Avoiding double roundings in scaled Newton-Raphson division

Abstract-When performing divisions using Newton-Raphson (or similar) iterations on a processor with a floating-point fused multiply-add instruction, one must sometimes scale the iterations, to avoid over/underflow and/or loss of accuracy. This may lead to double-roundings, resulting in output values that may not be correctly rounded when the quotient falls in the subnormal range. We show how to avoid this problem

Dedicated Hardware for Complex Mathematical Operations

New hardware FPGA implementations for the efficient computations of division, natural logarithm and exponential function are proposed. The proposed implementations use generic floating-point adder and multiplier with small additional resources that are shared to compute more frequently used multiply and accumulate operations. Hardware sharing improved the resource utilization. The time of the computation has been reduced to only 6 clock cycles when the natural logarithm and exponential function are calculated. The division is calculated in 5 clock cycles. They are designed as technology independent high throughput computing cores with minimized memory requirements which can be used in higher numbers to significantly increased calculation speed in spectral processing. A new universal arithmetic floating-point unit is also proposed

Vers une arithmétique efficace pour le chiffrement homomorphe basé sur le Ring-LWE

Fully homomorphic encryption is a kind of encryption offering the ability to manipulate encrypted data directly through their ciphertexts. In this way it is possible to process sensitive data without having to decrypt them beforehand, ensuring therefore the datas' confidentiality. At the numeric and cloud computing era this kind of encryption has the potential to considerably enhance privacy protection. However, because of its recent discovery by Gentry in 2009, we do not have enough hindsight about it yet. Therefore several uncertainties remain, in particular concerning its security and efficiency in practice, and should be clarified before an eventual widespread use. This thesis deals with this issue and focus on performance enhancement of this kind of encryption in practice. In this perspective we have been interested in the optimization of the arithmetic used by these schemes, either the arithmetic underlying the Ring Learning With Errors problem on which the security of these schemes is based on, or the arithmetic specific to the computations required by the procedures of some of these schemes. We have also considered the optimization of the computations required by some specific applications of homomorphic encryption, and in particular for the classification of private data, and we propose methods and innovative technics in order to perform these computations efficiently. We illustrate the efficiency of our different methods through different software implementations and comparisons to the related art.Le chiffrement totalement homomorphe est un type de chiffrement qui permet de manipuler directement des données chiffrées. De cette manière, il est possible de traiter des données sensibles sans avoir à les déchiffrer au préalable, permettant ainsi de préserver la confidentialité des données traitées. À l'époque du numérique à outrance et du "cloud computing" ce genre de chiffrement a le potentiel pour impacter considérablement la protection de la vie privée. Cependant, du fait de sa découverte récente par Gentry en 2009, nous manquons encore de recul à son propos. C'est pourquoi de nombreuses incertitudes demeurent, notamment concernant sa sécurité et son efficacité en pratique, et devront être éclaircies avant une éventuelle utilisation à large échelle.Cette thèse s'inscrit dans cette problématique et se concentre sur l'amélioration des performances de ce genre de chiffrement en pratique. Pour cela nous nous sommes intéressés à l'optimisation de l'arithmétique utilisée par ces schémas, qu'elle soit sous-jacente au problème du "Ring-Learning With Errors" sur lequel la sécurité des schémas considérés est basée, ou bien spécifique aux procédures de calculs requises par certains de ces schémas. Nous considérons également l'optimisation des calculs nécessaires à certaines applications possibles du chiffrement homomorphe, et en particulier la classification de données privées, de sorte à proposer des techniques de calculs innovantes ainsi que des méthodes pour effectuer ces calculs de manière efficace. L'efficacité de nos différentes méthodes est illustrée à travers des implémentations logicielles et des comparaisons aux techniques de l'état de l'art

Avoiding double roundings in scaled Newton-Raphson division

Abstract—When performing divisions using Newton-Raphson (or similar) iterations on a processor with a floating-point fused multiply-add instruction, one must sometimes scale the iterations, to avoid over/underflow and/or loss of accuracy. This may lead to double-roundings, resulting in output values that may not be correctly rounded when the quotient falls in the subnormal range. We show how to avoid this problem. I

Vector Graphics for Real-time 3D Rendering

Algorithms are presented that enable the use of vector graphics representations of images in texture maps for 3D real time rendering. Vector graphics images are resolution independent and can be zoomed arbitrarily without losing detail or crispness. Many important types of images, including text and other symbolic information, are best represented in vector form. Vector graphics textures can also be used as transparency mattes to augment geometric detail in models via trim curves. Spline curves are used to represent boundaries around regions in standard vector graphics representations, such as PDF and SVG. Antialiased rendering of such content can be obtained by thresholding implicit representations of these curves. The distance function is an especially useful implicit representation. Accurate distance function computations would also allow the implementation of special effects such as embossing. Unfortunately, computing the true distance to higher order spline curves is too expensive for real time rendering. Therefore, normally either the distance is approximated by normalizing some other implicit representation or the spline curves are approximated with simpler primitives. In this thesis, three methods for rendering vector graphics textures in real time are introduced, based on various approximations of the distance computation. The first and simplest approach to the distance computation approximates curves with line segments. Unfortunately, approximation with line segments gives only C0 continuity. In order to improve smoothness, spline curves can also be approximated with circular arcs. This approximation has C1 continuity and computing the distance to a circular arc is only slightly more expensive than computing the distance to a line segment. Finally an iterative algorithm is discussed that has good performance in practice and can compute the distance to any parametrically differentiable curve (including polynomial splines of any order) robustly. This algorithm is demonstrated in the context of a system capable of real-time rendering of SVG content in a texture map on a GPU. Data structures and acceleration algorithms in the context of massively parallel GPU architectures are also discussed. These data structures and acceleration structures allow arbitrary vector content (with space-variant complexity, and overlapping regions) to be represented in a random-access texture

Quantifying the performance of natural ventilation windcatchers

This thesis was submitted for the degree of Doctor of Doctor of Environmental Technology and awarded by Brunel University, 2010.The significant energy consumption of non- domestic buildings has led to renewed interest in natural ventilation strategies that utilise the action of the wind, and the buoyancy of hot air. One natural ventilation element is the Windcatcher, a roof mounted device that works by channelling air into a room under the action of wind pressure, whilst simultaneously drawing air out of the room by virtue of a low pressure region created downstream of the element. A significant number of Windcatchers are fitted in UK schools where good indoor air quality is essential for the health and performance of children. The performance of a ventilation system in a school classroom is determined by its ability to provide ventilation in accordance with UK government ventilation, air quality, and acoustic requirements. However, there is only limited performance data available for a Windcatcher, particularly when operating in-situ. Accordingly, this thesis investigates the performance of a Windcatcher in three ways: First, a semi-empirical model is developed that combines an envelope flow model with existing experimental data. Second, measurements of air temperature, relative humidity, carbon dioxide, and noise levels in school classrooms are assessed over summer and winter months and the results compared against UK Government requirements. Finally, air flow rates are measured in twenty four classrooms and compared against the semi-empirical predictions. The monitoring reveals that air quality in classrooms ventilated by a Windcatcher has the potential to be better than that reported for conventional natural ventilation strategies such as windows. Furthermore, an autonomous Windcatcher is shown to deliver the minimum ventilation rates specified by the UK Government, and when combined with open windows a Windcatcher is also capable of providing the required mean and purge ventilation rates. These findings are then used to develop an algorithm that will size a Windcatcher for a particular application, as well as helping to improve the ventilation strategy for a building that employs a Windcatcher.This research was funded by the Engineering and Physical Sciences Research Council and Monodraught Ltd

Study of the vibration behavior of rotatory blades using the Finite Element Method

The physics lying behind rotordynamics is complex to model, so that in many cases numerical processing is the only feasible approach. Being rotordynamics a field of great interest in the aerospace industry, the efforts devoted to its understanding are increasing day by day. Following this tendency, the aim of the present study is to develop a simplified elastodynamic model for the case of rotating structures such that can be addressed through numerical tools, built using the finite element method. For the purpose of analysing the vibration phenomena, modal decomposition and numerical integration have been taken advantage from. In this context, it has been found that the singular value decomposition could be applied in structural analysis to extract dominant displacement fluctuations, allowing the unfolding of global properties of the dynamic response. In the present report, the singular value decomposition has been applied to cantilever beams undergoing a single rotation, giving rise to reasonably satisfactory results

Quantifying the performance of natural ventilation windcatchers

The significant energy consumption of non- domestic buildings has led to renewed interest in natural ventilation strategies that utilise the action of the wind, and the buoyancy of hot air. One natural ventilation element is the Windcatcher, a roof mounted device that works by channelling air into a room under the action of wind pressure, whilst simultaneously drawing air out of the room by virtue of a low pressure region created downstream of the element. A significant number of Windcatchers are fitted in UK schools where good indoor air quality is essential for the health and performance of children. The performance of a ventilation system in a school classroom is determined by its ability to provide ventilation in accordance with UK government ventilation, air quality, and acoustic requirements. However, there is only limited performance data available for a Windcatcher, particularly when operating in-situ. Accordingly, this thesis investigates the performance of a Windcatcher in three ways: First, a semi-empirical model is developed that combines an envelope flow model with existing experimental data. Second, measurements of air temperature, relative humidity, carbon dioxide, and noise levels in school classrooms are assessed over summer and winter months and the results compared against UK Government requirements. Finally, air flow rates are measured in twenty four classrooms and compared against the semi-empirical predictions. The monitoring reveals that air quality in classrooms ventilated by a Windcatcher has the potential to be better than that reported for conventional natural ventilation strategies such as windows. Furthermore, an autonomous Windcatcher is shown to deliver the minimum ventilation rates specified by the UK Government, and when combined with open windows a Windcatcher is also capable of providing the required mean and purge ventilation rates. These findings are then used to develop an algorithm that will size a Windcatcher for a particular application, as well as helping to improve the ventilation strategy for a building that employs a Windcatcher.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research CouncilMonodraught LtdGBUnited Kingdo

Quantifying the performance of natural ventilation windcatchers

The significant energy consumption of non- domestic buildings has led to renewed interest in natural ventilation strategies that utilise the action of the wind, and the buoyancy of hot air. One natural ventilation element is the Windcatcher, a roof mounted device that works by channelling air into a room under the action of wind pressure, whilst simultaneously drawing air out of the room by virtue of a low pressure region created downstream of the element. A significant number of Windcatchers are fitted in UK schools where good indoor air quality is essential for the health and performance of children. The performance of a ventilation system in a school classroom is determined by its ability to provide ventilation in accordance with UK government ventilation, air quality, and acoustic requirements. However, there is only limited performance data available for a Windcatcher, particularly when operating in-situ. Accordingly, this thesis investigates the performance of a Windcatcher in three ways: First, a semi-empirical model is developed that combines an envelope flow model with existing experimental data. Second, measurements of air temperature, relative humidity, carbon dioxide, and noise levels in school classrooms are assessed over summer and winter months and the results compared against UK Government requirements. Finally, air flow rates are measured in twenty four classrooms and compared against the semi-empirical predictions. The monitoring reveals that air quality in classrooms ventilated by a Windcatcher has the potential to be better than that reported for conventional natural ventilation strategies such as windows. Furthermore, an autonomous Windcatcher is shown to deliver the minimum ventilation rates specified by the UK Government, and when combined with open windows a Windcatcher is also capable of providing the required mean and purge ventilation rates. These findings are then used to develop an algorithm that will size a Windcatcher for a particular application, as well as helping to improve the ventilation strategy for a building that employs a Windcatcher.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research CouncilMonodraught LtdGBUnited Kingdo