Three Methods of Finding Remainder on the Operation of Modular
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Transmit Processing in MIMO Wireless Systems
IEEE 6th CAS Symp. on Emerging Technologies: Mobile and Wireless Comm Shanghai, China, May 31-June 2,2004 Transmit Processing in MIMO Wireless Systems Josef A. Nossek, Michael Joham, and Wolfgang Utschick Institute for Circuit Theory and Signal Processing, Munich University of Technology, 80333 Munich, Germany Phone: +49 (89) 289-28501, Email: [email protected] Abstract-By restricting the receive filter to he scalar, we weighted by a scalar in Section IV. In Section V, we compare derive the optimizations for linear transmit processing from the linear transmit and receive processing. respective joint optimizations of transmit and receive filters. We A popular nonlinear transmit processing scheme is Tom- can identify three filter types similar to receive processing: the nmamit matched filter (TxMF), the transmit zero-forcing filter linson Harashima precoding (THP) originally proposed for (TxZE), and the transmil Menerfilter (TxWF). The TxW has dispersive single inpur single output (SISO) systems in [IO], similar convergence properties as the receive Wiener filter, i.e. [Ill, but can also be applied to MlMO systems [12], [13]. it converges to the matched filter and the zero-forcing Pter for THP is similar to decision feedback equalization (DFE), hut low and high signal to noise ratio, respectively. Additionally, the contrary to DFE, THP feeds back the already transmitted mean square error (MSE) of the TxWF is a lower hound for the MSEs of the TxMF and the TxZF. symbols to reduce the interference caused by these symbols The optimizations for the linear transmit filters are extended at the receivers. Although THP is based on the application of to obtain the respective Tomlinson-Harashimp precoding (THP) nonlinear modulo operators at the receivers and the transmitter, solutions. -
Download the Basketballplayer.Ngql Fle Here
Nebula Graph Database Manual v1.2.1 Min Wu, Amber Zhang, XiaoDan Huang 2021 Vesoft Inc. Table of contents Table of contents 1. Overview 4 1.1 About This Manual 4 1.2 Welcome to Nebula Graph 1.2.1 Documentation 5 1.3 Concepts 10 1.4 Quick Start 18 1.5 Design and Architecture 32 2. Query Language 43 2.1 Reader 43 2.2 Data Types 44 2.3 Functions and Operators 47 2.4 Language Structure 62 2.5 Statement Syntax 76 3. Build Develop and Administration 128 3.1 Build 128 3.2 Installation 134 3.3 Configuration 141 3.4 Account Management Statement 161 3.5 Batch Data Management 173 3.6 Monitoring and Statistics 192 3.7 Development and API 199 4. Data Migration 200 4.1 Nebula Exchange 200 5. Nebula Graph Studio 224 5.1 Change Log 224 5.2 About Nebula Graph Studio 228 5.3 Deploy and connect 232 5.4 Quick start 237 5.5 Operation guide 248 6. Contributions 272 6.1 Contribute to Documentation 272 6.2 Cpp Coding Style 273 6.3 How to Contribute 274 6.4 Pull Request and Commit Message Guidelines 277 7. Appendix 278 7.1 Comparison Between Cypher and nGQL 278 - 2/304 - 2021 Vesoft Inc. Table of contents 7.2 Comparison Between Gremlin and nGQL 283 7.3 Comparison Between SQL and nGQL 298 7.4 Vertex Identifier and Partition 303 - 3/304 - 2021 Vesoft Inc. 1. Overview 1. Overview 1.1 About This Manual This is the Nebula Graph User Manual. -
The Best of Both Worlds?
The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge Thesis submitted for the degree of Master in Informatics: Programming and Networks 60 credits Department of Informatics Faculty of mathematics and natural sciences UNIVERSITY OF OSLO Autumn 2019 The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge © 2019 Erik Bugge The Best of Both Worlds? http://www.duo.uio.no/ Printed: Reprosentralen, University of Oslo Abstract Programming paradigms are categories that classify languages based on their features. Each paradigm category contains rules about how the program is built. Comparing programming paradigms and languages is important, because it lets developers make more informed decisions when it comes to choosing the right technology for a system. Making meaningful comparisons between paradigms and languages is challenging, because the subjects of comparison are often so dissimilar that the process is not always straightforward, or does not always yield particularly valuable results. Therefore, multiple avenues of comparison must be explored in order to get meaningful information about the pros and cons of these technologies. This thesis looks at the difference between the object-oriented and functional programming paradigms on a higher level, before delving in detail into a development process that consisted of reimplementing parts of an object- oriented system into functional code. Using results from major comparative studies, exploring high-level differences between the two paradigms’ tools for modular programming and general program decompositions, and looking at the development process described in detail in this thesis in light of the aforementioned findings, a comparison on multiple levels was done. -
1.3 Division of Polynomials; Remainder and Factor Theorems
1-32 CHAPTER 1. POLYNOMIAL AND RATIONAL FUNCTIONS 1.3 Division of Polynomials; Remainder and Factor Theorems Objectives • Perform long division of polynomials • Perform synthetic division of polynomials • Apply remainder and factor theorems In previous courses, you may have learned how to factor polynomials using various techniques. Many of these techniques apply only to special kinds of polynomial expressions. For example, the the previous two sections of this chapter dealt only with polynomials that could easily be factored to find the zeros and x-intercepts. In order to be able to find zeros and x-intercepts of polynomials which cannot readily be factored, we first introduce long division of polynomials. We will then use the long division algorithm to make a general statement about factors of a polynomial. Long division of polynomials Long division of polynomials is similar to long division of numbers. When divid- ing polynomials, we obtain a quotient and a remainder. Just as with numbers, if a remainder is 0, then the divisor is a factor of the dividend. Example 1 Determining Factors by Division Divide to determine whether x − 1 is a factor of x2 − 3x +2. Solution Here x2 − 3x +2is the dividend and x − 1 is the divisor. Step 1 Set up the division as follows: divisor → x − 1 x2−3x+2 ← dividend Step 2 Divide the leading term of the dividend (x2) by the leading term of the divisor (x). The result (x)is the first term of the quotient, as illustrated below. x ← first term of quotient x − 1 x2 −3x+2 1.3. -
Functional C
Functional C Pieter Hartel Henk Muller January 3, 1999 i Functional C Pieter Hartel Henk Muller University of Southampton University of Bristol Revision: 6.7 ii To Marijke Pieter To my family and other sources of inspiration Henk Revision: 6.7 c 1995,1996 Pieter Hartel & Henk Muller, all rights reserved. Preface The Computer Science Departments of many universities teach a functional lan- guage as the first programming language. Using a functional language with its high level of abstraction helps to emphasize the principles of programming. Func- tional programming is only one of the paradigms with which a student should be acquainted. Imperative, Concurrent, Object-Oriented, and Logic programming are also important. Depending on the problem to be solved, one of the paradigms will be chosen as the most natural paradigm for that problem. This book is the course material to teach a second paradigm: imperative pro- gramming, using C as the programming language. The book has been written so that it builds on the knowledge that the students have acquired during their first course on functional programming, using SML. The prerequisite of this book is that the principles of programming are already understood; this book does not specifically aim to teach `problem solving' or `programming'. This book aims to: ¡ Familiarise the reader with imperative programming as another way of imple- menting programs. The aim is to preserve the programming style, that is, the programmer thinks functionally while implementing an imperative pro- gram. ¡ Provide understanding of the differences between functional and imperative pro- gramming. Functional programming is a high level activity. -
Fast Integer Division – a Differentiated Offering from C2000 Product Family
Application Report SPRACN6–July 2019 Fast Integer Division – A Differentiated Offering From C2000™ Product Family Prasanth Viswanathan Pillai, Himanshu Chaudhary, Aravindhan Karuppiah, Alex Tessarolo ABSTRACT This application report provides an overview of the different division and modulo (remainder) functions and its associated properties. Later, the document describes how the different division functions can be implemented using the C28x ISA and intrinsics supported by the compiler. Contents 1 Introduction ................................................................................................................... 2 2 Different Division Functions ................................................................................................ 2 3 Intrinsic Support Through TI C2000 Compiler ........................................................................... 4 4 Cycle Count................................................................................................................... 6 5 Summary...................................................................................................................... 6 6 References ................................................................................................................... 6 List of Figures 1 Truncated Division Function................................................................................................ 2 2 Floored Division Function................................................................................................... 3 3 Euclidean -
Grade 7/8 Math Circles Modular Arithmetic the Modulus Operator
Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 7/8 Math Circles April 3, 2014 Modular Arithmetic The Modulus Operator The modulo operator has symbol \mod", is written as A mod N, and is read \A modulo N" or "A mod N". • A is our - what is being divided (just like in division) • N is our (the plural is ) When we divide two numbers A and N, we get a quotient and a remainder. • When we ask for A ÷ N, we look for the quotient of the division. • When we ask for A mod N, we are looking for the remainder of the division. • The remainder A mod N is always an integer between 0 and N − 1 (inclusive) Examples 1. 0 mod 4 = 0 since 0 ÷ 4 = 0 remainder 0 2. 1 mod 4 = 1 since 1 ÷ 4 = 0 remainder 1 3. 2 mod 4 = 2 since 2 ÷ 4 = 0 remainder 2 4. 3 mod 4 = 3 since 3 ÷ 4 = 0 remainder 3 5. 4 mod 4 = since 4 ÷ 4 = 1 remainder 6. 5 mod 4 = since 5 ÷ 4 = 1 remainder 7. 6 mod 4 = since 6 ÷ 4 = 1 remainder 8. 15 mod 4 = since 15 ÷ 4 = 3 remainder 9.* −15 mod 4 = since −15 ÷ 4 = −4 remainder Using a Calculator For really large numbers and/or moduli, sometimes we can use calculators to quickly find A mod N. This method only works if A ≥ 0. Example: Find 373 mod 6 1. Divide 373 by 6 ! 2. Round the number you got above down to the nearest integer ! 3. -
Strength Reduction of Integer Division and Modulo Operations
Strength Reduction of Integer Division and Modulo Operations Saman Amarasinghe, Walter Lee, Ben Greenwald M.I.T. Laboratory for Computer Science Cambridge, MA 02139, U.S.A. g fsaman,walt,beng @lcs.mit.edu http://www.cag.lcs.mit.edu/raw Abstract Integer division, modulo, and remainder operations are expressive and useful operations. They are logical candidates to express complex data accesses such as the wrap-around behavior in queues using ring buffers, array address calculations in data distribution, and cache locality compiler-optimizations. Experienced application programmers, however, avoid them because they are slow. Furthermore, while advances in both hardware and software have improved the performance of many parts of a program, few are applicable to division and modulo operations. This trend makes these operations increasingly detrimental to program performance. This paper describes a suite of optimizations for eliminating division, modulo, and remainder operations from programs. These techniques are analogous to strength reduction techniques used for multiplications. In addition to some algebraic simplifications, we present a set of optimization techniques which eliminates division and modulo operations that are functions of loop induction variables and loop constants. The optimizations rely on number theory, integer programming and loop transformations. 1 Introduction This paper describes a suite of optimizations for eliminating division, modulo, and remainder operations from pro- grams. In addition to some algebraic simplifications, we present a set of optimization techniques which eliminates division and modulo operations that are functions of loop induction variables and loop constants. These techniques are analogous to strength reduction techniques used for multiplications. Integer division, modulo, and remainder are expressive and useful operations. -
Basic Math Quick Reference Ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference eBOOK Click on The math facts listed in this eBook are explained with Contents or Examples, Notes, Tips, & Illustrations Index in the in the left Basic Math Quick Reference Handbook. panel ISBN: 978-0-615-27390-7 to locate a topic. Peter J. Mitas Quick Reference Handbooks Facts from the Basic Math Quick Reference Handbook Contents Click a CHAPTER TITLE to jump to a page in the Contents: Whole Numbers Probability and Statistics Fractions Geometry and Measurement Decimal Numbers Positive and Negative Numbers Universal Number Concepts Algebra Ratios, Proportions, and Percents … then click a LINE IN THE CONTENTS to jump to a topic. Whole Numbers 7 Natural Numbers and Whole Numbers ............................ 7 Digits and Numerals ........................................................ 7 Place Value Notation ....................................................... 7 Rounding a Whole Number ............................................. 8 Operations and Operators ............................................... 8 Adding Whole Numbers................................................... 9 Subtracting Whole Numbers .......................................... 10 Multiplying Whole Numbers ........................................... 11 Dividing Whole Numbers ............................................... 12 Divisibility Rules ............................................................ 13 Multiples of a Whole Number ....................................... -
Computing Mod Without Mod
Computing Mod Without Mod Mark A. Will and Ryan K. L. Ko Cyber Security Lab The University of Waikato, New Zealand fwillm,[email protected] Abstract. Encryption algorithms are designed to be difficult to break without knowledge of the secrets or keys. To achieve this, the algorithms require the keys to be large, with some algorithms having a recommend size of 2048-bits or more. However most modern processors only support computation on 64-bits at a time. Therefore standard operations with large numbers are more complicated to implement. One operation that is particularly challenging to implement efficiently is modular reduction. In this paper we propose a highly-efficient algorithm for solving large modulo operations; it has several advantages over current approaches as it supports the use of a variable sized lookup table, has good spatial and temporal locality allowing data to be streamed, and only requires basic processor instructions. Our proposed algorithm is theoretically compared to widely used modular algorithms, before practically compared against the state-of-the-art GNU Multiple Precision (GMP) large number li- brary. 1 Introduction Modular reduction, also known as the modulo or mod operation, is a value within Y, such that it is the remainder after Euclidean division of X by Y. This operation is heavily used in encryption algorithms [6][8][14], since it can \hide" values within large prime numbers, often called keys. Encryption algorithms also make use of the modulo operation because it involves more computation when compared to other operations like add. Meaning that computing the modulo operation is not as simple as just adding bits. -
Faster Chinese Remaindering Joris Van Der Hoeven
Faster Chinese remaindering Joris van der Hoeven To cite this version: Joris van der Hoeven. Faster Chinese remaindering. 2016. hal-01403810 HAL Id: hal-01403810 https://hal.archives-ouvertes.fr/hal-01403810 Preprint submitted on 27 Nov 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Faster Chinese remaindering Joris van der Hoeven Laboratoire d'informatique, UMR 7161 CNRS Campus de l'École polytechnique 1, rue Honoré d'Estienne d'Orves Bâtiment Alan Turing, CS35003 91120 Palaiseau November 27, 2016 The Chinese remainder theorem is a key tool for the design of ecient multi-modular algorithms. In this paper, we study the case when the moduli m1; :::; m` are xed and can even be chosen by the user. Through an appropriate use of the technique of FFT-trading, we will show that this assumption allows for the gain of an asymptotic factor O(log log `) in the complexity of Chinese remaindering. For small `, we will also show how to choose gentle moduli that allow for further gains at the other end. The multiplication of integer matrices is one typical application where we expect practical gains for various common matrix dimensions and integer bitsizes. -
Haskell-Like S-Expression-Based Language Designed for an IDE
Department of Computing Imperial College London MEng Individual Project Haskell-Like S-Expression-Based Language Designed for an IDE Author: Supervisor: Michal Srb Prof. Susan Eisenbach June 2015 Abstract The state of the programmers’ toolbox is abysmal. Although substantial effort is put into the development of powerful integrated development environments (IDEs), their features often lack capabilities desired by programmers and target primarily classical object oriented languages. This report documents the results of designing a modern programming language with its IDE in mind. We introduce a new statically typed functional language with strong metaprogramming capabilities, targeting JavaScript, the most popular runtime of today; and its accompanying browser-based IDE. We demonstrate the advantages resulting from designing both the language and its IDE at the same time and evaluate the resulting environment by employing it to solve a variety of nontrivial programming tasks. Our results demonstrate that programmers can greatly benefit from the combined application of modern approaches to programming tools. I would like to express my sincere gratitude to Susan, Sophia and Tristan for their invaluable feedback on this project, my family, my parents Michal and Jana and my grandmothers Hana and Jaroslava for supporting me throughout my studies, and to all my friends, especially to Harry whom I met at the interview day and seem to not be able to get rid of ever since. ii Contents Abstract i Contents iii 1 Introduction 1 1.1 Objectives ........................................ 2 1.2 Challenges ........................................ 3 1.3 Contributions ...................................... 4 2 State of the Art 6 2.1 Languages ........................................ 6 2.1.1 Haskell ....................................