FFT-Based Fast Computation of Multivariate Kernel Estimators with Unconstrained Bandwidth Matrices

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes the fast Fourier transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In this paper we describe the problem and give a satisfactory solution. The proposed solution may be successfully used also in other research problems, for example for the fast computation of the optimal bandwidth for KDE.Comment: 10 pages, 1 figure, R source code

FPGA-Based Bandwidth Selection for Kernel Density Estimation Using High Level Synthesis Approach

FPGA technology can offer significantly hi\-gher performance at much lower power consumption than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using ha\-rdware description languages, HDL) is a difficult and not-trivial task and is not intuitive for C/C++/Java programmers. To bring the gap between programming effectiveness and difficulty the High Level Synthesis (HLS) approach is promoting by main FPGA vendors. Nowadays, time-intensive calculations are mainly performed on GPU/CPU architectures, but can also be successfully performed using HLS approach. In the paper we implement a bandwidth selection algorithm for kernel density estimation (KDE) using HLS and show techniques which were used to optimize the final FPGA implementation. We are also going to show that FPGA speedups, comparing to highly optimized CPU and GPU implementations, are quite substantial. Moreover, power consumption for FPGA devices is usually much less than typical power consumption of the present CPUs and GPUs.Comment: 23 pages, 6 figures, extended version of initial pape

Lichttransportsimulation auf Spezialhardware

It cannot be denied that the developments in computer hardware and in computer algorithms strongly influence each other, with new instructions added to help with video processing, encryption, and in many other areas. At the same time, the current cap on single threaded performance and wide availability of multi-threaded processors has increased the focus on parallel algorithms. Both influences are extremely prominent in computer graphics, where the gaming and movie industries always strive for the best possible performance on the current, as well as future, hardware. In this thesis we examine the hardware-algorithm synergies in the context of ray tracing and Monte-Carlo algorithms. First, we focus on the very basic element of all such algorithms - the casting of rays through a scene, and propose a dedicated hardware unit to accelerate this common operation. Then, we examine existing and novel implementations of many Monte-Carlo rendering algorithms on massively parallel hardware, as full hardware utilization is essential for peak performance. Lastly, we present an algorithm for tackling complex interreflections of glossy materials, which is designed to utilize both powerful processing units present in almost all current computers: the Centeral Processing Unit (CPU) and the Graphics Processing Unit (GPU). These three pieces combined show that it is always important to look at hardware-algorithm mapping on all levels of abstraction: instruction, processor, and machine.Zweifelsohne beeinflussen sich Computerhardware und Computeralgorithmen gegenseitig in ihrer Entwicklung: Prozessoren bekommen neue Instruktionen, um zum Beispiel Videoverarbeitung, Verschlüsselung oder andere Anwendungen zu beschleunigen. Gleichzeitig verstärkt sich der Fokus auf parallele Algorithmen, bedingt durch die limitierte Leistung von für einzelne Threads und die inzwischen breite Verfügbarkeit von multi-threaded Prozessoren. Beide Einflüsse sind im Grafikbereich besonders stark , wo es z.B. für die Spiele- und Filmindustrie wichtig ist, die bestmögliche Leistung zu erreichen, sowohl auf derzeitiger und zukünftiger Hardware. In Rahmen dieser Arbeit untersuchen wir die Synergie von Hardware und Algorithmen anhand von Ray-Tracing- und Monte-Carlo-Algorithmen. Zuerst betrachten wir einen grundlegenden Hardware-Bausteins für alle diese Algorithmen, die Strahlenverfolgung in einer Szene, und präsentieren eine spezielle Hardware-Einheit zur deren Beschleunigung. Anschließend untersuchen wir existierende und neue Implementierungen verschiedener MonteCarlo-Algorithmen auf massiv-paralleler Hardware, wobei die maximale Auslastung der Hardware im Fokus steht. Abschließend stellen wir dann einen Algorithmus zur Berechnung von komplexen Beleuchtungseffekten bei glänzenden Materialien vor, der versucht, die heute fast überall vorhandene Kombination aus Hauptprozessor (CPU) und Grafikprozessor (GPU) optimal auszunutzen. Zusammen zeigen diese drei Aspekte der Arbeit, wie wichtig es ist, Hardware und Algorithmen auf allen Ebenen gleichzeitig zu betrachten: Auf den Ebenen einzelner Instruktionen, eines Prozessors bzw. eines gesamten Systems

Contributions to the efficient use of general purpose coprocessors: kernel density estimation as case study

142 p.The high performance computing landscape is shifting from assemblies of homogeneous nodes towards heterogeneous systems, in which nodes consist of a combination of traditional out-of-order execution cores and accelerator devices. Accelerators provide greater theoretical performance compared to traditional multi-core CPUs, but exploiting their computing power remains as a challenging task.This dissertation discusses the issues that arise when trying to efficiently use general purpose accelerators. As a contribution to aid in this task, we present a thorough survey of performance modeling techniques and tools for general purpose coprocessors. Then we use as case study the statistical technique Kernel Density Estimation (KDE). KDE is a memory bound application that poses several challenges for its adaptation to the accelerator-based model. We present a novel algorithm for the computation of KDE that reduces considerably its computational complexity, called S-KDE. Furthermore, we have carried out two parallel implementations of S-KDE, one for multi and many-core processors, and another one for accelerators. The latter has been implemented in OpenCL in order to make it portable across a wide range of devices. We have evaluated the performance of each implementation of S-KDE in a variety of architectures, trying to highlight the bottlenecks and the limits that the code reaches in each device. Finally, we present an application of our S-KDE algorithm in the field of climatology: a novel methodology for the evaluation of environmental models

Video Processing Acceleration using Reconfigurable Logic and Graphics Processors

A vexing question is `which architecture will prevail as the core feature of the next state of the art video processing system?' This thesis examines the substitutive and collaborative use of the two alternatives of the reconfigurable logic and graphics processor architectures. A structured approach to executing architecture comparison is presented - this includes a proposed `Three Axes of Algorithm Characterisation' scheme and a formulation of perfor- mance drivers. The approach is an appealing platform for clearly defining the problem, assumptions and results of a comparison. In this work it is used to resolve the advanta- geous factors of the graphics processor and reconfigurable logic for video processing, and the conditions determining which one is superior. The comparison results prompt the exploration of the customisable options for the graphics processor architecture. To clearly define the architectural design space, the graphics processor is first identifed as part of a wider scope of homogeneous multi-processing element (HoMPE) architectures. A novel exploration tool is described which is suited to the investigation of the customisable op- tions of HoMPE architectures. The tool adopts a systematic exploration approach and a high-level parameterisable system model, and is used to explore pre- and post-fabrication customisable options for the graphics processor. A positive result of the exploration is the proposal of a reconfigurable engine for data access (REDA) to optimise graphics processor performance for video processing-specific memory access patterns. REDA demonstrates the viability of the use of reconfigurable logic as collaborative `glue logic' in the graphics processor architecture