DOCSLIB.ORG

Shared Variables Interaction Diagrams

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Shared Variables Interaction Diagrams Shared Variables Interaction Diagrams Rajeev Alur Radu Grosu Department of Computer and Information Science Department of Computer Science University of Pennsylvania State University of New York at Stony Brook [email protected] [email protected] Abstract variables paradigm. Textbooks on concurrent programming (e.g., [14, 17]) contain many pictures describing the interac- Scenario-based specifications offer an intuitive and vi- tions of processes communicating by shared variables, and sual way of describing design requirements of distributed similar scenarios arise in diverse areas such as transaction software systems. For the communication paradigm based processing in concurrent databases (c.f. [18]) and consis- on messages, message sequence charts (MSC) offer a stan- tency in shared-memory multiprocessors [13]. dardized and formal notation amenable to formal analysis. In our definition of an SVID, an action corresponds to, In this paper, we define shared variables interaction dia- possibly multiple, reading/writing of shared variables. The grams (SVID) as the counterpart of MSCs when processes actions of one process are visually ordered. The causal de- communicate via shared variables. After formally defining pendence among actions of different processes is illustrated SVIDs, we develop an intuitive as well as formal definition Ô by arrows: an arrow from an action a of process to an ac- of refinement for SVIDs. This notion provides a basis for Õ Õ tion b of process means that reads a value that was writ- systematically adding details to SVID requirements. ten by Ô. If the variable involved in this communication is write-shared, then there is an implicit additional constraint b that between these two actions a and , there is no interven- 1. Introduction ing action that writes to this variable. Checking whether all such implicit constraints are consistent with one another can Message Sequence Charts (MSCs) are a commonly used be computationally hard, and is shown to be NP-complete in visual description of design requirements for concurrent general. We also establish that the problem can be solved in systems such as telecommunications software [19], and linear-time when all the variables are read-shared but write- have been incorporated into software design notations such exclusive. Benefits of SVIDs are the same as that of MSCs: as UML [6]. On one hand, the clear graphical layout of an they give an intuitive and visual understanding of interac- MSC immediately gives an intuitive understanding of the tions among processes in a single execution, and have a intended system behavior, and on the other, the notation formal semantics. The execution of a concurrent program has been standardized (ITU standard Z.120) with precise can also be depicted by a linear trace involving actions of semantics, and hence, can be subjected to analysis. This all processes, but a single SVID captures many such execu- has already motivated the development of algorithms for a tions succinctly, and makes causal dependencies explicit. variety of analyses including detecting race conditions and An appealing notion for systematic hierarchical develop- timing conflicts [3], pattern matching [16], detecting non- ment of specifications or models involves refinement (this is local choice [7], and model checking [4], and tools such as present in all concurrency formalisms [20]). The definition uBET [11] and MESA [5]. of SVIDs, and the underlying shared-variables paradigm, An MSC depicts the desired exchange of messages suggests many natural ways of refining SVIDs. We identify among communicating entities in distributed software sys- different ways of visually adding more details to an SVID: tems. An alternative paradigm for communication in dis- by moving arrows depicting dependencies, by introducing tributed systems involves shared variables. Communication new variables, actions, and/or new arrows, by splitting com- and synchronization via shared objects provides a higher posite actions, and by splitting processes into subprocesses. level of abstraction, and is supported by many modern con- All these cases are captured by our formal definition of re- current programming languages. In this paper, we propose finement for SVIDs. The definition requires existence of a shared variables interaction diagrams (SVID) as a formal mapping of implementation actions to specification actions and visual notation for describing scenarios in the shared consistent with the dependencies. We show the problem of checking refinement to be NP-complete. When the commu- The inter-process communication via shared variables is nication is point-to-point, that is, each variable has a sin- depicted by arrows (or edges) between boxes. An arrow b b ¾ gle writer and a single reader, the problem can be solved in pointing from a box ½ to a box indicates that the value of b b ¾ polynomial time. the variables updated by ½ is read (or checked) by .For Å b b ½¾ ¾4 The remaining paper is organized as follows. Section 2 instance, in Figure 1, in ¾ , the arrow from to spec- f Ô b ¾ ¾4 introduces the definition of SVIDs. Section 3 defines the ifies that the value of ½ read by in box is the value f Ô b ½ ½¾ notion of refinement for SVIDs. Section 4 compares SVIDs written to ½ by in box . Thus, the arrows establish a to related formalisms, and in particular to message sequence causal order between actions of different processes: the ac- Ô b ¾4 charts (MSCs). tion of ¾ corresponding to must happen after the action Ô b ½¾ of ½ corresponding to . For write-shared variables, the arrows establish an additional causal dependence between 2. Shared Variables Interaction Diagrams reads and writes, namely, not only the read should happen after the write, but in addition, there should be no interven- Å Peterson’s mutual exclusion protocol. In order to il- ing write to the shared variable. For instance, in ¾ ,the b b Ø ½¿ lustrate the use and utility of shared variables interaction arrow from box ¾¾ to says that the value of read by Ô b Ø Ô b ½¿ ¾ ¾¾ diagrams (SVID) let us consider the Peterson’s mutual ex- ½ in box is the value written to by in box .This Ô Ô Ô b ½ ¾ ½¿ clusion protocol for two asynchronous processes and . means that the action of ½ corresponding to happens af- Ô Ô Ô b ½ ¾ ¾¾ The protocol makes sure that and never simultane- ter the action of ¾ corresponding to , and between these ously reach their critical sections and that each may eventu- two actions there is no action involving writing to the shared ally enter its critical section provided it desires to do so. variable Ø. In this case, this enforces an implicit causal de- Ô Ô b b Ô Ø ¾ ½¾ ¾¾ ¾ To achieve the desired synchronization among ½ and pendence between box and (i.e, writes to after f Ô ½ the protocol uses three variables. The first variable ½ is a in this scenario). Ô boolean variable (or flag), that when set, signals that ½ de- To simplify the notation we adopt the (usual) convention Ô sires to enter its critical section. It is writable only by ½ but that, write exclusive variables of a process preserve their Ô f b ¾ it can be read by ¾ . The second variable, the flag ,plays values if not explicitly updated. Hence, a box contained Ô Ô f Ô Ø ½ ½ thesamerolefor ¾ as does for . Finally, the variable by a process exports not only the variables explicitly up- Ô (turn) is used to resolve the conflict when both processes try dated by b but also the write exclusive variables of that are to simultaneously enter their critical sections. The variable not updated by b. This allows the use of empty boxes (not is written and read by both processes and ranges over the explicitly drawn) as sources for arrows. Similarly to MSCs ½; ¾g set of process identifiers, i.e., f in the binary case. the arrows may be labeled. However, the arrow labels are not messages. They are conditions over variables that have Exemplary SVIDs for the protocol. In Figure 1 we to hold in order to perform the update operation at the head show four typical scenarios for the Peterson’s protocol as of the arrow. basic SVIDs. They intuitively capture the synchronization The vertical process lines define a top down linear or- Ô Ô ¾ (communication) patterns between the processes ½ and . der among the update operations (boxes) of the same pro- Å Å ¿ The SVIDs ½ and describe the situations where only cess (like in MSCs time flows top/down). Hence, verti- Ô Ô Å ¾ ¾ ½ or only requests the critical section. The SVIDs cal lines describe local synchronization whereas arrows de- Å and 4 show how the tie is resolved when both processes scribe global synchronization. Ô Ô ¾ ½ and request the critical section. These scenarios can To improve readability we use, as with MSCs, condi- be used for understanding the behavior of the protocol, or tions. They are drawn inside hexagonal boxes. Intuitively, they can be used as a specification for designing the proto- a condition is an update of the program counter variable as- col. Clearly, there are many more scenarios that are possi- sociated with the relevant process. ble, and the specified ones serve only as a guide. In the following we define SVIDs in a formal way. To As with message sequence charts (MSCs), vertical lines simplify the definition we do not consider arrow labels. correspond to processes. However, in contrast to MSCs, They might be understood simply as comments that reflect the processes do not communicate with each other via mes- the most recent value of the associated variables. Similarly, sages. Instead, they communicate via shared variables.The we do not include the conditions in the formal definition. way a process updates its variables is given textually in the left compartment of rectangular boxes (or vertices). The Definition 1 (Shared variables interaction diagram) A variables needed (or read) by the update operations in a box shared variables interaction diagram Å consists of the fol- are given in the right compartment of the same box.
Load more

Recommended publications
  • An Array-Oriented Language with Static Rank Polymorphism
    An array-oriented language with static rank polymorphism Justin Slepak, Olin Shivers, and Panagiotis Manolios Northeastern University fjrslepak,shivers,[email protected] Abstract. The array-computational model pioneered by Iverson's lan- guages APL and J offers a simple and expressive solution to the \von Neumann bottleneck." It includes a form of rank, or dimensional, poly- morphism, which renders much of a program's control structure im- plicit by lifting base operators to higher-dimensional array structures. We present the first formal semantics for this model, along with the first static type system that captures the full power of the core language. The formal dynamic semantics of our core language, Remora, illuminates several of the murkier corners of the model. This allows us to resolve some of the model's ad hoc elements in more general, regular ways. Among these, we can generalise the model from SIMD to MIMD computations, by extending the semantics to permit functions to be lifted to higher- dimensional arrays in the same way as their arguments. Our static semantics, a dependent type system of carefully restricted power, is capable of describing array computations whose dimensions cannot be determined statically. The type-checking problem is decidable and the type system is accompanied by the usual soundness theorems. Our type system's principal contribution is that it serves to extract the implicit control structure that provides so much of the language's expres- sive power, making this structure explicitly apparent at compile time. 1 The Promise of Rank Polymorphism Behind every interesting programming language is an interesting model of com- putation.
    [Show full text]
  • Compendium of Technical White Papers
    COMPENDIUM OF TECHNICAL WHITE PAPERS Compendium of Technical White Papers from Kx Technical Whitepaper Contents Machine Learning 1. Machine Learning in kdb+: kNN classification and pattern recognition with q ................................ 2 2. An Introduction to Neural Networks with kdb+ .......................................................................... 16 Development Insight 3. Compression in kdb+ ................................................................................................................. 36 4. Kdb+ and Websockets ............................................................................................................... 52 5. C API for kdb+ ............................................................................................................................ 76 6. Efficient Use of Adverbs ........................................................................................................... 112 Optimization Techniques 7. Multi-threading in kdb+: Performance Optimizations and Use Cases ......................................... 134 8. Kdb+ tick Profiling for Throughput Optimization ....................................................................... 152 9. Columnar Database and Query Optimization ............................................................................ 166 Solutions 10. Multi-Partitioned kdb+ Databases: An Equity Options Case Study ............................................. 192 11. Surveillance Technologies to Effectively Monitor Algo and High Frequency Trading ..................
    [Show full text]
  • Application and Interpretation
    Programming Languages: Application and Interpretation Shriram Krishnamurthi Brown University Copyright c 2003, Shriram Krishnamurthi This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. If you create a derivative work, please include the version information below in your attribution. This book is available free-of-cost from the author’s Web site. This version was generated on 2007-04-26. ii Preface The book is the textbook for the programming languages course at Brown University, which is taken pri- marily by third and fourth year undergraduates and beginning graduate (both MS and PhD) students. It seems very accessible to smart second year students too, and indeed those are some of my most successful students. The book has been used at over a dozen other universities as a primary or secondary text. The book’s material is worth one undergraduate course worth of credit. This book is the fruit of a vision for teaching programming languages by integrating the “two cultures” that have evolved in its pedagogy. One culture is based on interpreters, while the other emphasizes a survey of languages. Each approach has significant advantages but also huge drawbacks. The interpreter method writes programs to learn concepts, and has its heart the fundamental belief that by teaching the computer to execute a concept we more thoroughly learn it ourselves. While this reasoning is internally consistent, it fails to recognize that understanding definitions does not imply we understand consequences of those definitions. For instance, the difference between strict and lazy evaluation, or between static and dynamic scope, is only a few lines of interpreter code, but the consequences of these choices is enormous.
    [Show full text]
  • Handout 16: J Dictionary
    J Dictionary Roger K.W. Hui Kenneth E. Iverson Copyright © 1991-2002 Jsoftware Inc. All Rights Reserved. Last updated: 2002-09-10 www.jsoftware.com . Table of Contents 1 Introduction 2 Mnemonics 3 Ambivalence 4 Verbs and Adverbs 5 Punctuation 6 Forks 7 Programs 8 Bond Conjunction 9 Atop Conjunction 10 Vocabulary 11 Housekeeping 12 Power and Inverse 13 Reading and Writing 14 Format 15 Partitions 16 Defined Adverbs 17 Word Formation 18 Names and Displays 19 Explicit Definition 20 Tacit Equivalents 21 Rank 22 Gerund and Agenda 23 Recursion 24 Iteration 25 Trains 26 Permutations 27 Linear Functions 28 Obverse and Under 29 Identity Functions and Neutrals 30 Secondaries 31 Sample Topics 32 Spelling 33 Alphabet and Numbers 34 Grammar 35 Function Tables 36 Bordering a Table 37 Tables (Letter Frequency) 38 Tables 39 Classification 40 Disjoint Classification (Graphs) 41 Classification I 42 Classification II 43 Sorting 44 Compositions I 45 Compositions II 46 Junctions 47 Partitions I 48 Partitions II 49 Geometry 50 Symbolic Functions 51 Directed Graphs 52 Closure 53 Distance 54 Polynomials 55 Polynomials (Continued) 56 Polynomials in Terms of Roots 57 Polynomial Roots I 58 Polynomial Roots II 59 Polynomials: Stopes 60 Dictionary 61 I. Alphabet and Words 62 II. Grammar 63 A. Nouns 64 B. Verbs 65 C. Adverbs and Conjunctions 66 D. Comparatives 67 E. Parsing and Execution 68 F. Trains 69 G. Extended and Rational Arithmeti 70 H. Frets and Scripts 71 I. Locatives 72 J. Errors and Suspensions 73 III. Definitions 74 Vocabulary 75 = Self-Classify - Equal 76 =. Is (Local) 77 < Box - Less Than 78 <.
    [Show full text]
  • Design Automation for Integrated Optics
    DESIGN AUTOMATION FOR INTEGRATED OPTICS by Christopher Condrat A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical and Computer Engineering The University of Utah August 2014 Copyright © Christopher Condrat 2014 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Christopher Condrat has been approved by the following supervisory committee members: Priyank Kalla , Chair 12 / 18 / 2013 Date Approved Steven Blair , Member 12 / 18 / 2013 Date Approved Chris Myers , Member 12 / 18 / 2013 Date Approved Kenneth Stevens , Member 12 / 18 / 2013 Date Approved Erik Brunvand , Member 12 / 18 / 2013 Date Approved and by Gianluca Lazzi , Chair/Dean of the Department/College/School of Electrical and Computer Engineering and by David B. Kieda, Dean of The Graduate School. ABSTRACT Recent breakthroughs in silicon photonics technology are enabling the integration of optical devices into silicon-based semiconductor processes. Photonics technology enables high-speed, high-bandwidth, and high-fidelity communications on the chip-scale—an important development in an increasingly communications-oriented semiconductor world. Significant developments in silicon photonic manufacturing and integration are also enabling investigations into applications beyond that of traditional telecom: sensing, filtering, signal processing, quantum technology—and even optical computing. In effect, we are now seeing a convergence of communications and computation, where the traditional roles of optics and microelectronics are becoming blurred. As the applications for opto-electronic integrated circuits (OEICs) are developed, and manufac- turing capabilities expand, design support is necessary to fully exploit the potential of this optics technology.
    [Show full text]
  • The C Programming Language
    The C programming Language The C programming Language By Brian W. Kernighan and Dennis M. Ritchie. Published by Prentice-Hall in 1988 ISBN 0-13-110362-8 (paperback) ISBN 0-13-110370-9 Contents ● Preface ● Preface to the first edition ● Introduction 1. Chapter 1: A Tutorial Introduction 1. Getting Started 2. Variables and Arithmetic Expressions 3. The for statement 4. Symbolic Constants 5. Character Input and Output 1. File Copying 2. Character Counting 3. Line Counting 4. Word Counting 6. Arrays 7. Functions 8. Arguments - Call by Value 9. Character Arrays 10. External Variables and Scope 2. Chapter 2: Types, Operators and Expressions 1. Variable Names 2. Data Types and Sizes 3. Constants 4. Declarations http://freebooks.by.ru/view/CProgrammingLanguage/kandr.html (1 of 5) [5/15/2002 10:12:59 PM] The C programming Language 5. Arithmetic Operators 6. Relational and Logical Operators 7. Type Conversions 8. Increment and Decrement Operators 9. Bitwise Operators 10. Assignment Operators and Expressions 11. Conditional Expressions 12. Precedence and Order of Evaluation 3. Chapter 3: Control Flow 1. Statements and Blocks 2. If-Else 3. Else-If 4. Switch 5. Loops - While and For 6. Loops - Do-While 7. Break and Continue 8. Goto and labels 4. Chapter 4: Functions and Program Structure 1. Basics of Functions 2. Functions Returning Non-integers 3. External Variables 4. Scope Rules 5. Header Files 6. Static Variables 7. Register Variables 8. Block Structure 9. Initialization 10. Recursion 11. The C Preprocessor 1. File Inclusion 2. Macro Substitution 3. Conditional Inclusion 5. Chapter 5: Pointers and Arrays 1.
    [Show full text]
  • Reducing State Explosion for Software Model Checking with Relaxed Mcms 3 We Do Not Distinguish the Framework from Its Implementation and Refer to Both As Mc- SPIN
    Reducing State Explosion for Software Model Checking with Relaxed Memory Consistency Models Tatsuya Abe1, Tomoharu Ugawa2, Toshiyuki Maeda1, and Kousuke Matsumoto2 1 {abet,tosh}@stair.center STAIR Lab, Chiba Institute of Technology 2 {ugawa,matsumoto}@plas.info.kochi-tech.ac.jp Kochi University of Technology Abstract. Software model checking suffers from the so-called state explosion problem, and relaxed memory consistency models even worsen this situation. What is worse, parameterizing model checking by memory consistency mod- els, that is, to make the model checker as flexible as we can supply definitions of memory consistency models as an input, intensifies state explosion. This pa- per explores specific reasons for state explosion in model checking with multi- ple memory consistency models, provides some optimizations intended to mit- igate the problem, and applies them to McSPIN, a model checker for memory consistency models that we are developing. The effects of the optimizations and the usefulness of McSPIN are demonstrated experimentally by verifying copying protocols of concurrent copying garbage collection algorithms. To the best of our knowledge, this is the first model checking of the concurrent copying protocols under relaxed memory consistency models. Keywords: software model checking; relaxed memory consistency models; state explosion; reordering of instructions; integration of states; concurrent copying garbage collection 1 Introduction Modern computing systems are based on concurrent/parallel processing designs for their performance advantages, and programs therefore must also be written to exploit these designs. However, writing such programs is quite difficult and error-prone, be- cause humans cannot exhaustively consider the behaviors of computers very well. One approach to this problem is to use software model checking, in which all possible states that can be reached during a program’sexecutionare explored.Many such model check- ers have been developed (e.g., [12,18,26,25,7,8]).
    [Show full text]
  • Chapter 1 Basic Principles of Programming Languages
    Chapter 1 Basic Principles of Programming Languages Although there exist many programming languages, the differences among them are insignificant compared to the differences among natural languages. In this chapter, we discuss the common aspects shared among different programming languages. These aspects include: programming paradigms that define how computation is expressed; the main features of programming languages and their impact on the performance of programs written in the languages; a brief review of the history and development of programming languages; the lexical, syntactic, and semantic structures of programming languages, data and data types, program processing and preprocessing, and the life cycles of program development. At the end of the chapter, you should have learned: what programming paradigms are; an overview of different programming languages and the background knowledge of these languages; the structures of programming languages and how programming languages are defined at the syntactic level; data types, strong versus weak checking; the relationship between language features and their performances; the processing and preprocessing of programming languages, compilation versus interpretation, and different execution models of macros, procedures, and inline procedures; the steps used for program development: requirement, specification, design, implementation, testing, and the correctness proof of programs. The chapter is organized as follows. Section 1.1 introduces the programming paradigms, performance, features, and the development of programming languages. Section 1.2 outlines the structures and design issues of programming languages. Section 1.3 discusses the typing systems, including types of variables, type equivalence, type conversion, and type checking during the compilation. Section 1.4 presents the preprocessing and processing of programming languages, including macro processing, interpretation, and compilation.
    [Show full text]
  • A Modern Reversible Programming Language April 10, 2015
    Arrow: A Modern Reversible Programming Language Author: Advisor: Eli Rose Bob Geitz Abstract Reversible programming languages are those whose programs can be run backwards as well as forwards. This condition impacts even the most basic constructs, such as =, if and while. I discuss Janus, the first im- perative reversible programming language, and its limitations. I then introduce Arrow, a reversible language with modern features, including functions. Example programs are provided. April 10, 2015 Introduction: Many processes in the world have the property of reversibility. To start washing your hands, you turn the knob to the right, and the water starts to flow; the process can be undone, and the water turned off, by turning the knob to the left. To turn your computer on, you press the power button; this too can be undone, by again pressing the power button. In each situation, we had a process (turning the knob, pressing the power button) and a rule that told us how to \undo" that process (turning the knob the other way, and pressing the power button again). Call the second two the inverses of the first two. By a reversible process, I mean a process that has an inverse. Consider two billiard balls, with certain positions and velocities such that they are about to collide. The collision is produced by moving the balls accord- ing to the laws of physics for a few seconds. Take that as our process. It turns out that we can find an inverse for this process { a set of rules to follow which will undo the collision and restore the balls to their original states1.
    [Show full text]
  • APL-The Language Debugging Capabilities, Entirely in APL Terms (No Core Symbol Denotes an APL Function Named' 'Compress," Dumps Or Other Machine-Related Details)
    DANIEL BROCKLEBANK APL - THE LANGUAGE Computer programming languages, once the specialized tools of a few technically trained peo­ p.le, are now fundamental to the education and activities of millions of people in many profes­ SIons, trades, and arts. The most widely known programming languages (Basic, Fortran, Pascal, etc.) have a strong commonality of concepts and symbols; as a collection, they determine our soci­ ety's general understanding of what programming languages are like. There are, however, several ~anguages of g~eat interest and quality that are strikingly different. One such language, which shares ItS acronym WIth the Applied Physics Laboratory, is APL (A Programming Language). A SHORT HISTORY OF APL it struggled through the 1970s. Its international con­ Over 20 years ago, Kenneth E. Iverson published tingent of enthusiasts was continuously hampered by a text with the rather unprepossessing title, A inefficient machine use, poor availability of suitable terminal hardware, and, as always, strong resistance Programming Language. I Dr. Iverson was of the opinion that neither conventional mathematical nota­ to a highly unconventional language. tions nor the emerging Fortran-like programming lan­ At the Applied Physics Laboratory, the APL lan­ guages were conducive to the fluent expression, guage and its practical use have been ongoing concerns publication, and discussion of algorithms-the many of the F. T. McClure Computing Center, whose staff alternative ideas and techniques for carrying out com­ has long been convinced of its value. Addressing the putation. His text presented a solution to this nota­ inefficiency problems, the Computing Center devel­ tion dilemma: a new formal language for writing clear, oped special APL systems software for the IBM concise computer programs.
    [Show full text]
  • Subsistence-Based Socioeconomic Systems in Alaska: an Introduction
    Special Publication No. SP1984-001 Subsistence-Based Socioeconomic Systems in Alaska: An Introduction by Robert J. Wolfe 1984 Alaska Department of Fish and Game Division of Subsistence Symbols and Abbreviations The following symbols and abbreviations, and others approved for the Système International d'Unités (SI), are used without definition in the reports by the Division of Subsistence. All others, including deviations from definitions listed below, are noted in the text at first mention, as well as in the titles or footnotes of tables, and in figure or figure captions. Weights and measures (metric) General Mathematics, statistics centimeter cm Alaska Administrative Code AAC all standard mathematical signs, symbols deciliter dL all commonly-accepted and abbreviations gram g abbreviations e.g., alternate hypothesis HA hectare ha Mr., Mrs., base of natural logarithm e kilogram kg AM, PM, etc. catch per unit effort CPUE kilometer km all commonly-accepted coefficient of variation CV liter L professional titles e.g., Dr., Ph.D., common test statistics (F, t, χ2, etc.) meter m R.N., etc. confidence interval CI milliliter mL at @ correlation coefficient (multiple) R millimeter mm compass directions: correlation coefficient (simple) r east E covariance cov Weights and measures (English) north N degree (angular ) ° cubic feet per second ft3/s south S degrees of freedom df foot ft west W expected value E gallon gal copyright greater than > inch in corporate suffixes: greater than or equal to ≥ mile mi Company Co. harvest per unit effort HPUE nautical mile nmi Corporation Corp. less than < ounce oz Incorporated Inc. less than or equal to ≤ pound lb Limited Ltd.
    [Show full text]
  • The C Programming Language
    The C programming Language By Brian W. Kernighan and Dennis M. Ritchie. Published by Prentice-Hall in 1988 ISBN 0-13-110362-8 (paperback) ISBN 0-13-110370-9 Contents Preface Preface to the first edition Introduction 1. Chapter 1: A Tutorial Introduction 1. Getting Started 2. Variables and Arithmetic Expressions 3. The for statement 4. Symbolic Constants 5. Character Input and Output 1. File Copying 2. Character Counting 3. Line Counting 4. Word Counting 6. Arrays 7. Functions 8. Arguments - Call by Value 9. Character Arrays 10. External Variables and Scope 2. Chapter 2: Types, Operators and Expressions 1. Variable Names 2. Data Types and Sizes 3. Constants 4. Declarations 5. Arithmetic Operators 6. Relational and Logical Operators 7. Type Conversions 8. Increment and Decrement Operators 9. Bitwise Operators 10. Assignment Operators and Expressions 11. Conditional Expressions 12. Precedence and Order of Evaluation 3. Chapter 3: Control Flow 1. Statements and Blocks 2. If-Else 3. Else-If 4. Switch 5. Loops - While and For 6. Loops - Do-While 7. Break and Continue 8. Goto and labels 4. Chapter 4: Functions and Program Structure 1. Basics of Functions 2. Functions Returning Non-integers 3. External Variables 4. Scope Rules 5. Header Files 6. Static Variables 7. Register Variables 8. Block Structure 9. Initialization 10. Recursion 11. The C Preprocessor 1. File Inclusion 2. Macro Substitution 3. Conditional Inclusion 5. Chapter 5: Pointers and Arrays 1. Pointers and Addresses 2. Pointers and Function Arguments 3. Pointers and Arrays 4. Address Arithmetic 5. Character Pointers and Functions 6. Pointer Arrays; Pointers to Pointers 7.
    [Show full text]