Solving shallow-water systems in 2D domains using Finite Volume methods and multimedia SSE instructions

AbstractThe goal of this paper is to construct efficient parallel solvers for 2D hyperbolic systems of conservation laws with source terms and nonconservative products. The method of lines is applied: at every intercell a projected Riemann problem along the normal direction is considered which is discretized by means of well-balanced Roe methods. The resulting 2D numerical scheme is explicit and first-order accurate. In [M.J. Castro, J.A. García, J.M. González, C. Pares, A parallel 2D Finite Volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows, Comput. Methods Appl. Mech. Engrg. 196 (2006) 2788–2815] a domain decomposition method was used to parallelize the resulting numerical scheme, which was implemented in a PC cluster by means of MPI techniques.In this paper, in order to optimize the computations, a new parallelization of SIMD type is performed at each MPI thread, by means of SSE (“Streaming SIMD Extensions”), which are present in common processors. More specifically, as the most costly part of the calculations performed at each processor consists of a huge number of small matrix and vector computations, we use the Intel© Integrated Performance Primitives small matrix library. To make easy the use of this library, which is implemented using assembler and SSE instructions, we have developed a C++ wrapper of this library in an efficient way. Some numerical tests were carried out to validate the performance of the C++ small matrix wrapper. The specific application of the scheme to one-layer Shallow-Water systems has been implemented on a PC’s cluster. The correct behavior of the one-layer model is assessed using laboratory data

On the design of architecture-aware algorithms for emerging applications

This dissertation maps various kernels and applications to a spectrum of programming models and architectures and also presents architecture-aware algorithms for different systems. The kernels and applications discussed in this dissertation have widely varying computational characteristics. For example, we consider both dense numerical computations and sparse graph algorithms. This dissertation also covers emerging applications from image processing, complex network analysis, and computational biology. We map these problems to diverse multicore processors and manycore accelerators. We also use new programming models (such as Transactional Memory, MapReduce, and Intel TBB) to address the performance and productivity challenges in the problems. Our experiences highlight the importance of mapping applications to appropriate programming models and architectures. We also find several limitations of current system software and architectures and directions to improve those. The discussion focuses on system software and architectural support for nested irregular parallelism, Transactional Memory, and hybrid data transfer mechanisms. We believe that the complexity of parallel programming can be significantly reduced via collaborative efforts among researchers and practitioners from different domains. This dissertation participates in the efforts by providing benchmarks and suggestions to improve system software and architectures.Ph.D.Committee Chair: Bader, David; Committee Member: Hong, Bo; Committee Member: Riley, George; Committee Member: Vuduc, Richard; Committee Member: Wills, Scot

Programming Dense Linear Algebra Kernels on Vectorized Architectures

The high performance computing (HPC) community is obsessed over the general matrix-matrix multiply (GEMM) routine. This obsession is not without reason. Most, if not all, Level 3 Basic Linear Algebra Subroutines (BLAS) can be written in terms of GEMM, and many of the higher level linear algebra solvers\u27 (i.e., LU, Cholesky) performance depend on GEMM\u27s performance. Getting high performance on GEMM is highly architecture dependent, and so for each new architecture that comes out, GEMM has to be programmed and tested to achieve maximal performance. Also, with emergent computer architectures featuring more vector-based and multi to many-core processors, GEMM performance becomes hinged to the utilization of these technologies. In this research, three Intel processor architectures are explored, including the new Intel MIC Architecture. Each architecture has different vector lengths and number of cores. The effort given to create three Level 3 BLAS routines (GEMM, TRSM, SYRK) is examined with respect to the architectural features as well as some parallel algorithmic nuances. This thorough examination culminates in a Cholesky (POTRF) routine which offers a legitimate test application. Lastly, four shared memory, parallel languages are explored for these routines to explore single-node supercomputing performance. These languages are OpenMP, Pthreads, Cilk and TBB. Each routine is developed in each language offering up information about which language is superior. A clear picture develops showing how these and similar routines should be written in OpenMP and exactly what architectural features chiefly impact performance

Classification algorithms on the cell processor

The rapid advancement in the capacity and reliability of data storage technology has allowed for the retention of virtually limitless quantity and detail of digital information. Massive information databases are becoming more and more widespread among governmental, educational, scientific, and commercial organizations. By segregating this data into carefully defined input (e.g.: images) and output (e.g.: classification labels) sets, a classification algorithm can be used develop an internal expert model of the data by employing a specialized training algorithm. A properly trained classifier is capable of predicting the output for future input data from the same input domain that it was trained on. Two popular classifiers are Neural Networks and Support Vector Machines. Both, as with most accurate classifiers, require massive computational resources to carry out the training step and can take months to complete when dealing with extremely large data sets. In most cases, utilizing larger training improves the final accuracy of the trained classifier. However, access to the kinds of computational resources required to do so is expensive and out of reach of private or under funded institutions. The Cell Broadband Engine (CBE), introduced by Sony, Toshiba, and IBM has recently been introduced into the market. The current most inexpensive iteration is available in the Sony Playstation 3 ® computer entertainment system. The CBE is a novel multi-core architecture which features many hardware enhancements designed to accelerate the processing of massive amounts of data. These characteristics and the cheap and widespread availability of this technology make the Cell a prime candidate for the task of training classifiers. In this work, the feasibility of the Cell processor in the use of training Neural Networks and Support Vector Machines was explored. In the Neural Network family of classifiers, the fully connected Multilayer Perceptron and Convolution Network were implemented. In the Support Vector Machine family, a Working Set technique known as the Gradient Projection-based Decomposition Technique, as well as the Cascade SVM were implemented

Efficient Linear

This thesis use the extreme powers of the GPU for linear algebra. Selected linear algebra algorithms, more specifically the LU and the conjugate gradient algorithm for solving linear systems, has been ported to execute its main computational load on the graphics processing unit available on most computers. The main contributions in the thesis is more efficient pivoting in the LU-algorithm, where a minimum of data is copied, and gathering of the inner products for simultainous readback and reduction on the GPU

Castell: a heterogeneous cmp architecture scalable to hundreds of processors

Technology improvements and power constrains have taken multicore architectures to dominate microprocessor designs over uniprocessors. At the same time, accelerator based architectures have shown that heterogeneous multicores are very efficient and can provide high throughput for parallel applications, but with a high-programming effort. We propose Castell a scalable chip multiprocessor architecture that can be programmed as uniprocessors, and provides the high throughput of accelerator-based architectures. Castell relies on task-based programming models that simplify software development. These models use a runtime system that dynamically finds, schedules, and adds hardware-specific features to parallel tasks. One of these features is DMA transfers to overlap computation and data movement, which is known as double buffering. This feature allows applications on Castell to tolerate large memory latencies and lets us design the memory system focusing on memory bandwidth. In addition to provide programmability and the design of the memory system, we have used a hierarchical NoC and added a synchronization module. The NoC design distributes memory traffic efficiently to allow the architecture to scale. The synchronization module is a consequence of the large performance degradation of application for large synchronization latencies. Castell is mainly an architecture framework that enables the definition of domain-specific implementations, fine-tuned to a particular problem or application. So far, Castell has been successfully used to propose heterogeneous multicore architectures for scientific kernels, video decoding (using H.264), and protein sequence alignment (using Smith-Waterman and clustalW). It has also been used to explore a number of architecture optimizations such as enhanced DMA controllers, and architecture support for task-based programming models. ii

SPICE²: A Spatial, Parallel Architecture for Accelerating the Spice Circuit Simulator

Spatial processing of sparse, irregular floating-point computation using a single FPGA enables up to an order of magnitude speedup (mean 2.8X speedup) over a conventional microprocessor for the SPICE circuit simulator. We deliver this speedup using a hybrid parallel architecture that spatially implements the heterogeneous forms of parallelism available in SPICE. We decompose SPICE into its three constituent phases: Model-Evaluation, Sparse Matrix-Solve, and Iteration Control and parallelize each phase independently. We exploit data-parallel device evaluations in the Model-Evaluation phase, sparse dataflow parallelism in the Sparse Matrix-Solve phase and compose the complete design in streaming fashion. We name our parallel architecture SPICE²: Spatial Processors Interconnected for Concurrent Execution for accelerating the SPICE circuit simulator. We program the parallel architecture with a high-level, domain-specific framework that identifies, exposes and exploits parallelism available in the SPICE circuit simulator. This design is optimized with an auto-tuner that can scale the design to use larger FPGA capacities without expert intervention and can even target other parallel architectures with the assistance of automated code-generation. This FPGA architecture is able to outperform conventional processors due to a combination of factors including high utilization of statically-scheduled resources, low-overhead dataflow scheduling of fine-grained tasks, and overlapped processing of the control algorithms. We demonstrate that we can independently accelerate Model-Evaluation by a mean factor of 6.5X(1.4--23X) across a range of non-linear device models and Matrix-Solve by 2.4X(0.6--13X) across various benchmark matrices while delivering a mean combined speedup of 2.8X(0.2--11X) for the two together when comparing a Xilinx Virtex-6 LX760 (40nm) with an Intel Core i7 965 (45nm). With our high-level framework, we can also accelerate Single-Precision Model-Evaluation on NVIDIA GPUs, ATI GPUs, IBM Cell, and Sun Niagara 2 architectures. We expect approaches based on exploiting spatial parallelism to become important as frequency scaling slows down and modern processing architectures turn to parallelism (\eg multi-core, GPUs) due to constraints of power consumption. This thesis shows how to express, exploit and optimize spatial parallelism for an important class of problems that are challenging to parallelize.</p

Running stream-like programs on heterogeneous multi-core systems

All major semiconductor companies are now shipping multi-cores. Phones, PCs, laptops, and mobile internet devices will all require software that can make effective use of these cores. Writing high-performance parallel software is difficult, time-consuming and error prone, increasing both time-to-market and cost. Software outlives hardware; it typically takes longer to develop new software than hardware, and legacy software tends to survive for a long time, during which the number of cores per system will increase. Development and maintenance productivity will be improved if parallelism and technical details are managed by the machine, while the programmer reasons about the application as a whole. Parallel software should be written using domain-specific high-level languages or extensions. These languages reveal implicit parallelism, which would be obscured by a sequential language such as C. When memory allocation and program control are managed by the compiler, the program's structure and data layout can be safely and reliably modified by high-level compiler transformations. One important application domain contains so-called stream programs, which are structured as independent kernels interacting only through one-way channels, called streams. Stream programming is not applicable to all programs, but it arises naturally in audio and video encode and decode, 3D graphics, and digital signal processing. This representation enables high-level transformations, including kernel unrolling and kernel fusion. This thesis develops new compiler and run-time techniques for stream programming. The first part of the thesis is concerned with a statically scheduled stream compiler. It introduces a new static partitioning algorithm, which determines which kernels should be fused, in order to balance the loads on the processors and interconnects. A good partitioning algorithm is crucial if the compiler is to produce efficient code. The algorithm also takes account of downstream compiler passes---specifically software pipelining and buffer allocation---and it models the compiler's ability to fuse kernels. The latter is important because the compiler may not be able to fuse arbitrary collections of kernels. This thesis also introduces a static queue sizing algorithm. This algorithm is important when memory is distributed, especially when local stores are small. The algorithm takes account of latencies and variations in computation time, and is constrained by the sizes of the local memories. The second part of this thesis is concerned with dynamic scheduling of stream programs. First, it investigates the performance of known online, non-preemptive, non-clairvoyant dynamic schedulers. Second, it proposes two dynamic schedulers for stream programs. The first is specifically for one-dimensional stream programs. The second is more general: it does not need to be told the stream graph, but it has slightly larger overhead. This thesis also introduces some support tools related to stream programming. StarssCheck is a debugging tool, based on Valgrind, for the StarSs task-parallel programming language. It generates a warning whenever the program's behaviour contradicts a pragma annotation. Such behaviour could otherwise lead to exceptions or race conditions. StreamIt to OmpSs is a tool to convert a streaming program in the StreamIt language into a dynamically scheduled task based program using StarSs.Totes les empreses de semiconductors produeixen actualment multi-cores. Mòbils,PCs, portàtils, i dispositius mòbils d’Internet necessitaran programari quefaci servir eficientment aquests cores. Escriure programari paral·lel d’altrendiment és difícil, laboriós i propens a errors, incrementant tant el tempsde llançament al mercat com el cost. El programari té una vida més llarga queel maquinari; típicament pren més temps desenvolupar nou programi que noumaquinari, i el programari ja existent pot perdurar molt temps, durant el qualel nombre de cores dels sistemes incrementarà. La productivitat dedesenvolupament i manteniment millorarà si el paral·lelisme i els detallstècnics són gestionats per la màquina, mentre el programador raona sobre elconjunt de l’aplicació.El programari paral·lel hauria de ser escrit en llenguatges específics deldomini. Aquests llenguatges extrauen paral·lelisme implícit, el qual és ocultatper un llenguatge seqüencial com C. Quan l’assignació de memòria i lesestructures de control són gestionades pel compilador, l’estructura iorganització de dades del programi poden ser modificades de manera segura ifiable per les transformacions d’alt nivell del compilador.Un dels dominis de l’aplicació importants és el que consta dels programes destream; aquest programes són estructurats com a nuclis independents queinteractuen només a través de canals d’un sol sentit, anomenats streams. Laprogramació de streams no és aplicable a tots els programes, però sorgeix deforma natural en la codificació i descodificació d’àudio i vídeo, gràfics 3D, iprocessament de senyals digitals. Aquesta representació permet transformacionsd’alt nivell, fins i tot descomposició i fusió de nucli.Aquesta tesi desenvolupa noves tècniques de compilació i sistemes en tempsd’execució per a programació de streams. La primera part d’aquesta tesi esfocalitza amb un compilador de streams de planificació estàtica. Presenta unnou algorisme de partició estàtica, que determina quins nuclis han de serfusionats, per tal d’equilibrar la càrrega en els processadors i en lesinterconnexions. Un bon algorisme de particionat és fonamental per tal de queel compilador produeixi codi eficient. L’algorisme també té en compte elspassos de compilació subseqüents---específicament software pipelining il’arranjament de buffers---i modela la capacitat del compilador per fusionarnuclis. Aquesta tesi també presenta un algorisme estàtic de redimensionament de cues.Aquest algorisme és important quan la memòria és distribuïda, especialment quanles memòries locals són petites. L’algorisme té en compte latències ivariacions en els temps de càlcul, i considera el límit imposat per la mida deles memòries locals.La segona part d’aquesta tesi es centralitza en la planificació dinàmica deprogrames de streams. En primer lloc, investiga el rendiment dels planificadorsdinàmics online, non-preemptive i non-clairvoyant. En segon lloc, proposa dosplanificadors dinàmics per programes de stream. El primer és específicament pera programes de streams unidimensionals. El segon és més general: no necessitael graf de streams, però els overheads són una mica més grans.Aquesta tesi també presenta un conjunt d’eines de suport relacionades amb laprogramació de streams. StarssCheck és una eina de depuració, que és basa enValgrind, per StarSs, un llenguatge de programació paral·lela basat en tasques.Aquesta eina genera un avís cada vegada que el comportament del programa estàen contradicció amb una anotació pragma. Aquest comportament d’una altra manerapodria causar excepcions o situacions de competició. StreamIt to OmpSs és unaeina per convertir un programa de streams codificat en el llenguatge StreamIt aun programa de tasques en StarSs planificat de forma dinàmica.Postprint (published version