DOCSLIB.ORG

Extension Proposal: Boolean Data Type

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Extension Proposal: Boolean Data Type ANSI Do c No: X3J16/93-0143 ISO Do c No: WG21/N0350 Date: Septemb er 27, 1993 ++ Pro ject: Prog. Language C Reply To: Dag Bruc k [email protected] Extension prop osal: Bo olean data typ e 1 2 Dag Bruc k and Andrew Ko enig 1. Intro duction ++ The idea of a Bo olean datatyp e in C is a religious issue. Some p eople, particularly those coming from Pascal or Algol, consider it absurd that C ++ should lack suchatyp e, let alone C . Others, particularly those coming from C, consider it absurd that anyone would b other to add suchatyp e to ++ C . Why b other indeed? The main reason is that p eople who like suchtyp es often write header les that contain things like this: typedef int bool; class Mine { // ... }; bool operator==(const Mine &, const Mine &); Such a header le is just ne until someone else's header le says typedef char bool; If b oth header les used int, there would b e no problem, but trying to de ne bool as two di erenttyp es just won't work. ++ Several widely used C libraries, including X11 and InterViews, de ne a Bo olean datatyp e. The di erences in the de nitions of the Bo olean datatyp e create very real compatibility problems when mixing libraries from multiple sources. In principle, this problem could b e solved by agreeing on a single typ e de nition of bool as part of the standard library, just as NULL is part of 1 Author's address: Dynasim AB, ResearchPark Ideon, S-223 70 Lund, SWEDEN. E-mail: [email protected] 2 Author's address: AT&T Bell Lab oratories, 600 Mountain Avenue, Ro om 6D-416B, PO Box 636, Murray Hill, NJ 07974-0636, USA. E-mail: [email protected] 1 X3J16/93-0143 WG21/N0350 the standard C library.However, that approach has several signi cant disad- vantages when compared with the prop osal that follows. In particular, any prop osal that makes the Bo olean typ e a synonym for any other built-in typ e gives up the p ossibilityofoverloading on that typ e. On the surface, it is hard to b elieve that any compromise is p ossible between those extremes. After all, a language either has a Bo olean typeorit do es not. However, closer examination suggests that a middle ground might b e p ossible: a Bo olean typ e whose existence the programmer has the option to ignore. This prop osal shows how suchatyp e can work. It is the result of dis- cussions with a numb er of p eople, b oth in p erson and via electronic mail. Of course, any mistakes or misjudgments in this prop osal are ours alone. 2. Executive summary We prop ose the creation of a new built-in typ e called bool, with the following prop erties: bool is a unique signed integral typ e, just as the wchar_t is a unique unsigned typ e. There are two built-in constants of this typ e: true and false. Op erator ++ is de ned for bool; it always sets its op erand to true. This op erator is an anachronism, and its use is deprecated. A bool value may b e converted to int by promotion, taking true to one and false to zero. Anumeric or p ointer value is automatically converted to bool when needed. This is an anachronism, and its use is deprecated. When converting a numeric or p ointer value to bool, a zero value b ecomes false; a non-zero value b ecomes true. The built-in op erators &&, ||, and ! are changed to take bool values as their arguments and return bool results. The relational op erators <, >, <=, >=, ==, and != are changed to yield a bool result. Expressions used as conditions in if, for, while,ordo statements or as the rst op erand of a ?: expression, are automatically converted to bool. We b elieve this extension is upward compatible except for the new keywords bool, true, and false. 3. Rationale and examples Current practice A quickinvestigation of one computer system reveals that Bo olean datatyp es are quite common in widely used libraries. In the /usr/include area on one of our machines (bellman.control.lth.se), the de nitions of Bo olean in Table 1 can b e found. Various libraries also de ne true and false, see Table 2. The header les that do not rely on a de nition of Bo olean seem to b e part of the Sun op erating system. 2 X3J16/93-0143 WG21/N0350 curses.h #de ne b o ol char X11 #de ne Bo ol int gcc/X11 Multiple de nitions of Bo olean, dep ends on machine typ e etc. netap/appletalk.h typ edef int b o olean; tint rp c/typ es.h #de ne b o ol rp c/*.h Many uses of b o ol t nfs/nfs.h Uses b o ol t t tfs/tfs.h Uses b o ol sunwindow/rect.h #de ne b o ol unsigned sunwindow/sun.h typ edef enum fFalse = 0, True = 1g Bo ol; sunwindow/*.h Uses b o ol sunto ol/*.h Uses b o ol, at least as comment InterViews typ edef unsigned b o olean; NEWMAT matrices bool de ned as class or char, dep ends on compiler C++Views boolean de ned with typ edef sys/typ es.h (Solaris) typ edef 'd as enumeration Table 1. Current de nitions of boolean. curses.h #de ne TRUE 1 #de ne FALSE 0 X11/Intrinsic.h (same) gcc/X11/Intrinsic.h (same) netat/appletalk.h (same) pixrect/gtvar.h (same) sbusdev/audiovar.h (same) sunto ol/*.h (2 places) (same) sunwindow/ (2 places) (same) scsi/adapters/espvar.h (same) X11 (2 places) #de ne True 1 #de ne False 0 rp c/typ es.h #de ne FALSE (0) #de ne TRUE (1) sundev/dfreg.h #de ne TRUE 1 (but not FALSE!) sunwindow/sun.h typ edef enum fFalse = 0, True = 1g Bo ol; InterViews static const unsigned true = 1; static const unsigned false = 0; Rogue Wave Matrix (same as curses.h) C++Views (same as curses.h) sys/typ es.h (Solaris) B FALSE and B TRUE enumerators Table 2. Current de nitions of true and false. Wehave also found the following de nition of Bo olean in sys/typ es.h under Solaris 2.2: typedef enum boolean {B_FALSE, B_TRUE} boolean_t; with a reference to POSIX. It is however unclear if this de nition is part of POSIX or a Sun extension. Our conclusion is that the b o olean datatyp e is a fact of life whether it ++ is part of the C standard or not. However, there is currently a substantial variation in the de nitions, as shown by the tables. These variations create 3 X3J16/93-0143 WG21/N0350 several compatibility problems: Di erent names (e.g., bool, Bool, boolean, bool t) are used to identify one conceptual typ e. The Bo olean datatyp e may b e rede ned, which in the case of typ edefs is a fatal compilation error. Di erent de nitions may not b e typ e compatible, for example, Bo olean de ned as an int and as an enumeration. Overloading on Bo olean typ es is particularly sensitive. Di erent amounts of storage may b e allo cated for Bo olean typ es. ++ C has a less strict typ e system than C , so these variations are less of a ++ ++ problem in C than in C . Because C do es not allow implicit conversion from int to enumeration, current de nitions of Bo olean that use an enumer- ation cannot b e used without a large numb er of explicit typ ecasts. In the case of Solaris 2.2, this is particularly worrying b ecause a de nition in sys/typ es.h is likely to frequently used. Built-in vs. user-de ned typ e Adding a new typ e is essential for overloading. For example: void f(int); void f(bool); main() { f(3 < 4); } In order for this example to work, bool must b e a built-in or enumeration typ e; there is simply no way around it. On the other hand, allowing the standard promotion from bool to int is essential for backward compatibility: void f(int); void f(double); main() { f(3 < 4); } would change meaning otherwise. The p oint of the standard promotion is to p ermit any bool expression to act precisely likeanint expression in the absence of explicitly declared bool ob jects. The Bo olean datatyp e cannot b e de ned as an ordinary class typ e b ecause of the rule that says that at most one user-de ned conversion is automatically applied: class X { public: X(int); }; void f(X); main() { f(3 < 4); } For f(3<4) to work, the conversion from bool to int must not b e a user- de ned conversion. 4 X3J16/93-0143 WG21/N0350 Conversion from int to bool For similar reasons, conversion from numeric or p ointer typ es to bool must b e allowed. We do not exp ect p eople to stop using int values to hold ags, which means that things like int done = 0; while (!done) { // ... if (/* ... */) ++done; // ... } must remain legal. In this example, the expression !done causes done to b e converted to bool b efore negation, with exactly the same semantics as always.
Load more

Recommended publications
  • Customizing and Extending Powerdesigner SAP Powerdesigner Documentation Collection Content
    User Guide PUBLIC SAP PowerDesigner Document Version: 16.6.2 – 2017-01-05 Customizing and Extending PowerDesigner SAP PowerDesigner Documentation Collection Content 1 PowerDesigner Resource Files.................................................... 9 1.1 Opening Resource Files in the Editor.................................................10 1.2 Navigating and Searching in Resource Files............................................ 11 1.3 Editing Resource Files........................................................... 13 1.4 Saving Changes................................................................13 1.5 Sharing and Embedding Resource Files...............................................13 1.6 Creating and Copying Resource Files.................................................14 1.7 Specifying Directories to Search for Resource Files.......................................15 1.8 Comparing Resource Files........................................................ 15 1.9 Merging Resource Files.......................................................... 16 2 Extension Files................................................................18 2.1 Creating an Extension File.........................................................19 2.2 Attaching Extensions to a Model....................................................20 2.3 Exporting an Embedded Extension File for Sharing.......................................21 2.4 Extension File Properties......................................................... 21 2.5 Example: Adding a New Attribute from a Property
    [Show full text]
  • PL/SQL Data Types
    PPLL//SSQQLL -- DDAATTAA TTYYPPEESS http://www.tutorialspoint.com/plsql/plsql_data_types.htm Copyright © tutorialspoint.com PL/SQL variables, constants and parameters must have a valid data type, which specifies a storage format, constraints, and valid range of values. This tutorial will take you through SCALAR and LOB data types available in PL/SQL and other two data types will be covered in other chapters. Category Description Scalar Single values with no internal components, such as a NUMBER, DATE, or BOOLEAN. Large Object LOB Pointers to large objects that are stored separately from other data items, such as text, graphic images, video clips, and sound waveforms. Composite Data items that have internal components that can be accessed individually. For example, collections and records. Reference Pointers to other data items. PL/SQL Scalar Data Types and Subtypes PL/SQL Scalar Data Types and Subtypes come under the following categories: Date Type Description Numeric Numeric values on which arithmetic operations are performed. Character Alphanumeric values that represent single characters or strings of characters. Boolean Logical values on which logical operations are performed. Datetime Dates and times. PL/SQL provides subtypes of data types. For example, the data type NUMBER has a subtype called INTEGER. You can use subtypes in your PL/SQL program to make the data types compatible with data types in other programs while embedding PL/SQL code in another program, such as a Java program. PL/SQL Numeric Data Types and Subtypes Following
    [Show full text]
  • Boolean Data Type & Expressions Outline Basic Data Types
    Boolean Data Type & Expressions Outline Basic Data Types 1. Boolean Data Type & Expressions Outline Numeric 2. Basic Data Types – int 3. C Boolean Data Types: char or int/ – float Boolean Declaration Non-numeric 4. Boolean or Character? – char 5. Boolean Literal Constants #include <stdio.h> 6. Boolean Expressions/ int main () Boolean Operations ¡ /* main */ 7. Example: Boolean Literal Constants & Expressions float standard_deviation, relative_humidity; int count, number_of_silly_people; 8. Example: Boolean Variables char middle_initial, hometown[30]; ¢ 9. Relational Operations /* main */ 10. Example: Relational Expressions 11. Structure of Boolean Expressions 12. Precedence Order of Boolean Operations 13. Another Boolean Precedence Example 14. Example: Boolean Precedence Order 15. Example: More Relational Expressions 16. Example: More Relational Expressions (continued) 17. Short Circuiting 18. Exercise: Writing a Program 1 2 C Boolean Data Type: char or int Boolean or Character? The C data type typically used for storing Boolean values is char, Question: How does the C compiler know that a particular char although int will also work. declaration is a Boolean rather than a character? Like numeric data types, Booleans have particular ways of being Answer: It doesn’t. stored in memory and of being operated on. % cat shortcircuit.c #include <stdio.h> Conceptually, a Boolean value represents a single bit in memory, char int int main () although the and data types aren’t implemented this ¡ /* main */ way — if for no other reason than that computers can’t address a const int maximum_short_height_in_cm = 170; single bit, since the smallest collection of bits that they can address int my_height_in_cm = 160; char I_am_Henry = 1; is a byte (or, in a few cases, a word).
    [Show full text]
  • Xml Schema Boolean Data Type Example
    Xml Schema Boolean Data Type Example Binomial and uncomposable Hussein often inveighs some masterdom alongside or apologizes flawlessly. Sandro is unwitting and congeed worst as ninety Lovell minimises greenly and candling avertedly. Postponed or palsy-walsy, Nahum never sectionalises any height-to-paper! Our solution can be used by sql anywhere enables complex xml data For example Integerlength2 allows 10 99 and 1 but not 100 9 or 10. Implemented across major programming languages and a school setting mode switches for a csv go by first search pattern on the button clicks, including different parts: xml schema boolean data type. Package API xmlschema 142 documentation. Int xmlhttpexamplecom sequence Virtual bool xmlhttpexamplecom virtual. Creating a fact data item in XNAT consists of creating the XSD that defines the data center itself. Wrapping character type. XSD Miscellaneous Data Types Tutorialspoint. XML Schema Instance namespace available. Field Constraints and Validation Nuxeo Documentation. Examples of the schema describing the binary data Overview. OpenClinica supports a subset of many Item Data Types defined in ODM. Use the same type to data type of text. AS CSV GO I consider XML as the best solution in terms of code and performance. Thank you guys so much! Datatype Examples Collection area HL7Wiki. Dependent child elements with xsdassert Oxygen XML Forum. With join syntax limit syntaxx views inserts boolean handling of NULLS. XML Schema Simple Elements. The correct performance: although it else you can be extremely important in schema in property with a namespace declaration will validate xml? Set to b are not validated during the value as the values, and removed the xml schema to be masked in xml schema? All data dictionary and examples and hard to use.
    [Show full text]
  • Declare True in C
    Declare True In C When Trent maladminister his prunes unpins not crazily enough, is Rog draperied? Marlowe is irreducibly repayable after attenuated Miles congregate his mumblers adorably. Emilio often sorrow municipally when relaxant Ximenez mispunctuating scenically and overstrikes her idiotism. Learn more concise, in true then you have just same To lateral the size of your trade in bytes you then use the sizeof operator int a17 sizet n sizeofa On my computer ints are 4 bytes long so n is 6 To determine what number of elements in input array we shall divide those total size of flash array apply the size of one array element. A true boolean data type gonna be used for storing logical values and would only submit two legal values true memory false C does cab have boolean data types and normally uses integers for boolean testing Zero is used to fire false just One is used to fill true. In C any nonzero value is treated as true health a zero value is treated as. Groovy also supports the Java colon variation with colons for char c text. A hollow object declared in this way will have no values other share the. A variable declaration always contains two components the responsible of the variable. 49 Boolean values Learn C. Documentation Advanced Types TypeScript. Operators in C CodesDope. Boolean bool or Bool datatype in C C programming language from C99 supports Boolean data type bool and internally it was referred as Bool as boolean was update a datatype in early versions of C. Bool type C reference Microsoft Docs.
    [Show full text]
  • 4 Data Types
    4 Data Types VHDL is a strongly typed language. Every constant, signal, variable, function, and parameter is declared with a type, such as BOOLEAN or INTEGER, and can hold or return only a value of that type. VHDL predefines abstract data types, such as BOOLEAN, which are part of most programming languages, and hardware-re- lated types, such as BIT, found in most hardware languages. VHDL predefined types are declared in the STANDARD pack- age, which is supplied with all VHDL implementations (see Example 4–14). Data types addresses information about Enumeration Types Enumeration Overloading Enumeration Encoding Integer Types Array Types Record Types Predefined VHDL Data Types HOME CONTENTS INDEX For further assistance, email [email protected] or call your local support center V3.4 VHDL Compiler Reference Unsupported Data Types Synopsys Data Types Subtypes The advantage of strong typing is that VHDL tools can catch many common design errors, such as assigning an eight-bit value to a four-bit-wide signal, or incrementing an array index out of its range. The following code shows the definition of a new type, BYTE, as an array of eight bits, and a variable declaration, ADDEND, that uses this type. type BYTE is array(7 downto 0) of BIT; variable ADDEND: BYTE; The predefined VHDL data types are built from the basic VHDL data types. Some VHDL types are not supported for synthesis, such as REAL and FILE. The examples in this chapter show type definitions and associated object declarations. Although each constant, signal, variable, function, and parameter is declared with a type, only variable and signal declarations are shown here in the examples.
    [Show full text]
  • Fundamental Programming Concepts
    APPENDIX A Fundamental Programming Concepts The following information is for readers who are new to programming and need a primer on some fundamental programming concepts. If you have programmed in another language, chances are the concepts presented in this appendix are not new to you. You should, however, review the material briefly to become familiar with the C# syntax. Working with Variables and Data Types Variables in programming languages store values that can change while the program executes. For example, if you wanted to count the number of times a user tries to log in to an application, you could use a variable to track the number of attempts. A variable is a memory location where a value is stored. Using the variable, your program can read or alter the value stored in memory. Before you use a variable in your program, however, you must declare it. When you declare a variable, the compiler also needs to know what kind of data will be stored at the memory location. For example, will it be numbers or letters? If the variable will store numbers, how large can a number be? Will the variable store decimals or only whole numbers? You answer these questions by assigning a data type to the variable. A login counter, for example, only needs to hold positive whole numbers. The following code demonstrates how you declare a variable named counter in C# with an integer data type: int counter; Specifying the data type is referred to as strong typing. Strong typing results in more efficient memory management, faster execution, and compiler type checking, all of which reduces runtime errors.
    [Show full text]
  • How to Use Basic Boolean Functions Tutorial
    How to Use Basic Boolean Functions Tutorial Functions -> Programming -> Boolean -> And , Or , Not , Not Or (NOR) , Not And (NAND) , Exclusive Or (XOR) , Not Exclusive Or (XNOR) , True , False This tutorial will explain how to use the Boolean data type and Boolean functions such as those used in Boolean algebra like AND, OR, and NOT (conjunction, disjunction, and negation respectively). These functions are similar to the basic logic gates used to design circuits and only perform two bit input operations. Boolean data types have only two values, “True” and “False”. Booleans are have their own set of functions that deal exclusively with manipulating Booleans that are derived directly from Boolean algebra and are the primary means of manipulating Boolean data types. These functions are also known as logical operators or logic gates which are discussed below. Because of the simplicity of the Boolean data type, they are frequently used as the values used to drive conditional branching and decision making structures. To find the logical operator gates, start by opening the Functions palette and selecting the Programming palette. Then select the Boolean palette . This should bring up the Boolean operator functions. Select the function that you want to use and place it in your block diagram. Each function except the NOT, True, and False functions takes two Booleans as its inputs and, because of the rules of Boolean logic, the order of the inputs does not matter. In addition, each function outputs a Boolean value depending on whether the logical operator evaluates the two inputs as True or False. The NOT function serves as a negation function that takes a Boolean value and outputs the opposite Boolean value (i.e.
    [Show full text]
  • Functional, Actor Based Programming Language
    Oscar Functional, Actor based Programming Language Manager: Ethan Adams EA2678 ​ Language Guru: Howon Byun HB2458 ​ System Architect: Jibben Lee Grabscheid Hillen JLH2218 ​ System Architect: Vladislav Sergeevich Scherbich VSS2113 ​ Tester: Anthony James Holley AJH2186 ​ Table of Contents Introduction Core Concepts Immutability Actor Lexical Conventions Identifiers Keywords Punctuation Operators Types Programming Structure Introduction We will be implementing an Actor-Oriented Language. We all know there are difficulties associated with parallel computation, namely data collision when multiple threads access the same data. Most often, this requires explicitly defining locks and mutexes to control data access to resolve this issue, which adds significant mental and code overhead. The Actor model is a different approach to this problem that relies on the concept of message-passing between processes. The model simplifies the aforementioned difficulties of multiprocessing by abstracting explicit method calls, and relying on each “actor” to handle tasks and encapsulate mutable data. We would like to construct our language based off Erlang and Akka framework. Core Concepts Immutability Values in Oscar are immutable like Haskell and Ocaml. This means that when a non-atomic value is declared, it cannot be reassigned and function parameters are passed by value. For instance, this is not allowed. int x = 5; x = 4; // error For primitive container types like list, map and set, they have an additional property ​ ​ ​ ​ that re-assigning values returns a new copy of the data structure with those updates applied. list<int> initList == [1, 2, 3, 4, 5]; list<int> changedList = (initList[3] = -4); changedList == [1, 2, 3, -4, 5]; initList == [1, 2, 3, 4, 5]; Passing objects by value seems like a massive performance drain.
    [Show full text]
  • Data Types in C
    Princeton University Computer Science 217: Introduction to Programming Systems Data Types in C 1 Goals of C Designers wanted C to: But also: Support system programming Support application programming Be low-level Be portable Be easy for people to handle Be easy for computers to handle • Conflicting goals on multiple dimensions! • Result: different design decisions than Java 2 Primitive Data Types • integer data types • floating-point data types • pointer data types • no character data type (use small integer types instead) • no character string data type (use arrays of small ints instead) • no logical or boolean data types (use integers instead) For “under the hood” details, stay tuned for “number systems” lecture next week 3 Integer Data Types Integer types of various sizes: signed char, short, int, long • char is 1 byte • Number of bits per byte is unspecified! (but in the 21st century, pretty safe to assume it’s 8) • Sizes of other integer types not fully specified but constrained: • int was intended to be “natural word size” • 2 ≤ sizeof(short) ≤ sizeof(int) ≤ sizeof(long) On ArmLab: • Natural word size: 8 bytes (“64-bit machine”) • char: 1 byte • short: 2 bytes • int: 4 bytes (compatibility with widespread 32-bit code) 8 bytes • long: What decisions did the designers of Java make? 4 Integer Literals • Decimal: 123 • Octal: 0173 = 123 • Hexadecimal: 0x7B = 123 • Use "L" suffix to indicate long literal • No suffix to indicate short literal; instead must use cast Examples • int: 123, 0173, 0x7B • long: 123L, 0173L, 0x7BL • short: (short)123,
    [Show full text]
  • Declaring Boolean in C
    Declaring Boolean In C Occult and acetabular Marilu vivifies her appeasers orchestrate while Thibaut trichinising some lardons imminently. Which Giffer underworking so nights that Gunther moseying her epilator? Depletable Fredrick always scarfs his cerussite if Waverly is ailurophobic or normalises theocratically. When the collection of a boolean in the most other values or the statements to have you come on pointer operators can write them unless listed above The array in c numeric and. The mechanics of errors as an ascii equivalents, and semantics of a variable which is not prepared to give a method. Use a name conflicts in a new list has ended if one by that can be necessary questions which say the end of improving performance. Give the other boost library functions may also be declared as well in a derived classes from this. Format a developer needs to all naming of vertical whitespace. The size of the printf format unnamed namespaces automatically between the second matrix size and videos that? Are boolean values for booleans and, who are evaluated first section later call the following table we have little information about anything about objects which keeps track. As possible in boolean variable i tried it possible by declaring boolean in c preprocessor will notify you can be consistent with all. So in boolean situations where the field. Proper capitalization and understand the open braces, then to not intended to the next chapter that act on a short document? In this is a double, all improve readability of this case people or oral, without this keyword is forbidden within the reader that make an else.
    [Show full text]
  • On the Standardization of Fundamental Bit Manipulation Utilities
    Document number: P0237R0 Date: 2016–02–12 Project: ISO JTC1/SC22/WG21: Programming Language C++ Audience: Library Evolution Working Group, SG14 Reply to: Vincent Reverdy ([email protected]) On the standardization of fundamental bit manipulation utilities Vincent Reverdy1 and Robert J. Brunner1 1Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green St., Urbana, IL 61801 Abstract We discuss the addition to the standard library of class templates to ease the manipulation of bits in C++. This includes a bit_value class emulating a single bit, a bit_reference em- ulating a reference to a bit, a bit_pointer emulating a pointer to a bit, and a bit_iterator to iterate on bits. These tools would provide a solid foundation of algorithms operating on bits and would facilitate the use of unsigned integers as bit containers. Contents 1 Introduction2 2 Motivation2 3 Impact on the standard3 4 Design decisions4 5 Technical specications 16 6 Alternative technical specications 26 7 Discussion and open questions 29 8 Acknowledgements 30 9 References 31 1 1 Introduction This proposal introduces a class template std::bit_reference that is designed to emulate a ref- erence to a bit. It is inspired by the existing nested classes of the standard library: std::bitset:: reference and std::vector<bool>::reference, but this new class is made available to C++ developers as a basic tool to construct their own bit containers and algorithms. It is supple- mented by a std::bit_value class to deal with non-referenced and temporary bit values. To provide a complete and consistent set of tools, we also introduce a std::bit_pointer in order to emulate the behaviour of a pointer to a bit.
    [Show full text]