High-Speed Function Approximation using a Minimax Quadratic Interpolator

A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs)

A Hybrid Decomposition Parallel Implementation of the Car-Parrinello Method

We have developed a flexible hybrid decomposition parallel implementation of the first-principles molecular dynamics algorithm of Car and Parrinello. The code allows the problem to be decomposed either spatially, over the electronic orbitals, or any combination of the two. Performance statistics for 32, 64, 128 and 512 Si atom runs on the Touchstone Delta and Intel Paragon parallel supercomputers and comparison with the performance of an optimized code running the smaller systems on the Cray Y-MP and C90 are presented.Comment: Accepted by Computer Physics Communications, latex, 34 pages without figures, 15 figures available in PostScript form via WWW at http://www-theory.chem.washington.edu/~wiggs/hyb_figures.htm

Inertial Load Compensation by a Model Spinal Circuit During Single Joint Movement

Office of Naval Research (N00014-92-J-1309); CONACYT (Mexico) (63462

Algorithms and architectures for decimal transcendental function computation

Nowadays, there are many commercial demands for decimal floating-point (DFP) arithmetic operations such as financial analysis, tax calculation, currency conversion, Internet based applications, and e-commerce. This trend gives rise to further development on DFP arithmetic units which can perform accurate computations with exact decimal operands. Due to the significance of DFP arithmetic, the IEEE 754-2008 standard for floating-point arithmetic includes it in its specifications. The basic decimal arithmetic unit, such as decimal adder, subtracter, multiplier, divider or square-root unit, as a main part of a decimal microprocessor, is attracting more and more researchers' attentions. Recently, the decimal-encoded formats and DFP arithmetic units have been implemented in IBM's system z900, POWER6, and z10 microprocessors. Increasing chip densities and transistor count provide more room for designers to add more essential functions on application domains into upcoming microprocessors. Decimal transcendental functions, such as DFP logarithm, antilogarithm, exponential, reciprocal and trigonometric, etc, as useful arithmetic operations in many areas of science and engineering, has been specified as the recommended arithmetic in the IEEE 754-2008 standard. Thus, virtually all the computing systems that are compliant with the IEEE 754-2008 standard could include a DFP mathematical library providing transcendental function computation. Based on the development of basic decimal arithmetic units, more complex DFP transcendental arithmetic will be the next building blocks in microprocessors. In this dissertation, we researched and developed several new decimal algorithms and architectures for the DFP transcendental function computation. These designs are composed of several different methods: 1) the decimal transcendental function computation based on the table-based first-order polynomial approximation method; 2) DFP logarithmic and antilogarithmic converters based on the decimal digit-recurrence algorithm with selection by rounding; 3) a decimal reciprocal unit using the efficient table look-up based on Newton-Raphson iterations; and 4) a first radix-100 division unit based on the non-restoring algorithm with pre-scaling method. Most decimal algorithms and architectures for the DFP transcendental function computation developed in this dissertation have been the first attempt to analyze and implement the DFP transcendental arithmetic in order to achieve faithful results of DFP operands, specified in IEEE 754-2008. To help researchers evaluate the hardware performance of DFP transcendental arithmetic units, the proposed architectures based on the different methods are modeled, verified and synthesized using FPGAs or with CMOS standard cells libraries in ASIC. Some of implementation results are compared with those of the binary radix-16 logarithmic and exponential converters; recent developed high performance decimal CORDIC based architecture; and Intel's DFP transcendental function computation software library. The comparison results show that the proposed architectures have significant speed-up in contrast to the above designs in terms of the latency. The algorithms and architectures developed in this dissertation provide a useful starting point for future hardware-oriented DFP transcendental function computation researches

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

py4DSTEM: a software package for multimodal analysis of four-dimensional scanning transmission electron microscopy datasets

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full 2D image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields and other sample-dependent properties. However, extracting this information requires complex analysis pipelines, from data wrangling to calibration to analysis to visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail, and present results from several experimental datasets. We have also implemented a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open source HDF5 standard. We hope this tool will benefit the research community, helps to move the developing standards for data and computational methods in electron microscopy, and invite the community to contribute to this ongoing, fully open-source project