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Floating-point arithmetic. --- Computer arithmetic

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This is the first book to focus on the problem of ensuring the correctness of floating-point hardware designs through mathematical methods. Formal Verification of Floating-Point Hardware Design, Second Edition advances a verification methodology based on a unified theory of register-transfer logic and floating-point arithmetic that has been developed and applied to the formal verification of commercial floating-point units over the course of more than two decades, during which the author was employed by several major microprocessor design companies. The theory is extended to the analysis of several algorithms and optimization techniques that are commonly used in commercial implementations of elementary arithmetic operations. As a basis for the formal verification of such implementations, high-level specifications of the basic arithmetic instructions of several major industry-standard floating-point architectures are presented, including all details pertaining to the handling of exceptional conditions. The methodology is illustrated in the comprehensive verification of a variety of state-of-the-art commercial floating-point designs developed by Arm Holdings. This revised edition reflects the evolving microarchitectures and increasing sophistication of Arm processors, and the variation in the design goals of execution speed, hardware area requirements, and power consumption. Many new results have been added to Parts I-III (Register-Transfer Logic, Floating-Point Arithmetic, and Implementation of Elementary Operations), extending the theory and describing new techniques. These were derived as required in the verification of the new RTL designs described in Part V.

Mathematical logic --- Mathematics --- Electronics --- Electrical engineering --- Computer architecture. Operating systems --- Computer. Automation --- microprocessoren --- computers --- hardware --- logica --- architectuur (informatica) --- elektrische circuits --- Floating-point arithmetic.

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Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. Key topics and features include: * Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards * Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots * Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages * Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints * Extensions of floating-point arithmetic such as certification, verification, and big precision Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research. .

Algorithms. --- Computer arithmetic. --- Floating-point arithmetic. --- Floating-point arithmetic --- Computer arithmetic --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Mathematics - General --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Digital arithmetic --- Digital computer arithmetic --- Mathematics. --- Programming languages (Electronic computers). --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Computational Mathematics and Numerical Analysis. --- Algorithm Analysis and Problem Complexity. --- Math Applications in Computer Science. --- Appl.Mathematics/Computational Methods of Engineering. --- Programming Languages, Compilers, Interpreters. --- Arithmetic --- Computer architecture --- Computer software. --- Computer science. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Informatics --- Science --- Algorism --- Algebra --- Software, Computer --- Computer systems --- Foundations --- Computer science—Mathematics. --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial

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Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: ‘A Parametric Kind of the Degenerate Fubini Numbers and Polynomials’; ‘On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals’; ‘Fractional Supersymmetric Hermite Polynomials’; ‘Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation’; ‘Iterating the Sum of Möbius Divisor Function and Euler Totient Function’; ‘Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations’; ‘Truncated Fubini Polynomials’; ‘On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights’; ‘Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity’; ‘Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials’; ‘Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros.’

differential equations, heat equation --- Hermite Kampé de Fériet polynomials --- Hermite polynomials --- generating functions --- degenerate Bernstein polynomials --- degenerate Bernstein operators --- degenerate Euler polynomials --- variational methods --- fractional Choquard equation --- ground state solution --- vanishing potential --- positively quadratically hyponormal --- quadratically hyponormal --- unilateral weighted shift --- recursively generated --- Fubini polynomials --- Euler polynomials --- Bernoulli polynomials --- truncated exponential polynomials --- Stirling numbers of the second kind --- differential equations --- Bell polynomials --- r-Bell polynomials --- (r, β)-Bell polynomials --- zeros --- Möbius function --- divisor functions --- Euler totient function --- hydraulic resistance --- pipe flow friction --- Colebrook equation --- Colebrook–White experiment --- floating-point computations --- approximations --- Padé polynomials --- symbolic regression --- orthogonal polynomials --- difference-differential operator --- supersymmetry --- Konhauser matrix polynomial --- generating matrix function --- integral representation --- fractional integral --- degenerate Fubini polynomials --- Stirling numbers

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Power electronics technology is still an emerging technology, and it has found its way into many applications, from renewable energy generation (i.e., wind power and solar power) to electrical vehicles (EVs), biomedical devices, and small appliances, such as laptop chargers. In the near future, electrical energy will be provided and handled by power electronics and consumed through power electronics; this not only will intensify the role of power electronics technology in power conversion processes, but also implies that power systems are undergoing a paradigm shift, from centralized distribution to distributed generation. Today, more than 1000 GW of renewable energy generation sources (photovoltaic (PV) and wind) have been installed, all of which are handled by power electronics technology. The main aim of this book is to highlight and address recent breakthroughs in the range of emerging applications in power electronics and in harmonic and electromagnetic interference (EMI) issues at device and system levels as discussed in ?robust and reliable power electronics technologies, including fault prognosis and diagnosis technique stability of grid-connected converters and ?smart control of power electronics in devices, microgrids, and at system levels.

Q-factor --- lithium-ion power battery pack --- electromagnetic field (EMF) --- expert systems --- total harmonic distortion (THD) --- current-fed inverter --- rotor design --- class-D amplifier --- LCL-S topology --- current switching ripple --- system in package --- energy storage modelling --- smart micro-grid --- embedded systems --- equivalent inductance --- SHIL --- permanent magnet --- static var generator (SVG) --- permanent magnet synchronous motor (PMSM) --- control strategy and algorithm --- digital control --- zero-voltage switching (ZVS) --- SOC estimator --- electric power --- optimal design --- electromagnetic field interference (EMI) --- line frequency instability --- analog phase control --- five-phase permanent magnet synchronous machine --- distribution generation --- leakage inductance --- adjacent two-phase open circuit fault (A2-Ph) --- chaotic PWM --- electric vehicles --- CMOS chaotic circuit --- series active filter --- cascaded topology --- total demand distortion --- efficiency motor --- triangular ramp generator --- 4T analog MOS control --- inductive coupling --- induction machines --- nanocrystalline core --- semi-active bridge --- multi-level control --- simulation models --- voltage source inverters (VSI) --- battery management system BMS --- voltage source converter --- current control loops --- droop control --- particle swarm optimization --- variable control gain --- state of charge SoC --- extended Kalman filter --- transient control --- multi-objective optimization --- composite equalizer --- converter --- DHIL --- five-leg voltage source inverter --- axial flux machines --- bifurcation --- active receivers --- field programmable gate array --- Nyquist stability analysis --- electric vehicle --- static compensator --- stability --- common-mode inductor --- DC–DC converters --- support vector machines --- electromagnetic compatibility --- real-time simulation --- passive equalization --- matrix converters --- wireless power transfer --- digital phase control --- compensation topology --- volt-per-hertz control (scalar control) --- switching losses --- voltage control --- hybrid converter --- bidirectional converter --- coupling factor --- selective harmonic elimination method --- power electronics --- soft switching --- optimization design --- multilevel inverter --- five-phase machine --- phase-shift control --- lithium-ion battery --- voltage boost --- VPI active damping control --- parameter identification --- electrical engineering communications --- current control --- DC–DC conversion --- battery management system --- GaN cascode --- single-switch --- high-frequency modeling --- synchronous motor --- power quality --- water purification --- power factor correction (PFC) --- composite active vectors modulation (CVM) --- digital signal controller --- line start --- power density --- hardware in loop --- n/a --- fault diagnosis --- multi-level converter (MLC) --- induction motor --- dual three-phase (DTP) permanent magnet synchronous motors (PMSMs) --- neural networks --- electromagnetic interference filter --- battery chargers --- power converter --- harmonics --- multiphase space vector modulation --- torque ripple --- power factor correction --- electrical drives --- modular multilevel converter (MMC) --- active power filter --- double layer capacitor (DLC) models --- PMSG --- response time --- resonator structure --- floating-point --- effect factors --- DC-link voltage control --- sliding mode control --- phasor model technique --- wireless power transfer (WPT) --- slim DC-link drive --- fault-tolerant control --- lithium-ion batteries --- DC-AC power converters --- conducting angle determination (CAD) techniques --- variable speed pumped storage system --- impedance-based model --- one cycle control --- renewable energy sources --- series-series compensation --- cogging torque --- active rectifiers --- three-level boost converter (TLBC) --- DC-link cascade H-bridge (DCLCHB) inverter --- battery energy storage systems --- filter --- power management system --- improved extended Kalman filter --- dead-time compensation --- disturbance observer --- reference phase calibration --- frequency locking --- space vector pulse width modulation (SVPWM) --- predictive controllers --- nine switch converter --- transmission line --- spread-spectrum technique --- energy storage --- electromagnetic interference --- renewable energy resources control --- harmonic linearization --- misalignment --- plug-in hybrid electric vehicles --- high level programing --- nearest level modulation (NLM) --- magnetic equivalent circuit --- EMI filter --- permanent-magnet machines --- real-time emulation --- switched capacitor --- back EMF --- fixed-point --- HF-link MPPT converter --- condition monitoring --- WPT standards --- switching frequency --- switching frequency modelling --- high frequency switching power supply --- field-programmable gate array --- three-phase bridgeless rectifier --- ice melting --- AC–DC power converters --- hybrid power filter --- PSpice --- microgrid control --- total harmonic distortion --- grid-connected inverter --- dynamic PV model --- fuzzy --- boost converter --- SiC PV Supply --- voltage doubling --- nonlinear control --- distributed control --- power system operation and control --- one phase open circuit fault (1-Ph) --- direct torque control (DTC) --- battery modeling --- non-linear phenomena --- frequency-domain analysis --- advanced controllers --- vector control --- fixed-frequency double integral sliding-mode (FFDISM) --- power converters --- modulation index --- DC-DC buck converter --- small signal stability analysis --- active equalization --- voltage source inverter --- hardware-in-the-loop --- current source --- synchronization --- grid-connected VSI --- synchronous generator --- fault tolerant control --- DC-DC converters --- DC-DC conversion --- AC-DC power converters