6 research outputs found

    Generalized explicit inversive generators of small p-weight degree

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    Using rational functions to generate pseudorandom number sequences is a popular research topic. In this paper, we study bounds on additive character sums of a new explicit generator based on rational functions with small p-weight degree. This extends the class of functions where a nontrivial character sum bound is known

    Parallel Streams of Nonlinear Congruential Pseudorandom Numbers

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    AbstractThis paper deals with the general nonlinear congruential method for generating uniform pseudorandom numbers, in which permutation polynomials over finite prime fields play an important role. It is known that these pseudorandom numbers exhibit an attractive equidistribution and statistical independence behavior. In the context of parallelized simulation methods, a large number of parallel streams of pseudorandom numbers with strong mutual statistical independence properties are required. In the present paper, such properties of parallelized nonlinear congruential generators are studied based on the discrepancy of certain point sets. Upper and lower bounds for the discrepancy both over the full period and over (sufficiently large) parts of the period are established. The method of proof rests on the classical Weil bound for exponential sums

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    Relevance of accurate Monte Carlo modeling in nuclear medical imaging

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    Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. This paper presents derivation and methodological basis for this approach and critically reviews their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed

    Analyse des synchronisations dans un programme parallèle ordonnancé par vol de travail. Applications à la génération déterministe de nombres pseudo-aléatoires.

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    We present two contributions to the field of parallel programming.The first contribution is theoretical: we introduce SIPS analysis, a novel approach to estimate the number of synchronizations performed during the execution of a parallel algorithm.Based on the concept of logical clocks, it allows us: on one hand, to deliver new bounds for the number of synchronizations, in expectation; on the other hand, to design more efficient parallel programs by dynamic adaptation of the granularity.The second contribution is pragmatic: we present an efficient parallelization strategy for pseudorandom number generation, independent of the number of concurrent processes participating in a computation.As an alternative to the use of one sequential generator per process, we introduce a generic API called Par-R, which is designed and analyzed using SIPS.Its main characteristic is the use of a sequential generator that can perform a ``jump-ahead'' directly from one number to another on an arbitrary distance within the pseudorandom sequence.Thanks to SIPS, we show that, in expectation, within an execution scheduled by work stealing of a "very parallel" program (whose depth or critical path is subtle when compared to the work or number of operations), these operations are rare.Par-R is compared with the parallel pseudorandom number generator DotMix, written for the Cilk Plus dynamic multithreading platform.The theoretical overhead of Par-R compares favorably to DotMix's overhead, what is confirmed experimentally, while not requiring a fixed generator underneath.Nous présentons deux contributions dans le domaine de la programmation parallèle.La première est théorique : nous introduisons l'analyse SIPS, une approche nouvelle pour dénombrer le nombre d'opérations de synchronisation durant l'exécution d'un algorithme parallèle ordonnancé par vol de travail.Basée sur le concept d'horloges logiques, elle nous permet,: d'une part de donner de nouvelles majorations de coût en moyenne; d'autre part de concevoir des programmes parallèles plus efficaces par adaptation dynamique de la granularité.La seconde contribution est pragmatique: nous présentons une parallélisation générique d'algorithmes pour la génération déterministe de nombres pseudo-aléatoires, indépendamment du nombre de processus concurrents lors de l'exécution.Alternative à l'utilisation d'un générateur pseudo-aléatoire séquentiel par processus, nous introduisons une API générique, appelée Par-R qui est conçue et analysée grâce à SIPS.Sa caractéristique principale est d'exploiter un générateur séquentiel qui peut "sauter" directement d'un nombre à un autre situé à une distance arbitraire dans la séquence pseudo-aléatoire.Grâce à l'analyse SIPS, nous montrons qu'en moyenne, lors d'une exécution par vol de travail d'un programme très parallèle (dont la profondeur ou chemin critique est très petite devant le travail ou nombre d'opérations), ces opérations de saut sont rares.Par-R est comparé au générateur pseudo-aléatoire DotMix, écrit pour Cilk Plus, une extension de C/C++ pour la programmation parallèle par vol de travail.Le surcout théorique de Par-R se compare favorablement au surcoput de DotMix, ce qui apparait aussi expériemntalement.De plus, étant générique, Par-R est indépendant du générateur séquentiel sous-jacent

    Scalability in extensible and heterogeneous storage systems

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    The evolution of computer systems has brought an exponential growth in data volumes, which pushes the capabilities of current storage architectures to organize and access this information effectively: as the unending creation and demand of computer-generated data grows at an estimated rate of 40-60% per year, storage infrastructures need increasingly scalable data distribution layouts that are able to adapt to this growth with adequate performance. In order to provide the required performance and reliability, large-scale storage systems have traditionally relied on multiple RAID-5 or RAID-6 storage arrays, interconnected with high-speed networks like FibreChannel or SAS. Unfortunately, the performance of the current, most commonly-used storage technology-the magnetic disk drive-can't keep up with the rate of growth needed to sustain this explosive growth. Moreover, storage architectures based on solid-state devices (the successors of current magnetic drives) don't seem poised to replace HDD-based storage for the next 5-10 years, at least in data centers. Though the performance of SSDs significantly improves that of hard drives, it would cost the NAND industry hundreds of billions of dollars to build enough manufacturing plants to satisfy the forecasted demand. Besides the problems derived from technological and mechanical limitations, the massive data growth poses more challenges: to build a storage infrastructure, the most flexible approach consists in using pools of storage devices that can be expanded as needed by adding new devices or replacing older ones, thus seamlessly increasing the system's performance and capacity. This approach however, needs data layouts that can adapt to these topology changes and also exploit the potential performance offered by the hardware. Such strategies should be able to rebuild the data layout to accommodate the new devices in the infrastructure, extracting the utmost performance from the hardware and offering a balanced workload distribution. An inadequate data layout might not effectively use the enlarged capacity or better performance provided by newer devices, thus leading to unbalancing problems like bottlenecks or resource underusage. Besides, massive storage systems will inevitably be composed of a collection of heterogeneous hardware: as capacity and performance requirements grow, new storage devices must be added to cope with demand, but it is unlikely that these devices will have the same capacity or performance of those installed. Moreover, upon failure, disks are most commonly replaced by faster and larger ones, since it is not always easy (or cheap) to find a particular model of drive. In the long run, any large-scale storage system will have to cope with a myriad of devices. The title of this dissertation, "Scalability in Extensible and Heterogeneous Storage Systems", refers to the main focus of our contributions in scalable data distributions that can adapt to increasing volumes of data. Our first contribution is the design of a scalable data layout that can adapt to hardware changes while redistributing only the minimum data to keep a balanced workload. With the second contribution, we perform a comparative study on the influence of pseudo-random number generators in the performance and distribution quality of randomized layouts and prove that a badly chosen generator can degrade the quality of the strategy. Our third contribution is an an analysis of long-term data access patterns in several real-world traces to determine if it is possible to offer high performance and a balanced load with less than minimal data rebalancing. In our final contribution, we apply the knowledge learnt about long-term access patterns to design an extensible RAID architecture that can adapt to changes in the number of disks without migrating large amounts of data, and prove that it can be competitive with current RAID arrays with an overhead of at most 1.28% the storage capacity.L'evolució dels sistemes de computació ha dut un creixement exponencial dels volums de dades, que porta al límit la capacitat d'organitzar i accedir informació de les arquitectures d'emmagatzemament actuals. Amb una incessant creació de dades que creix a un ritme estimat del 40-60% per any, les infraestructures de dades requereixen de distribucions de dades cada cop més escalables que puguin adaptar-se a aquest creixement amb un rendiment adequat. Per tal de proporcionar aquest rendiment, els sistemes d'emmagatzemament de gran escala fan servir agregacions RAID5 o RAID6 connectades amb xarxes d'alta velocitat com FibreChannel o SAS. Malauradament, el rendiment de la tecnologia més emprada actualment, el disc magnètic, no creix prou ràpid per sostenir tal creixement explosiu. D'altra banda, les prediccions apunten que els dispositius d'estat sòlid, els successors de la tecnologia actual, no substituiran els discos magnètics fins d'aquí 5-10 anys. Tot i que el rendiment és molt superior, la indústria NAND necessitarà invertir centenars de milions de dòlars per construir prou fàbriques per satisfer la demanda prevista. A més dels problemes derivats de limitacions tècniques i mecàniques, el creixement massiu de les dades suposa més problemes: la solució més flexible per construir una infraestructura d'emmagatzematge consisteix en fer servir grups de dispositius que es poden fer créixer bé afegint-ne de nous, bé reemplaçant-ne els més vells, incrementant així la capacitat i el rendiment del sistema de forma transparent. Aquesta solució, però, requereix distribucions de dades que es puguin adaptar a aquests canvis a la topologia i explotar el rendiment potencial que el hardware ofereix. Aquestes distribucions haurien de poder reconstruir la col.locació de les dades per acomodar els nous dispositius, extraient-ne el màxim rendiment i oferint una càrrega de treball balancejada. Una distribució inadient pot no fer servir de manera efectiva la capacitat o el rendiment addicional ofert pels nous dispositius, provocant problemes de balanceig com colls d¿ampolla o infrautilització. A més, els sistemes d'emmagatzematge massius estaran inevitablement formats per hardware heterogeni: en créixer els requisits de capacitat i rendiment, es fa necessari afegir nous dispositius per poder suportar la demanda, però és poc probable que els dispositius afegits tinguin la mateixa capacitat o rendiment que els ja instal.lats. A més, en cas de fallada, els discos són reemplaçats per d'altres més ràpids i de més capacitat, ja que no sempre és fàcil (o barat) trobar-ne un model particular. A llarg termini, qualsevol arquitectura d'emmagatzematge de gran escala estarà formada per una miríade de dispositius diferents. El títol d'aquesta tesi, "Scalability in Extensible and Heterogeneous Storage Systems", fa referència a les nostres contribucions a la recerca de distribucions de dades escalables que es puguin adaptar a volums creixents d'informació. La primera contribució és el disseny d'una distribució escalable que es pot adaptar canvis de hardware només redistribuint el mínim per mantenir un càrrega de treball balancejada. A la segona contribució, fem un estudi comparatiu sobre l'impacte del generadors de números pseudo-aleatoris en el rendiment i qualitat de les distribucions pseudo-aleatòries de dades, i provem que una mala selecció del generador pot degradar la qualitat de l'estratègia. La tercera contribució és un anàlisi dels patrons d'accés a dades de llarga duració en traces de sistemes reals, per determinar si és possible oferir un alt rendiment i una bona distribució amb una rebalanceig inferior al mínim. A la contribució final, apliquem el coneixement adquirit en aquest estudi per dissenyar una arquitectura RAID extensible que es pot adaptar a canvis en el número de dispositius sense migrar grans volums de dades, i demostrem que pot ser competitiva amb les distribucions ideals RAID actuals, amb només una penalització del 1.28% de la capacita
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