and commonly used state-of-the-art libraries, with an improvement of up to 1.47x with respect to NVIDIA's complex CUFFT, and up to 33.2x in comparison with NVIDIA's CUSPARSE for real data tridiagonal systems

Parallelization of shallow water simulations on current multi-threaded systems

Lobeiras, J., Viñas, M., Amor, M., Fraguela, B.B., Arenaz, M., García, J., Castro, M. Parallelization of shallow water simulations on current multi-threaded systems. The International Journal of High Performance Computing Applications 27, 493–512. © 2013 The Author(s), © SAGE Publications. https://doi.org/10.1177/1094342012464800[Abstract]: In this work, several parallel implementations of a numerical model of pollutant transport on a shallow water system are presented. These parallel implementations are developed in two phases. First, the sequential code is rewritten to exploit the stream programming model. And second, the streamed code is targeted for current multi-threaded systems, in particular, multi-core CPUs and modern GPUs. The performance is evaluated on a multi-core CPU using OpenMP, and on a GPU using the streaming-oriented programming language Brook+, as well as the standard language for heterogeneous systems, OpenCL.Funding This work was supported by the Galician Government (Consolidation of Competitive Research Groups, Xunta de Galicia ref. 2010/6, projects INCITE08PXIB105161PR and 08TIC001206PR), the Ministry of Science and Innovation, cofunded by the FEDER funds of the European Union (grant number TIN2010-16735, and project numbers MTM2009-11923 and MTM2010-21135).Xunta de Galicia; INCITE08PXIB105161PRXunta de Galicia; 08TIC001206P

A multi-GPU shallow-water simulation with transport of contaminants

[Abstract] This work presents cost-effective multi-graphics processing unit (GPU) parallel implementations of a finite-volume numerical scheme for solving pollutant transport problems in bidimensional domains. The fluid is modeled by 2D shallow-water equations, whereas the transport of pollutant is modeled by a transport equation. The 2D domain is discretized using a first-order Roe finite-volume scheme. Specifically, this paper presents multi-GPU implementations of both a solution that exploits recomputation on the GPU and an optimized solution that is based on a ghost cell decoupling approach. Our multi-GPU implementations have been optimized using nonblocking communications, overlapping communications and computations and the application of ghost cell expansion to minimize communications. The fastest one reached a speedup of 78 × using four GPUs on an InfiniBand network with respect to a parallel execution on a multicore CPU with six cores and two-way hyperthreading per core. Such performance, measured using a realistic problem, enabled the calculation of solutions not only in real time but also in orders of magnitude faster than the simulated time.Copyright © 2012 John Wiley & Sons, Ltd