The use of reversible logic gates in the design of residue number systems

Reversible computing is an emerging technique to achieve ultra-low-power circuits. Reversible arithmetic circuits allow for achieving energy-efficient high-performance computational systems. Residue number systems (RNS) provide parallel and fault-tolerant additions and multiplications without carry propagation between residue digits. The parallelism and fault-tolerance features of RNS can be leveraged to achieve high-performance reversible computing. This paper proposed RNS full reversible circuits, including forward converters, modular adders and multipliers, and reverse converters used for a class of RNS moduli sets with the composite form {2k, 2p-1}. Modulo 2n-1, 2n, and 2n+1 adders and multipliers were designed using reversible gates. Besides, reversible forward and reverse converters for the 3-moduli set {2n-1, 2n+k, 2n+1} have been designed. The proposed RNS-based reversible computing approach has been applied for consecutive multiplications with an improvement of above 15% in quantum cost after the twelfth iteration, and above 27% in quantum depth after the ninth iteration. The findings show that the use of the proposed RNS-based reversible computing in convolution results in a significant improvement in quantum depth in comparison to conventional methods based on weighted binary adders and multipliers

Perception-motivated parallel algorithms for haptics

Negli ultimi anni l\u2019utilizzo di dispositivi aptici, atti cio\ue8 a riprodurre l\u2019interazione fisica con l\u2019ambiente remoto o virtuale, si sta diffondendo in vari ambiti della robotica e dell\u2019informatica, dai videogiochi alla chirurgia robotizzata eseguita in teleoperazione, dai cellulari alla riabilitazione. In questo lavoro di tesi abbiamo voluto considerare nuovi punti di vista sull\u2019argomento, allo scopo di comprendere meglio come riportare l\u2019essere umano, che \ue8 l\u2019unico fruitore del ritorno di forza, tattile e di telepresenza, al centro della ricerca sui dispositivi aptici. Allo scopo ci siamo focalizzati su due aspetti: una manipolazione del segnale di forza mutuata dalla percezione umana e l\u2019utilizzo di architetture multicore per l\u2019implementazione di algoritmi aptici e robotici. Con l\u2019aiuto di un setup sperimentale creato ad hoc e attraverso l\u2019utilizzo di un joystick con ritorno di forza a 6 gradi di libert\ue0, abbiamo progettato degli esperimenti psicofisici atti all\u2019identificazione di soglie differenziali di forze/coppie nel sistema mano-braccio. Sulla base dei risultati ottenuti abbiamo determinato una serie di funzioni di scalatura del segnale di forza, una per ogni grado di libert\ue0, che permettono di aumentare l\u2019abilit\ue0 umana nel discriminare stimoli differenti. L\u2019utilizzo di tali funzioni, ad esempio in teleoperazione, richiede la possibilit\ue0 di variare il segnale di feedback e il controllo del dispositivo sia in relazione al lavoro da svolgere, sia alle peculiari capacit\ue0 dell\u2019utilizzatore. La gestione del dispositivo deve quindi essere in grado di soddisfare due obbiettivi tendenzialmente in contrasto, e cio\ue8 il raggiungimento di alte prestazioni in termini di velocit\ue0, stabilit\ue0 e precisione, abbinato alla flessibilit\ue0 tipica del software. Una soluzione consiste nell\u2019affidare il controllo del dispositivo ai nuovi sistemi multicore che si stanno sempre pi\uf9 prepotentemente affacciando sul panorama informatico. Per far ci\uf2 una serie di algoritmi consolidati deve essere portata su sistemi paralleli. In questo lavoro abbiamo dimostrato che \ue8 possibile convertire facilmente vecchi algoritmi gi\ue0 implementati in hardware, e quindi intrinsecamente paralleli. Un punto da definire rimane per\uf2 quanto costa portare degli algoritmi solitamente descritti in VLSI e schemi in un linguaggio di programmazione ad alto livello. Focalizzando la nostra attenzione su un problema specifico, la pseudoinversione di matrici che \ue8 presente in molti algoritmi di dinamica e cinematica, abbiamo mostrato che un\u2019attenta progettazione e decomposizione del problema permette una mappatura diretta sulle unit\ue0 di calcolo disponibili. In aggiunta, l\u2019uso di parallelismo a livello di dati su macchine SIMD permette di ottenere buone prestazioni utilizzando semplici operazioni vettoriali come addizioni e shift. Dato che di solito tali istruzioni fanno parte delle implementazioni hardware la migrazione del codice risulta agevole. Abbiamo testato il nostro approccio su una Sony PlayStation 3 equipaggiata con un processore IBM Cell Broadband Engine.In the last years the use of haptic feedback has been used in several applications, from mobile phones to rehabilitation, from video games to robotic aided surgery. The haptic devices, that are the interfaces that create the stimulation and reproduce the physical interaction with virtual or remote environments, have been studied, analyzed and developed in many ways. Every innovation in the mechanics, electronics and technical design of the device it is valuable, however it is important to maintain the focus of the haptic interaction on the human being, who is the only user of force feedback. In this thesis we worked on two main topics that are relevant to this aim: a perception based force signal manipulation and the use of modern multicore architectures for the implementation of the haptic controller. With the help of a specific experimental setup and using a 6 dof haptic device we designed a psychophysical experiment aimed at identifying of the force/torque differential thresholds applied to the hand-arm system. On the basis of the results obtained we determined a set of task dependent scaling functions, one for each degree of freedom of the three-dimensional space, that can be used to enhance the human abilities in discriminating different stimuli. The perception based manipulation of the force feedback requires a fast, stable and configurable controller of the haptic interface. Thus a solution is to use new available multicore architectures for the implementation of the controller, but many consolidated algorithms have to be ported to these parallel systems. Focusing on specific problem, i.e. the matrix pseudoinversion, that is part of the robotics dynamic and kinematic computation, we showed that it is possible to migrate code that was already implemented in hardware, and in particular old algorithms that were inherently parallel and thus not competitive on sequential processors. The main question that still lies open is how much effort is required in order to write these algorithms, usually described in VLSI or schematics, in a modern programming language. We show that a careful task decomposition and design permit a mapping of the code on the available cores. In addition, the use of data parallelism on SIMD machines can give good performance when simple vector instructions such as add and shift operations are used. Since these instructions are present also in hardware implementations the migration can be easily performed. We tested our approach on a Sony PlayStation 3 game console equipped with IBM Cell Broadband Engine processor

Implementation and Evaluation of Algorithmic Skeletons: Parallelisation of Computer Algebra Algorithms

This thesis presents design and implementation approaches for the parallel algorithms of computer algebra. We use algorithmic skeletons and also further approaches, like data parallel arithmetic and actors. We have implemented skeletons for divide and conquer algorithms and some special parallel loops, that we call ‘repeated computation with a possibility of premature termination’. We introduce in this thesis a rational data parallel arithmetic. We focus on parallel symbolic computation algorithms, for these algorithms our arithmetic provides a generic parallelisation approach. The implementation is carried out in Eden, a parallel functional programming language based on Haskell. This choice enables us to encode both the skeletons and the programs in the same language. Moreover, it allows us to refrain from using two different languages—one for the implementation and one for the interface—for our implementation of computer algebra algorithms. Further, this thesis presents methods for evaluation and estimation of parallel execution times. We partition the parallel execution time into two components. One of them accounts for the quality of the parallelisation, we call it the ‘parallel penalty’. The other is the sequential execution time. For the estimation, we predict both components separately, using statistical methods. This enables very confident estimations, although using drastically less measurement points than other methods. We have applied both our evaluation and estimation approaches to the parallel programs presented in this thesis. We haven also used existing estimation methods. We developed divide and conquer skeletons for the implementation of fast parallel multiplication. We have implemented the Karatsuba algorithm, Strassen’s matrix multiplication algorithm and the fast Fourier transform. The latter was used to implement polynomial convolution that leads to a further fast multiplication algorithm. Specially for our implementation of Strassen algorithm we have designed and implemented a divide and conquer skeleton basing on actors. We have implemented the parallel fast Fourier transform, and not only did we use new divide and conquer skeletons, but also developed a map-and-transpose skeleton. It enables good parallelisation of the Fourier transform. The parallelisation of Karatsuba multiplication shows a very good performance. We have analysed the parallel penalty of our programs and compared it to the serial fraction—an approach, known from literature. We also performed execution time estimations of our divide and conquer programs. This thesis presents a parallel map+reduce skeleton scheme. It allows us to combine the usual parallel map skeletons, like parMap, farm, workpool, with a premature termination property. We use this to implement the so-called ‘parallel repeated computation’, a special form of a speculative parallel loop. We have implemented two probabilistic primality tests: the Rabin–Miller test and the Jacobi sum test. We parallelised both with our approach. We analysed the task distribution and stated the fitting configurations of the Jacobi sum test. We have shown formally that the Jacobi sum test can be implemented in parallel. Subsequently, we parallelised it, analysed the load balancing issues, and produced an optimisation. The latter enabled a good implementation, as verified using the parallel penalty. We have also estimated the performance of the tests for further input sizes and numbers of processing elements. Parallelisation of the Jacobi sum test and our generic parallelisation scheme for the repeated computation is our original contribution. The data parallel arithmetic was defined not only for integers, which is already known, but also for rationals. We handled the common factors of the numerator or denominator of the fraction with the modulus in a novel manner. This is required to obtain a true multiple-residue arithmetic, a novel result of our research. Using these mathematical advances, we have parallelised the determinant computation using the Gauß elimination. As always, we have performed task distribution analysis and estimation of the parallel execution time of our implementation. A similar computation in Maple emphasised the potential of our approach. Data parallel arithmetic enables parallelisation of entire classes of computer algebra algorithms. Summarising, this thesis presents and thoroughly evaluates new and existing design decisions for high-level parallelisations of computer algebra algorithms

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing