Composite Iterative Algorithm and Architecture for q-th Root Calculation

An algorithm for the q-th root extraction, being q any integer, is presented in this paper. The algorithm is based on an optimized implementation of X^{1/q} by a sequence of parallel and/or overlapped operations: (1) reciprocal, (2) digit-recurrence logarithm, (3) left-to-right carry-free multiplication and (4) on-line exponential. A detailed error analysis and two architectures are proposed, for low precision q and for higher precision q. The execution time and hardware requirements are estimated for single and double precision floating-point computations for several radices; this helps to determine which radices result in the most efficient implementations. The architectures proposed improve the features of other architectures for q-th root extraction.Dans cet article, nous présentons un algorithme matériel pour l'extraction de la racine q-ième d'un nombre X, où q est un entier naturel non nul. Cet algorithme est basé sur une implantation optimisée de la fonction X^{1/q} par une séquence d'opérations parallèles et/ou superposées: (1) réciproque, (2) logarithme chiffre par chiffre, (3) multiplication de gauche-à-droite sans propagation de retenue et (4) exponentielle en ligne. Une analyse détaillée des erreurs et deux architectures sont proposées, pour q de basse précision et pour q de précision plus haute. Le temps d'exécution et les composants matériels à utiliser sont estimés pour des calculs en virgule flottante simple et double précision et pour plusieurs bases. Cette étude aide à déterminer quelles bases mènent aux implantations les plus efficaces. Les architectures proposées améliorent les caractéristiques d'architectures précédentes destinées à l'extraction des racines

Reconciling Synthesis and Decomposition: A Composite Approach to Capability Identification

Stakeholders' expectations and technology constantly evolve during the lengthy development cycles of a large-scale computer based system. Consequently, the traditional approach of baselining requirements results in an unsatisfactory system because it is ill-equipped to accommodate such change. In contrast, systems constructed on the basis of Capabilities are more change-tolerant; Capabilities are functional abstractions that are neither as amorphous as user needs nor as rigid as system requirements. Alternatively, Capabilities are aggregates that capture desired functionality from the users' needs, and are designed to exhibit desirable software engineering characteristics of high cohesion, low coupling and optimum abstraction levels. To formulate these functional abstractions we develop and investigate two algorithms for Capability identification: Synthesis and Decomposition. The synthesis algorithm aggregates detailed rudimentary elements of the system to form Capabilities. In contrast, the decomposition algorithm determines Capabilities by recursively partitioning the overall mission of the system into more detailed entities. Empirical analysis on a small computer based library system reveals that neither approach is sufficient by itself. However, a composite algorithm based on a complementary approach reconciling the two polar perspectives results in a more feasible set of Capabilities. In particular, the composite algorithm formulates Capabilities using the cohesion and coupling measures as defined by the decomposition algorithm and the abstraction level as determined by the synthesis algorithm.Comment: This paper appears in the 14th Annual IEEE International Conference and Workshop on the Engineering of Computer Based Systems (ECBS); 10 pages, 9 figure

Characterization of robotics parallel algorithms and mapping onto a reconfigurable SIMD machine

The kinematics, dynamics, Jacobian, and their corresponding inverse computations are six essential problems in the control of robot manipulators. Efficient parallel algorithms for these computations are discussed and analyzed. Their characteristics are identified and a scheme on the mapping of these algorithms to a reconfigurable parallel architecture is presented. Based on the characteristics including type of parallelism, degree of parallelism, uniformity of the operations, fundamental operations, data dependencies, and communication requirement, it is shown that most of the algorithms for robotic computations possess highly regular properties and some common structures, especially the linear recursive structure. Moreover, they are well-suited to be implemented on a single-instruction-stream multiple-data-stream (SIMD) computer with reconfigurable interconnection network. The model of a reconfigurable dual network SIMD machine with internal direct feedback is introduced. A systematic procedure internal direct feedback is introduced. A systematic procedure to map these computations to the proposed machine is presented. A new scheduling problem for SIMD machines is investigated and a heuristic algorithm, called neighborhood scheduling, that reorders the processing sequence of subtasks to reduce the communication time is described. Mapping results of a benchmark algorithm are illustrated and discussed

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table