# Chapter 8. Arithmetic in C++

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1 Christian Jacob Chapter 8 Arithmetic in C The C++ Vocabulary 8.2 Variables and Types Data Objects Variables Declaration of Variables 8.3 Elementary C++ Data Types Integers Floating Point Numbers Type Conversions in Expressions Qualifiers for Variable Declarations Chapter Overview

2 Christian Jacob 8.4 Arithmetic Expressions Standard Arithmetic Operators Assignments and Compound Assignments Operator Priorities 8.5 Symbolic Constants Declaration of Symbolic Constants Hexadecimal and Octal Constants 8.6 The char Data Type 8.7 References Chapter Overview

3 Page 3 Chapter 8: Arithmetic in C++ Christian Jacob 8.1 The C++ Vocabulary asm do if reinterpret_cast try auto double inline return typedef bool dynamic_cast int short typeid break else long signed typename case enum main sizeof union catch explicit mutable static unsigned char export namespace static_cast using class extern new struct virtual const false operator switch void const_cast float private template volatile continue for protected this wchar_t default friend public throw while delete goto register true types type qualifiers execution control structures First Back TOC Prev Next Last

4 Page 4 Chapter 8: Arithmetic in C++ Christian Jacob 8.2 Variables and Types Data Objects The operational model of computing / programming considers a programs as a sequence of instructions for manipulating data objects. Data objects can be distinguished by their reference levels: 0 Constant an actual value (a number, a character,...) 1 Variable contains a value (= constant) 2 Level-1 pointer refers to a variable, points to a variable 3 Level-2 pointer refers to a level-1 pointer 4 First Back TOC Prev Next Last

5 Page 5 Chapter 8: Arithmetic in C++ Christian Jacob Constant: Const_Name Example: internal object internal representation Variable: Name A data objects has a name reference (address) lvalue internal representation rvalue an internal object (determined by its data type) First Back TOC Prev Next Last

6 Page 6 Chapter 8: Arithmetic in C++ Christian Jacob Variables Variables are data objects with the following properties: Identifier, name - Defined in its declaration (example: int size = 12) Type - Defined in its declaration (example: int size = 12) Internal object = address of the manipulable memory section (lvalue) Value = alterable contents of the addressed memory section - Its interpretation depends on its type. - Its value can be changed by assignments (=) or specific operators (++). Lifespan: - Dynamically defined by the program structure (see: functions). First Back TOC Prev Next Last

7 Page 7 Chapter 8: Arithmetic in C++ Christian Jacob Declaration of Variables basic_variable_declaration ::= type {name,} * name; bool correct_input; // true or false int number_of_items; // number of items float width, height; // width and height Initializing Variables basic_variable_declaration ::= type {name_init,} * name_init; name_init ::= { name name ( init ) name = init } int counter(0); // C++ initialization int counter = 0; // older C style syntax First Back TOC Prev Next Last

8 Page 8 Chapter 8: Arithmetic in C++ Christian Jacob 8.3 Elementary C++ Data Types Integers int normal_integer; long int long_integer; short int short_integer; unsigned short int unsigned_short_int; Floating Point Numbers float normal_float; double double_float; long double high_precision_float; Characters char single_character; First Back TOC Elementary C++ Data Types Prev Next Last

9 Page 9 Chapter 8: Arithmetic in C++ Christian Jacob Integers Integers (= whole numbers) have no fractional part or decimal point. Range of values 32 bit = 4 bytes (UNIX, Mac) 16 bit = 2 bytes (PC DOS) to to ,147,483,648 to 2,147,483,647-32,768 to 32,767 Types of Integers int: the most efficient size for the machine is chosen (2 or 4 bytes) long int: extra storage for integer (4 bytes guaranteed) short int: reduced storage (2 bytes) unsigned: uses all bits for the number (for 1 byte: range 0 to 65,535) First Back TOC Elementary C++ Data Types Prev Next Last

10 Page 10 Chapter 8: Arithmetic in C++ Christian Jacob Floating Point Numbers Floating point numbers have a decimal point or mantissa and exponent specification e34 ( = 1.2 * ) Range of values The range of floating point numbers (which are always signed) and their accuracy varies widely among different computer and operating systems For further details consult: S. Qualline, Practical C++ Programming, O Reilly, 1997, Chapter 19. First Back TOC Elementary C++ Data Types Prev Next Last

11 Page 11 Chapter 8: Arithmetic in C++ Christian Jacob Types of Floats float: double: long double: normal precision (usually 4 bytes = 32 bits) twice the range and precision of float (usually 8 bytes = 64 bits) extended precision (at least 8 bytes) First Back TOC Elementary C++ Data Types Prev Next Last

12 Page 12 Chapter 8: Arithmetic in C++ Christian Jacob Type Conversions in Expressions If an expression (see chapter 8.4) contains perands of different types, an automatic type conversion (to the type which is highest in the following hierarchy) is performed. double float long int This diagram is a simplified version of all possible type conversions. int char short int First Back TOC Elementary C++ Data Types Prev Next Last

13 Page 13 Chapter 8: Arithmetic in C++ Christian Jacob Examples of binary operators and implicit type conversions Operator Meaning Integer example Floating-point example + Addition Subtraction * Multiplication 5 * * / Division 5 / / % Modulus, or remainder 5 % % 2.2 type error First Back TOC Elementary C++ Data Types Prev Next Last

14 Page 14 Chapter 8: Arithmetic in C++ Christian Jacob Operator Meaning Integer / floating-point example + Addition Subtraction * Multiplication 4 * / Division 6.0 / % Modulus, or remainder 5.0 % 2.0 type error First Back TOC Elementary C++ Data Types Prev Next Last

15 Page 15 Chapter 8: Arithmetic in C++ Christian Jacob Qualifiers for Variable Declarations 1 variable_declaration ::= [ special ] [ class ] [ size ] [ sign ] type {name_init,} * name_init; Special Class Size Sign Type volatile register short signed int <blank> static long unsigned float extern <blank> <blank> double auto <blank> (bool) 1. S. Qualline, Practical C++ Programming, O Reilly, 1997, p. 76. First Back TOC Elementary C++ Data Types Prev Next Last

16 Page 16 Chapter 8: Arithmetic in C++ Christian Jacob Special: - volatile: special variable whose value may change at any time - <blank>: normal variable Class: - register: frequently used variable, kept in a machine register - static: meaning depends on context - extern: defined in another file - auto: variable allocated from the stack - <blank>: auto default class is selected Size: - long: larger than normal integer or very large float - short: smaller than normal integer - <blank>: normal size number (integer or float) First Back TOC Elementary C++ Data Types Prev Next Last

17 Page 17 Chapter 8: Arithmetic in C++ Christian Jacob Sign: - signed: signed integer or character - unsigned: use all integer or character bits (no sign bit) Type: - int: integer - float: floating point number - double: double-size float - char: single character, also used for very short integer - bool: Boolean value, true or false First Back TOC Elementary C++ Data Types Prev Next Last

18 Page 18 Chapter 8: Arithmetic in C++ Christian Jacob 8.4 Arithmetic Expressions expression simple value function call unary expression binary expression... simple value number constant string constant character constant identifier (declared)... First Back TOC Arithmetic Expressions Prev Next Last

19 Page 19 Chapter 8: Arithmetic in C++ Christian Jacob unary expression unary operator simple value expression binary expression simple value binary operator simple value expression expression First Back TOC Arithmetic Expressions Prev Next Last

20 Page 20 Chapter 8: Arithmetic in C++ Christian Jacob unary operator binary operator + - * / % << >> =... For assignments the simple value must be an identifier! First Back TOC Arithmetic Expressions Prev Next Last

21 Page 21 Chapter 8: Arithmetic in C++ Christian Jacob Standard Arithmetic Operators Arithmetics op int int +, - op float float +, - int op int int +, -, *, /, % float op float float +, -, *, / Comparisons int op int int ==,!=, <=, <, >, >= float op float float ==,!=, <=, <, >, >= First Back TOC Arithmetic Expressions Prev Next Last

22 Page 22 Chapter 8: Arithmetic in C++ Christian Jacob Logical Operators op int int! (not) int op int int && (and), (or) Bitwise Logical Operators op int int ~ (not) int op int int & (and), (or), ^ (xor), >> (right shift), << (left shift) x ~x x x << First Back TOC Arithmetic Expressions Prev Next Last

23 Page 23 Chapter 8: Arithmetic in C++ Christian Jacob The? Operator condition? true_expression : false_expression Example: int x = 15; cout << (x < 7? 4 : 2); // Output: 2 First Back TOC Arithmetic Expressions Prev Next Last

24 Page 24 Chapter 8: Arithmetic in C++ Christian Jacob The Comma Operator: Concatenation of Two Expressions expression 1, expression 2 Evaluates expression 1 and then expression 2, and finally returns the value of expression 2 as the result. Example: int x = 0, y = 1; cout << (x = x + y, y = y * 2); More useful in loops (see later): for (i=1, j=9;...; i = i+2, j = j-3) {... // loop body } First Back TOC Arithmetic Expressions Prev Next Last

25 Page 25 Chapter 8: Arithmetic in C++ Christian Jacob Assignments and Compound Assignments assignment Syntax Diagram for Assignments type identifier = expression ; int pounds = 0; float kilos = pounds / 2.2; int x, y, z; int f(int n);... x = -y * (z++ - f(4)); First Back TOC Arithmetic Expressions Prev Next Last

26 Page 26 Chapter 8: Arithmetic in C++ Christian Jacob Compound Assignments A common operation in programming is to apply an operator to a variable, and then store the result in the same variable. For example, the following assignment doubles the value of j: j = j * 2; This can be rewritten as: j *= 2; This works for the following operators in C++ : +=, -=, *=, /*, %=, <<=, >>=, &=, ^=, = First Back TOC Arithmetic Expressions Prev Next Last

27 Page 27 Chapter 8: Arithmetic in C++ Christian Jacob Special Case: Increments and Decrements by One For increasing or decreasing a variable value by 1, there is even a shorter notation in C++. Instead of writing k = k + 1; one can write or k++; // return value of k, then increment ++k; // increment, then return value of k This also works for the decrement operator -- : k--; // or --k; equivalent to k = k -1; First Back TOC Arithmetic Expressions Prev Next Last

28 Page 28 Chapter 8: Arithmetic in C++ Christian Jacob Examples: a = 1; // a = 1 b = ++a; // a = 2, b = 2 c = a++; // a = 3, c = 2 a = 5; b = 3; n = ++a + b--; // a = 6, b = 2, n = 9 a = 5; b = 3; n = ++a * ++b; // a = 6, b = 4, n = 24 n = a++ * b++; // a = 6, b = 4, n = 15 a = 5; b = 3; n = a++ * --b; // a = 6, b = 2, n = 10 First Back TOC Arithmetic Expressions Prev Next Last

29 Page 29 Chapter 8: Arithmetic in C++ Christian Jacob Operator Priorities Priority Operators Ass. Associativity high! ~ right to left * / % left to right + - left to right << >> left to right < <= > >= left to right ==!= left to right & left to right ^ left to right left to right && left to right left to right? : right to left = += -= *= /= %= &= ^= = <<= >>= right to left low, left to right First Back TOC Arithmetic Expressions Prev Next Last

30 Page 30 Chapter 8: Arithmetic in C++ Christian Jacob 8.5 Symbolic Constants Declaration of Symbolic Constants constant_declaration ::= const type {name_init,} * name_init; const float PI = ; // magic Pi The values of constants can not be changed by further assignments: PI = 3.0 // Doesn t work! First Back TOC Symbolic Constants Prev Next Last

31 Page 31 Chapter 8: Arithmetic in C++ Christian Jacob Hexadecimal and Octal Constants The C++ language has conventions for representing octal and hexadecimal values: Octal number: leading zeros Hexadecimal number: leading 0x (zero + x ): Examples: Base 10 Base 8 Base x x xF First Back TOC Symbolic Constants Prev Next Last

32 Page 32 Chapter 8: Arithmetic in C++ Christian Jacob 8.6 The char Data Type The type char represents a single character, enclosed in single quotation marks ( A, a,!, \b ). char capitala = A ; char smallb = b ; char lookoutchar =! ; char capitalb = 66; cout << capitalb; The backslash character (\) is called the escape character, signalling that a special character follows. char backspace = \b ; char newline = \n ; char backslash = \\ ; char quote = \ char doublequote = \ First Back TOC The char Data Type Prev Next Last

33 Page 33 Chapter 8: Arithmetic in C++ Christian Jacob A small selection of special characters: Character Name Meaning \b Backspace Move the cursor one character to the left \f Form feed Go to the top of a new page \n New line Go to the next line \r Return Go to the beginning of the current line \t Tab Advance to the next tab stop \ Single quote The character \ Double quote The character \nnn \NN The character with ASCII code nnn The character with ASCII code NN The ASCII character with number nnn (octal) The ASCII character with number NN (hexadecimal) First Back TOC The char Data Type Prev Next Last

34 Page 34 Chapter 8: Arithmetic in C++ Christian Jacob 8.7 References G. Blank and R. Barnes, The Universal Machine, Boston, MA: WCB/ McGraw-Hill, Chapter 3.2. First Back TOC References Prev Next Last

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