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Search results for: MULTIPLE-PRECISION ARITHMETIC
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Implementation of Addition and Subtraction Operations in Multiple Precision Arithmetic
PublicationIn this paper, we present a digital circuit of arithmetic unit implementing addition and subtraction operations in multiple-precision arithmetic (MPA). This adder-subtractor unit is a part of MPA coprocessor supporting and offloading the central processing unit (CPU) in computations requiring precision higher than 32/64 bits. Although addition and subtraction operations of two n-digit numbers require O(n) operations, the efficient...
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Open-Source Coprocessor for Integer Multiple Precision Arithmetic
PublicationThis paper presents an open-source digital circuit of the coprocessor for an integer multiple-precision arithmetic (MPA). The purpose of this coprocessor is to support a central processing unit (CPU) by offloading computations requiring integer precision higher than 32/64 bits. The coprocessor is developed using the very high speed integrated circuit hardware description language (VHDL) as an intellectual property (IP) core. Therefore,...
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FPGA implementation of the multiplication operation in multiple-precision arithmetic
PublicationAlthough standard 32/64-bit arithmetic is sufficient to solve most of the scientific-computing problems, there are still problems that require higher numerical precision. Multiple-precision arithmetic (MPA) libraries are software tools for emulation of computations in a user-defined precision. However, availability of a reconfigurable cards based on field-programmable gate arrays (FPGAs) in computing systems allows one to implement...
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IP Core of Coprocessor for Multiple-Precision-Arithmetic Computations
PublicationIn this paper, we present an IP core of coprocessor supporting computations requiring integer multiple-precision arithmetic (MPA). Whilst standard 32/64-bit arithmetic is sufficient to solve many computing problems, there are still applications that require higher numerical precision. Hence, the purpose of the developed coprocessor is to support and offload central processing unit (CPU) in such computations. The developed digital...
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Implementation of Coprocessor for Integer Multiple Precision Arithmetic on Zynq Ultrascale+ MPSoC
PublicationRecently, we have opened the source code of coprocessor for multiple-precision arithmetic (MPA). In this contribution, the implementation and benchmarking results for this MPA coprocessor are presented on modern Zynq Ultrascale+ multiprocessor system on chip, which combines field-programmable gate array with quad-core ARM Cortex-A53 64-bit central processing unit (CPU). In our benchmark, a single coprocessor can be up to 4.5 times...
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Electromagnetic Problems Requiring High-Precision Computations
PublicationAn overview of the applications of multiple-precision arithmetic in CEM was presented in this paper for the first time. Although double-precision floating-point arithmetic is sufficient for most scientific computations, there is an expanding body of electromagnetic problems requiring multiple-precision arithmetic. Software libraries facilitating these computations were described, and investigations requiring multiple-precision...
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Implementation of FDTD-Compatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision...
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Acceleration of the discrete Green's function computations
PublicationResults of the acceleration of the 3-D discrete Green's function (DGF) computations on the multicore processor are presented. The code was developed in the multiple precision arithmetic with use of the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained thus applicability of the DGF in FDTD simulations was significantly improved.
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Implementation of FDTD-compatible Green's function on heterogeneous CPU-GPU parallel processing system
PublicationThis paper presents an implementation of the FDTD-compatible Green's function on a heterogeneous parallel processing system. The developed implementation simultaneously utilizes computational power of the central processing unit (CPU) and the graphics processing unit (GPU) to the computational tasks best suited to each architecture. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates...
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A New Expression for the 3-D Dyadic FDTD-Compatible Green's Function Based on Multidimensional Z-Transform
PublicationIn this letter, a new analytic expression for the time-domain discrete Green's function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision...
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Fast implementation of FDTD-compatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Green's function on a multicore processor is presented. Recently, closed-form expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations...
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Analytical Expression for the Time-Domain Green's Function of a Discrete Plane Wave Propagating in the 3-D FDTD Grid
PublicationIn this paper, a closed-form expression for the time-domain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3-D finite-difference time-domain (FDTD) grid is derived. In order to verify our findings, the time-domain implementation of the DPW-injection technique is developed with the use of the derived expression for 3-D total-field/scattered-field (TFSF) FDTD simulations. This implementation requires computations...
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Analytical Expression for the Time-Domain Discrete Green's Function of a Plane Wave Propagating in the 2-D FDTD Grid
PublicationIn this letter, a new closed-form expression for the time-domain discrete Green's function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of...
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Analysis of radiation and scattering problems with the use of hybrid techniques based on the discrete Green's function formulation of the FDTD method
PublicationIn this contribution, simulation scenarios are presented which take advantage of the hybrid techniques based on the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method. DGF-FDTD solutions are compatible with the finite-difference grid and can be applied for perfect hybridization of the FDTD method. The following techniques are considered: (i) DGF-FDTD for antenna simulations, (ii) DGF-based...
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Verification and Benchmarking in MPA Coprocessor Design Process
PublicationThis paper presents verification and benchmarking required for the development of a coprocessor digital circuit for integer multiple-precision arithmetic (MPA). Its code is developed, with the use of very high speed integrated circuit hardware description language (VHDL), as an intellectual property core. Therefore, it can be used by a final user within their own computing system based on field-programmable gate arrays (FPGAs)....
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Marek Czachor prof. dr hab.
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Deep Learning Optimization for Edge Devices: Analysis of Training Quantization Parameters
PublicationThis paper focuses on convolution neural network quantization problem. The quantization has a distinct stage of data conversion from floating-point into integer-point numbers. In general, the process of quantization is associated with the reduction of the matrix dimension via limited precision of the numbers. However, the training and inference stages of deep learning neural network are limited by the space of the memory and a...
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GPU-Accelerated Finite-Element Matrix Generation for Lossless, Lossy, and Tensor Media [EM Programmer's Notebook]
PublicationThis paper presents an optimization approach for limiting memory requirements and enhancing the performance of GPU-accelerated finite-element matrix generation applied in the implementation of the higher-order finite-element method (FEM). It emphasizes the details of the implementation of the matrix-generation algorithm for the simulation of electromagnetic wave propagation in lossless, lossy, and tensor media. Moreover, the impact...
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A memory efficient and fast sparse matrix vector product on a Gpu
PublicationThis paper proposes a new sparse matrix storage format which allows an efficient implementation of a sparse matrix vector product on a Fermi Graphics Processing Unit (GPU). Unlike previous formats it has both low memory footprint and good throughput. The new format, which we call Sliced ELLR-T has been designed specifically for accelerating the iterative solution of a large sparse and complex-valued system of linear equations arising...
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Relativity of arithmetic as a fundamental symmetry of physics
PublicationArithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...
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If Gravity is Geometry, is Dark Energy just Arithmetic?
PublicationArithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R^4 and (−L/2,L/2)^4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms...
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Obliczanie składowej OEE przy wielu operacjach technologicznych
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Information Processing and Fechner’s Problem as a Choice of Arithmetic
PublicationFechner’s law and its modern generalizations can be regarded as manifestations of alternative forms of arithmetic, coexisting at stimulus and sensation levels. The world of sensations may be thus described by a generalization of the standard mathematical calculus.
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Simple Fractal Calculus from Fractal Arithmetic
PublicationNon-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...
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Executing Multiple Simulations in the MERPSYS Environment
PublicationThe chapter investigates the steps necessary to perform a simulation instance in the MERPSYS environment and discusses potential limitations in case when vast numbers of simulations are required. An extended architecture is proposed which includes a JMS-based simulation queue and multiple distributed simulators, overcoming the potential bottlenecks. The chapter introduces also methods for preparing suites of multiple simulations...
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Crystallization of space: Space-time fractals from fractal arithmetic
PublicationFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Scaling of numbers in residue arithmetic with the flexible selection of scaling factor
PublicationA scaling technique of numbers in resudue arithmetic with the flexible selection of the scaling factor is presented. The required scaling factor can be selected from the set of moduli products of the Residue Number System (RNS) base. By permutation of moduli of the number system base it is possible to create many auxilliary Mixed-Radix Systems associated with the given RNS with respect to the base, but they have different sets...
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublicationFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography
PublicationBell’s theorem is supposed to exclude all local hidden-variable models of quantum correlations. However,an explicit counterexample shows that a new class of local realistic models, based on generalized arith-metic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical oftwo-electron singlet states. Observable probabilities are consistent with the usual arithmetic employedby macroscopic observers...
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Neural network training with limited precision and asymmetric exponent
PublicationAlong with an extremely increasing number of mobile devices, sensors and other smart utilities, an unprecedented growth of data can be observed in today’s world. In order to address multiple challenges facing the big data domain, machine learning techniques are often leveraged for data analysis, filtering and classification. Wide usage of artificial intelligence with large amounts of data creates growing demand not only for storage...
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Multiple-Input Multiple-Output Technique for Underwater Acoustic Communication System
PublicationThe performance of an underwater acoustic communication (UAC) system is limited due to tough propagation conditions in the UAC channel. Multiple-Input Multiple-Output (MIMO) technique can improve the reliability of the data transmission system, increase its speed, increase its range, and reduce the energy consumption. The paper presents an implementation method of MIMO technique in the form of coding the Space-Time Block Code and...
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MULTIPLE SCLEROSIS
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Modular high precision high current source for special applications — Simulation and verification
PublicationThis paper presents selected issues concerning realization of high precision high current source for special applications, where high demands of output parameters of such device are required. A new 80 kW prototype of modular high precision high current source is presented, where output current accuracy reaches 5x10-5. This paper presents also results of operation of the simulation model and of the prototype converter. In order...
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New Method for Increasing Precision of Position Estimation in Hybrid Inertial Navigation System
PublicationIn article new method for increasing precision of position estimation by using inertial navigation in hybrid localization system with reduced number of reference nodes for radio distance measurements was presented. Measuring campaign using developed measuring stand were carried out to verify precision of position estimation of moving person in indoor environment.
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Advances and Trends in Non-Conventional, Abrasive and Precision Machining 2021
PublicationIn the modern, rapidly evolving industrial landscape, the quest for machining and production processes consistently delivering superior quality and precision is more pronounced than ever. This necessity and imperative are driven by the increasing complexity in the design and manufacturing of mechanical components, an evolution in lockstep with the swift advancements in material science. The real challenge of this evolution lies...
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Implementation of high-precision computation capabilities into the open-source dynamic simulation framework YADE
PublicationThis paper deals with the implementation of arbitrary precision calculations into the open-source discrete element framework YADE published under the GPL-2+ free software license. This new capability paves the way for the simulation framework to be used in many new fields such as quantum mechanics. The implementation details and associated gains in the accuracy of the results are discussed. Besides the "standard" double (64 bits)...
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Metrological analysis of precision of the system of delivering a water capsule for explosive production of water aerosol
PublicationIn this paper an analysis of precision of the system controlling delivery by a helicopter of water-capsule designed for extinguishing large scale fires is presented. The analysis was performed using the numerical method of distribution propagation (Monte Carlo method) supplemented with results of application of the uncertainty propagation method. In addition the optimum conditions for the airdrop are determined to ensure achievement...
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FPGA realization of fir filter in residue arithmetic
Publicationw pracy zaprezentowano realizację fpga przepływowego filtru fir o stałych współczynnikach w arytmetyce resztowej z użyciem 8 5-bitowych modułów o łącznym zakresie liczbowym 37.07 bita. zastosowano formębezpośrednią fir. mnożenia wykonywane są przy użyciu odczytu z pamięci. sumowania w każdym z kanałów są realizowane przy zastosowaniu wielopoziomowej struktury sumatora opartego o 4-operandowe sumatory csa. w stopniu końcowym wykonywane...
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New Method for Increasing Precision of Position Estimation of a Moving Person in Hybrid Inertial Navigation System
PublicationIn this article a new method for increasing precision of position estimation of inertial navigation in hybrid localization system with reduced number of reference nodes for radio distance measurements is presented. Measuring tests were carried out to verify precision of position estimation of moving person in indoor environment.
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Multiple Cues-Based Robust Visual Object Tracking Method
PublicationVisual object tracking is still considered a challenging task in computer vision research society. The object of interest undergoes significant appearance changes because of illumination variation, deformation, motion blur, background clutter, and occlusion. Kernelized correlation filter- (KCF) based tracking schemes have shown good performance in recent years. The accuracy and robustness of these trackers can be further enhanced...
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Simple Superstrate Antenna for Connectivity Improvement in Precision Farming Applications
PublicationIn this paper, a concept of a simple circularly polarized antenna with partially reflecting surface (PRS) has been adopted for precision farming applications. The investigation contains an analysis of the dependence of the antenna performance on the elements number in the PRS structure in X- and Ka-band frequencies. Especially meaningful parameters from point-to-point connectivity perspective are...
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Circular polarization diversity implementation for correlation reduction in wideband low-cost multiple-input-multiple-output antenna
PublicationIn this paper, a multiple-input-multiple-output (MIMO) antenna featuring circular polarization diversity, and designed on a common coplanar ground is presented. The proposed antenna design utilizes a coplanar waveguide (CPW) feeding technique with three parallel coplanar ground planes, and two feedlines in-between. For circular polarization (CP), quasi-loops are created by etching slots on the outermost ground planes. With this...
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Precision surface characterization for finish cylindrical milling with dynamic tool displacements model
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PRECISION AGRICULTURE
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Multiple Group Membership and Collective Action Intention
PublicationDatasets from two studies conducted in Poland on the relation between identity fusion, group identification, multiple group membership, perceived injustice, and collective action intention. The presented studies, in the context of protests against attempts to restrict abortion law, were conducted to examine the link between belonging to multiple groups, group efficacy & identification, perceived injustice and collective...
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Multiple Sclerosis International
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Zastosowanie algorytmu MSA (Multiple Similar Areas) do wyznaczania map głębi w wielowidokowych systemach widzenia komputerowego
PublicationArtykuł podejmuje temat pozyskiwania map głębi (ang. depth map) na podstawie zdjęć z wielu kamer w wyniku widzenia stereoskopowego. Mapa głębi zawierająca odległości od obiektów będących w zasięgu widzenia kamer pozyskana może zostać na podstawie zdjęć z co najmniej dwóch kamer pełniących funkcję kamery stereoskopowej. W mapach głębi pozyskanych w ten sposób występują jednak błędy. Artykuł dotyczy metod redukcji błędów dzięki zwiększeniu...
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The Influence of the Radio Channel on Precision of Position Estimation of the User Terminal Using the NB-IoT Radio Interface
PublicationIn the article the method of user terminal position estimation using the broadcast signals transmitted in the downlink of the NB-IoT interface was presented, including the analysis of the radio channel influence on precision of position estimation as well as the eNodeB (Evolved Node B) synchronization. The practical ability to estimate the position in the test area has been verified in the laboratory conditions, using the reference...
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Distributed Evacuation in Graphs with Multiple Exits
PublicationWe consider the problem of efficient evacuation using multiple exits. We formulate this problem as a discrete problem on graphs where mobile agents located in distinct nodes of a given graph must quickly reach one of multiple possible exit nodes, while avoiding congestion and bottlenecks. Each node of the graph has the capacity of holding at most one agent at each time step. Thus, the agents must choose their movements strategy...
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Laser Beam as a Precision Tool to Increase Fatigue Resistance in an Eyelet of Undercarriage Drag Strut
PublicationThe article contains the results of tests on a laser-processed eyelet of undercarriage drag strut to increase its fatigue strength. Laser processing concentrated on both sides around the hole of eye for connecting the undercarriage drag strut caused that the material in this area withstood more than twice the number of load cycles established for this material. In order to determine the reasons for the increase in fatigue strength,...