High Performance Reconfigurable Computing for Linear Algebra: Design and Performance Analysis

Field Programmable Gate Arrays (FPGAs) enable powerful performance acceleration for scientific computations because of their intrinsic parallelism, pipeline ability, and flexible architecture. This dissertation explores the computational power of FPGAs for an important scientific application: linear algebra. First of all, optimized linear algebra subroutines are presented based on enhancements to both algorithms and hardware architectures. Compared to microprocessors, these routines achieve significant speedup. Second, computing with mixed-precision data on FPGAs is proposed for higher performance. Experimental analysis shows that mixed-precision algorithms on FPGAs can achieve the high performance of using lower-precision data while keeping higher-precision accuracy for finding solutions of linear equations. Third, an execution time model is built for reconfigurable computers (RC), which plays an important role in performance analysis and optimal resource utilization of FPGAs. The accuracy and efficiency of parallel computing performance models often depend on mean maximum computations. Despite significant prior work, there have been no sufficient mathematical tools for this important calculation. This work presents an Effective Mean Maximum Approximation method, which is more general, accurate, and efficient than previous methods. Together, these research results help address how to make linear algebra applications perform better on high performance reconfigurable computing architectures

Efficiency analysis methodology of FPGAs based on lost frequencies, area and cycles

We propose a methodology to study and to quantify efficiency and the impact of overheads on runtime performance. Most work on High-Performance Computing (HPC) for FPGAs only studies runtime performance or cost, while we are interested in how far we are from peak performance and, more importantly, why. The efficiency of runtime performance is defined with respect to the ideal computational runtime in absence of inefficiencies. The analysis of the difference between actual and ideal runtime reveals the overheads and bottlenecks. A formal approach is proposed to decompose the efficiency into three components: frequency, area and cycles. After quantification of the efficiencies, a detailed analysis has to reveal the reasons for the lost frequencies, lost area and lost cycles. We propose a taxonomy of possible causes and practical methods to identify and quantify the overheads. The proposed methodology is applied on a number of use cases to illustrate the methodology. We show the interaction between the three components of efficiency and show how bottlenecks are revealed

Performance comparison of single-precision SPICE Model-Evaluation on FPGA, GPU, Cell, and multi-core processors

Automated code generation and performance tuning techniques for concurrent architectures such as GPUs, Cell and FPGAs can provide integer factor speedups over multi-core processor organizations for data-parallel, floating-point computation in SPICE model-evaluation. Our Verilog AMS compiler produces code for parallel evaluation of non-linear circuit models suitable for use in SPICE simulations where the same model is evaluated several times for all the devices in the circuit. Our compiler uses architecture specific parallelization strategies (OpenMP for multi-core, PThreads for Cell, CUDA for GPU, statically scheduled VLIW for FPGA) when producing code for these different architectures. We automatically explore different implementation configurations (e.g. unroll factor, vector length) using our performance-tuner to identify the best possible configuration for each architecture. We demonstrate speedups of 3- 182times for a Xilinx Virtex5 LX 330T, 1.3-33times for an IBM Cell, and 3-131times for an NVIDIA 9600 GT GPU over a 3 GHz Intel Xeon 5160 implementation for a variety of single-precision device models

A Model-based Design Framework for Application-specific Heterogeneous Systems

The increasing heterogeneity of computing systems enables higher performance and power efficiency. However, these improvements come at the cost of increasing the overall complexity of designing such systems. These complexities include constructing implementations for various types of processors, setting up and configuring communication protocols, and efficiently scheduling the computational work. The process for developing such systems is iterative and time consuming, with no well-defined performance goal. Current performance estimation approaches use source code implementations that require experienced developers and time to produce. We present a framework to aid in the design of heterogeneous systems and the performance tuning of applications. Our framework supports system construction: integrating custom hardware accelerators with existing cores into processors, integrating processors into cohesive systems, and mapping computations to processors to achieve overall application performance and efficient hardware usage. It also facilitates effective design space exploration using processor models (for both existing and future processors) that do not require source code implementations to estimate performance. We evaluate our framework using a variety of applications and implement them in systems ranging from low power embedded systems-on-chip (SoC) to high performance systems consisting of commercial-off-the-shelf (COTS) components. We show how the design process is improved, reducing the number of design iterations and unnecessary source code development ultimately leading to higher performing efficient systems

Using reconfigurable computing technology to accelerate matrix decomposition and applications

Matrix decomposition plays an increasingly significant role in many scientific and engineering applications. Among numerous techniques, Singular Value Decomposition (SVD) and Eigenvalue Decomposition (EVD) are widely used as factorization tools to perform Principal Component Analysis for dimensionality reduction and pattern recognition in image processing, text mining and wireless communications, while QR Decomposition (QRD) and sparse LU Decomposition (LUD) are employed to solve the dense or sparse linear system of equations in bioinformatics, power system and computer vision. Matrix decompositions are computationally expensive and their sequential implementations often fail to meet the requirements of many time-sensitive applications. The emergence of reconfigurable computing has provided a flexible and low-cost opportunity to pursue high-performance parallel designs, and the use of FPGAs has shown promise in accelerating this class of computation. In this research, we have proposed and implemented several highly parallel FPGA-based architectures to accelerate matrix decompositions and their applications in data mining and signal processing. Specifically, in this dissertation we describe the following contributions: • We propose an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. • We implement a floating-point Hestenes-Jacobi architecture for SVD, which is capable of analyzing arbitrary sized matrices. • We introduce a novel deeply pipelined reconfigurable architecture for QRD, which can be dynamically configured to perform either Householder transformation or Givens rotation in a manner that takes advantage of the strengths of each. • We design a configurable architecture for sparse LUD that supports both symmetric and asymmetric sparse matrices with arbitrary sparsity patterns. • By further extending the proposed hardware solution for SVD, we parallelize a popular text mining tool-Latent Semantic Indexing with an FPGA-based architecture. • We present a configurable architecture to accelerate Homotopy l1-minimization, in which the modification of the proposed FPGA architecture for sparse LUD is used at its core to parallelize both Cholesky decomposition and rank-1 update. Our experimental results using an FPGA-based acceleration system indicate the efficiency of our proposed novel architectures, with application and dimension-dependent speedups over an optimized software implementation that range from 1.5ÃÂ to 43.6ÃÂ in terms of computation time

FBLAS: Streaming Linear Algebra on FPGA

Spatial computing architectures pose an attractive alternative to mitigate control and data movement overheads typical of load-store architectures. In practice, these devices are rarely considered in the HPC community due to the steep learning curve, low productivity and lack of available libraries for fundamental operations. High-level synthesis (HLS) tools are facilitating hardware programming, but optimizing for these architectures requires factoring in new transformations and resources/performance trade-offs. We present FBLAS, an open-source HLS implementation of BLAS for FPGAs, that enables reusability, portability and easy integration with existing software and hardware codes. FBLAS' implementation allows scaling hardware modules to exploit on-chip resources, and module interfaces are designed to natively support streaming on-chip communications, allowing them to be composed to reduce off-chip communication. With FBLAS, we set a precedent for FPGA library design, and contribute to the toolbox of customizable hardware components necessary for HPC codes to start productively targeting reconfigurable platforms

Efficient architectures and power modelling of multiresolution analysis algorithms on FPGA

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In the past two decades, there has been huge amount of interest in Multiresolution Analysis Algorithms (MAAs) and their applications. Processing some of their applications such as medical imaging are computationally intensive, power hungry and requires large amount of memory which cause a high demand for efficient algorithm implementation, low power architecture and acceleration. Recently, some MAAs such as Finite Ridgelet Transform (FRIT) Haar Wavelet Transform (HWT) are became very popular and they are suitable for a number of image processing applications such as detection of line singularities and contiguous edges, edge detection (useful for compression and feature detection), medical image denoising and segmentation. Efficient hardware implementation and acceleration of these algorithms particularly when addressing large problems are becoming very chal-lenging and consume lot of power which leads to a number of issues including mobility, reliability concerns. To overcome the computation problems, Field Programmable Gate Arrays (FPGAs) are the technology of choice for accelerating computationally intensive applications due to their high performance. Addressing the power issue requires optimi- sation and awareness at all level of abstractions in the design flow. The most important achievements of the work presented in this thesis are summarised here. Two factorisation methodologies for HWT which are called HWT Factorisation Method1 and (HWTFM1) and HWT Factorasation Method2 (HWTFM2) have been explored to increase number of zeros and reduce hardware resources. In addition, two novel efficient and optimised architectures for proposed methodologies based on Distributed Arithmetic (DA) principles have been proposed. The evaluation of the architectural results have shown that the proposed architectures results have reduced the arithmetics calculation (additions/subtractions) by 33% and 25% respectively compared to direct implementa-tion of HWT and outperformed existing results in place. The proposed HWTFM2 is implemented on advanced and low power FPGA devices using Handel-C language. The FPGAs implementation results have outperformed other existing results in terms of area and maximum frequency. In addition, a novel efficient architecture for Finite Radon Trans-form (FRAT) has also been proposed. The proposed architecture is integrated with the developed HWT architecture to build an optimised architecture for FRIT. Strategies such as parallelism and pipelining have been deployed at the architectural level for efficient im-plementation on different FPGA devices. The proposed FRIT architecture performance has been evaluated and the results outperformed some other existing architecture in place. Both FRAT and FRIT architectures have been implemented on FPGAs using Handel-C language. The evaluation of both architectures have shown that the obtained results out-performed existing results in place by almost 10% in terms of frequency and area. The proposed architectures are also applied on image data (256 £ 256) and their Peak Signal to Noise Ratio (PSNR) is evaluated for quality purposes. Two architectures for cyclic convolution based on systolic array using parallelism and pipelining which can be used as the main building block for the proposed FRIT architec-ture have been proposed. The first proposed architecture is a linear systolic array with pipelining process and the second architecture is a systolic array with parallel process. The second architecture reduces the number of registers by 42% compare to first architec-ture and both architectures outperformed other existing results in place. The proposed pipelined architecture has been implemented on different FPGA devices with vector size (N) 4,8,16,32 and word-length (W=8). The implementation results have shown a signifi-cant improvement and outperformed other existing results in place. Ultimately, an in-depth evaluation of a high level power macromodelling technique for design space exploration and characterisation of custom IP cores for FPGAs, called func-tional level power modelling approach have been presented. The mathematical techniques that form the basis of the proposed power modeling has been validated by a range of custom IP cores. The proposed power modelling is scalable, platform independent and compares favorably with existing approaches. A hybrid, top-down design flow paradigm integrating functional level power modelling with commercially available design tools for systematic optimisation of IP cores has also been developed. The in-depth evaluation of this tool enables us to observe the behavior of different custom IP cores in terms of power consumption and accuracy using different design methodologies and arithmetic techniques on virous FPGA platforms. Based on the results achieved, the proposed model accuracy is almost 99% true for all IP core's Dynamic Power (DP) components.Thomas Gerald Gray Charitable Trus