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7th IEEE International Advance Computing Conference (IACC)

作者： Das, Jayanta Kumar Choudhury, Pabitra Pal Indian Stat Inst Appl Stat Unit Kolkata 700108 India

ISBN: (纸本)9781509015603

Previously many works regarding addition and subtraction of two integers are done in CVT-XOR paradigm. It has been also seen that performance using Cellular automata machine (CAM) for addition and subtraction in CVT and XOR paradigm is much faster. In this current study, we mainly focus to handle the division algorithm and associated complexity in this paradigm. We also proposed a block diagram model of division algorithm which could be very much helpful for VLSI implementation on using recursive CAM.

关键词： CVT-XOR Operations division algorithm Complexity

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Computing GCD's by normalized division

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Applicable Algebra in Engineering, Communication and Computing 1992年第4期2卷 275-295页

作者： Norton, G.H. Centre for Communications Research Faculty of Engineering University of Bristol Bristol BS8 1TR United Kingdom

关键词： Complexity analysis division algorithm Greatest common divisor

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Newton-Raphson algorithms for Floating-Point division Using an FMA

Newton-Raphson Algorithms for Floating-Point Division Using ...

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21st IEEE International Conference on Application-Specific Systems, Architectures and Processors

作者： Louvet, Nicolas Muller, Jean-Michel Panhaleux, Adrien Univ Lyon UCBL INRIA ENS LyonCNRSLIP Lyon France

ISBN: (纸本)9781424469673

Since the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-2008 standard [6] for floating-point arithmetic, division based on Newton-Raphson's iterations becomes a viable alternative to SRT-based divisions. The Newton-Raphson iterations were already used in some architecture prior to the revision of the IEEE-754 norm. For example, Itanium architecture already used this kind of iterations [8]. Unfortunately, the proofs of the correctness of binary algorithms do not extend to the case of decimal floating-point arithmetic. In this paper, we present general methods to prove the correct rounding of division algorithms using Newton-Raphson's iterations in software, for radix 2 and radix 10 floating-point arithmetic.

关键词： floating-point arithmetic decimal floating-point arithmetic division algorithm Newton-Raphson iterations

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Quotient Prediction for Low Power division

Quotient Prediction for Low Power Division

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IEEE 26th International System-on-Chip Conference (SOCC)

作者： Krishnamoorthy, Prakash Tekumalla, Ramesh LSI Corp APAC SOC Design Allentown PA 18109 USA LSI Corp APAC SOC Dev Allentown PA 18109 USA

ISBN: (纸本)9781479911660

This work presents a variation of the non restoring division algorithm that has been optimized for low power consumption. The approach uses the value of the partial remainder at any stage in the computation to predict the quotient bits for a certain number of steps thereby allowing an equal number of computation steps to be skipped. This results in a significant reduction in switching activity in the computational stages. Simulations using the novel divider show up to 40% reduction in sequential switching activity and 20% reduction in combinational switching activity. On an average, this method uses 59% less addition operations as compared to the regular non restoring division algorithm.

关键词： division algorithm Quotient Sequential switching arithmetic

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On Complement division

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Communications of the ACM 1971年第4期14卷 260-264页

作者： Stein, Marvin L. Munro, William D. University of Minnesota Minneapolis United States

The division algorithm theorem is expressed in a form that permits it to serve as the basis for devising division operations that produce both quotient and remainder in complement form. algorithms for division yielding complement results are derived for numbers represented in any base greater than one. Both radix and radix-less-one complementation schemes are considered. The binary form of the algorithms thus includes both two's and one's complement implementation. The problem of quotient overflow for complement results is dealt with as is that of selecting an appropriate form of the remainder condition for complement division. © 1971, ACM. All rights reserved.

关键词： complement arithmetic complement division division algorithm one's complement arithmetic two's complement arithmetic

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Design of High-Speed Iterative Dividers in GF(2^m)

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2011年第3期27卷 953-967页

作者： Shieh, Mng-Der Lin, Wen-Ching Wu, Chien-Ming Natl Cheng Kung Univ Dept Elect Engn Tainan 701 Taiwan Natl Appl Res Labs Chip Implementat Ctr Hsinchu 300 Taiwan

Fast algorithms for high-speed divider design in finite fields GF(2(m)) are very crucial in applications like cryptosystems. In this paper, we reformulated the conventional iterative division algorithm by changing the pre-defined variable and then updating its initial value accordingly. The reformulated division algorithm allows a restructuring of the divider architecture to further improve its operating speed without increasing latency or area cost. Using the proposed fast algorithm, we developed two high-speed iterative dividers based on the semi-systolic and bit-serial systolic architectures. Analytical results show that the cost of the initial value update and variable transformation in the reformulated algorithm is almost negligible in the hardware implementation. Our divider designs improve the critical path delay. Compared with related divider designs, the proposed designs have time and area advantages.

关键词： division algorithm finite field high-speed Stein's algorithm systolic array

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Obtaining more Karatsuba-like formulae over the binary field

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IET INFORMATION SECURITY 2012年第1期6卷 14-19页

作者： Fan, H. Gu, M. Sun, J. Lam, K. -Y. Tsinghua Univ Sch Software Tsinghua Natl Lab Informat Sci & Technol Key Lab Informat Syst SecurMinist Educ Beijing 100084 Peoples R China

The aim of this study is to find more Karatsuba-like formulae for a fixed set of moduli polynomials in GF(2)[x]. To this end, a theoretical framework is established. The authors first generalise the division algorithm, and then present a generalised definition of the remainder of integer division. Finally, a generalised Chinese remainder theorem is used to achieve their initial goal. As a by-product of the generalised remainder of integer division, the authors rediscover Montgomery's N-residue and present a systematic interpretation of definitions of Montgomery's multiplication and addition operations.

关键词： Montgomery N-residue Montgomery multiplication generalised Chinese remainder theorem Algebra cryptography moduli polynomials addition operations integer division remainder Data security Cryptography Combinatorial mathematics Karatsuba-like formulae number theory polynomials binary field division algorithm

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An optimised solar-based microgrid integrated with desalination to enhance exergy sustainability

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INTERNATIONAL JOURNAL OF EXERGY 2023年第2期41卷 111-130页

作者： Kiehbadroudinezhad, Mohammadali Merabet, Adel Hosseinzadeh-Bandbafha, Homa St Marys Univ Div Engn Halifax NS B3H 3C3 Canada Univ Tehran Coll Agr & Nat Resources Fac Agr Engn & Technol Dept Mech Engn Agr Machinery Karaj Iran

The size of a solar microgrid system should be designed based on aspects of sustainability, such as cost, exergy, etc. This study by the division algorithm finds the optimal size with maximum reliability vs. the cumulative exergy demand. Larak Island, Iran, is used as an example of how the concept could be applied to the real world. According to the introduced optimal size, 1 m(3) of freshwater generated by the solar energy system leads to an average cumulative exergy demand of 17 MJ. While integrating a diesel generator into system means, exergy demand reaches 33 MJ/m(3) of freshwater.

关键词： solar energy cumulative exergy demand desalination optimisation reliability division algorithm

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Computation of Grobner Basis for Systematic Encoding of Generalized Quasi-Cyclic Codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第9期E92A卷 2345-2359页

作者： Van, Vo Tam Matsui, Hajime Mita, Seiichi Toyota Technol Inst Dept Elect & Informat Sci Nagoya Aichi 4688511 Japan

Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Grobner basis of modules, there has been no algorithm that computes Grobner basis for all types of GQC codes. In this paper, we propose two algorithms to compute Grobner basis for GQC codes from their parity check matrices;we call them echelon canonical form algorithm and transpose algorithm. Both algorithms require sufficiently small number of finite-field operations with the order of the third power of code-length. Each algorithm has its own characteristic. The first algorithm is composed of elementary methods and is appropriate for low-rate codes. The second algorithm is based oil a novel formula and has smaller computational complexity than the first one for high-rate codes with the number of orbits (cyclic parts) less than half of the code length. Moreover, we show that a serial-in serial-out encoder architecture for FG LDPC codes is composed of linear feedback shift registers with the size of the linear order of code-length;to encode a binary codeword of length it, it takes less than 2n adder and 2n memory elements.

关键词： automorphism group Buchberger's algorithm division algorithm circulant matrix finite geometry low density parity check (LDPC) codes

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PV_LOO-Based Training Set Selection Improves the External Predictability of QSAR/QSPR Models

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JOURNAL OF CHEMICAL INFORMATION AND MODELING 2017年第5期57卷 1055-1067页

作者： Dong, Ying Xiang, Bingren Du, Ding China Pharmaceut Univ Dept Organ Chem Coll Sci 639 Longmian Ave Nanjing 211198 Jiangsu Peoples R China China Pharmaceut Univ Inst Pharmaceut Sci 24 Tongjiaxiang Nanjing 210009 Jiangsu Peoples R China

In QSAR/QSPR modeling, the indispensable way to validate the predictability of a model is to perform its statistical external validation. It is common that a division algorithm should be used to select training sets from chemical compound libraries or collections prior to external validations. In this study, a division method based on the posterior variante of leave-one-out cross-validation (PVLOO) of the Gaussian process (GP) has been developed with the goal of producing more predictive models. Four structurally diverse data sets of good quality are collected from the literature and then redeveloped and validated on the basis of training set selection methods, namely, four kinds of PVLOO-based training set selection methods with three types of covariance functions (squared exponential, rational quadratic, and neural network covariance functions), the Kennard Stone algorithm, and random division. The root mean squared error (RMSE) of external validation reported for each model serves as a basis for the final comparison. The results of this study indicate that the training sets with higher values of PVLOO have statistically better external predictability than the training sets generated from other division methods discussed here. These findings could be explained by proposing that the PVLOO value of GP could indicate the mechanism diversity of a specific compound in QSAR/QSPR data sets.

关键词： division algorithm Basis Set (Psychology) ROOT-MEAN-SQUARE ERRORS GRAPHIC PANEL Geometric progression division method Training selection methods Functional training SETTING Set

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