Chapter 6 Fundamental Types Dept of Computer Engineering Khon Kaen University

178110: Computer Programming (II/2546) 2 Major Concepts Data types Numeric types Boolean type Enumeration type Character type Arithmetic operations Type conversions Run-time errors: Numeric overflow Round-off error

178110: Computer Programming (II/2546) 3 Numeric Data Types There are two kinds of numbers Whole numbers, Integers ( จำนวนเต็ม ) Including negative whole numbers, 0, and positive whole numbers Examples: 0, 1, 2, -1, -2 Decimal numbers Fraction where the denominator is a power of ten and is therefore expressed using a decimal point. Examples: 0.37 Rational numbers: จำนวนจริงเป็นตัวเลขที่ สามารถเขียนอยู่ในรูปทศนิยม, such as 2/10 Irrational numbers: cannot be expressed as a fraction, such as

178110: Computer Programming (II/2546) 4 Fundamental Types Standard C++ has 14 different fundamental types: 11 integral types and 3 floating-point types Integral Types Boolean Type bool Enumeration Type enum

178110: Computer Programming (II/2546) 5 Fundamental Types (Cont.) Integral Types Character Types char unsigned char wchar_t Integer Types short int long

178110: Computer Programming (II/2546) 6 Fundamental Types (Cont.) Integral Types Integer Types unsigned short unsigned int unsigned long Floating-point Types float double long double

178110: Computer Programming (II/2546) 7 The Boolean Type A boolean type is an integral type whose variables can have only two values: False and true These values are stored as the integers 0 and 1 The boolean type in Standard C++ is named bool

178110: Computer Programming (II/2546) 8 Boolean Variables #include using namespace std; int main() {// print the value of a boolean variable bool flag = false; cout << “flag = “ << flag << endl; flag = true; cout << “flag = “ << flag << endl; }

178110: Computer Programming (II/2546) 9 Enumeration Types An enumeration type is an integral type that is defined by the user with the syntax enum typename { enumerator-list }; enum is a C++ keyword typename is an identifier that names the type being defined enumerator-list is a list of acceptable values of the variable that has that typename

178110: Computer Programming (II/2546) 10 Enumeration Types (Cont.) Example: enum Semester {FALL, WINTER, SPRING, SUMMER}; We can then declare variables of this type Semester s1, s2; We can use those variables and those type values as we would with predefined types s1 = FALL; s2 = WINTER;

178110: Computer Programming (II/2546) 11 Enumeration Types The actual values defined in the enumerator-list are called enumerators In fact, they are ordinary integer constants Example: the enumerators FALL, WINTER, SPRING, and SUMMER that are defined for the semester type could have been defined like this: const int FALL = 0; const int WINTER = 1; const int SPRING = 2; const int SUMMER = 3;

178110: Computer Programming (II/2546) 12 Enumeration Types (Cont.) The values 0, 1, … are assigned automatically when the type is defined These default values can be overridden in the enumerator-list: enum Coin {PENNY = 1, NICKEL = 5, DIME = 10, QUARTER = 25};

178110: Computer Programming (II/2546) 13 Enumeration Types (Cont.) If integer values are assigned to only some of the enumerators, then the ones that follow are given consecutive values enum Month {JAN=1, FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV, DEC}; Since enumerators are simply integer constants, it is legal to have several different enumerators with the same value: enum Answer {NO = 0, FALSE = 0, YES = 1, TRUE = 1, OK = 1}

178110: Computer Programming (II/2546) 14 Enumeration Types (Cont.) Enumeration types are usually defined to make code more self-documenting, i.e., easier for humans to understand enum Sex {FEMALE, MALE}; enum Day {SUN, MON, TUE, WED, THU, FRI, SAT}; enum Radix {BIN=2, OCT=8, DEC=10, HEX=16};

178110: Computer Programming (II/2546) 15 Enumeration Types (Cont.) Enumerators must be valid identifiers This following definition would not be valid enum Grade {F, D, C-, C, C+, B-, B, A-, A}; Why is it invalid? ‘+’ and ‘-’ cannot be used in identifiers Same values cannot be used in the same scope (same place) enum Month {JAN, …, OCT, …} enum Radix {BIN, OCT, …}

178110: Computer Programming (II/2546) 16 Character Types A character type is an integral type whose variables represent characters like the letter ‘A’ or the digit ‘s’ Characters are delimited by the apostrophe (‘) Like all integral type values, character values are stored as integers In C++, the type name for a character is char

178110: Computer Programming (II/2546) 17 Character Types (Cont.) Using the ASCII encoding standard, the examples of the values that represent these characters are as follow: ‘ ’represented by 32 ‘+’ represented by 43 ‘A’represented by 65 ‘a’represented by 97

178110: Computer Programming (II/2546) 18 Escape Sequences Escape sequences are used to print out special characters \‘Single quote \“Double quote \\ Backslash \nNewline \tHorizontal tab \vVertical tab

178110: Computer Programming (II/2546) 19 Integer Types There are 6 integer types in Standard C++ short: 2 bytes int: 4 bytes long: 4 bytes unsigned short: 2 bytes unsigned int: 4 bytes unsigned long:4 bytes The least value of variables with unsigned types are 0

178110: Computer Programming (II/2546) 20 Integer Type Ranges This program prints the numeric ranges of the 6 integer types in C++ #include #include // defines the constants SHRT_MIN, etc. using namespace std; int main() { // prints some of the constants stored in the header: cout << "minimum short = " << SHRT_MIN << endl; cout << "maximum short = " << SHRT_MAX << endl; cout << "minimum unsigned short = 0" << endl; cout << "maximum unsigned short = " << USHRT_MAX << endl; cout << "minimum int = " << INT_MIN << endl; cout << "maximum int = " << INT_MAX << endl; cout << "minimum unsigned int = 0" << endl; cout << "maximum unsigned int = " << UINT_MAX << endl; cout << "minimum long= " << LONG_MIN << endl; cout << "maximum long= " << LONG_MAX << endl; cout << "minimum unsigned long = 0" << endl; cout << "maximum unsigned long = " << ULONG_MAX << endl; }

178110: Computer Programming (II/2546) 21 Integer Type Ranges (Cont.) The output of the program minimum short = maximum short = minimum unsigned short = 0 maximum unsigned short = minimum int = maximum int = minimum unsigned int = 0 maximum unsigned int = minimum long= maximum long= minimum unsigned long = 0 maximum unsigned long =

178110: Computer Programming (II/2546) 22 Arithmetic Operations C++ performs its numerical calculations by means of the five arithmetic operators: +, -, *, /, and % Operations are performed in this order 1. ( ) Perform the operation inside ( ) first 2. +,- Then, perform unary plus and unary minus, such as +32, *,/,% 4. +, - If there is more than one operation with the same order, perform from left to right

178110: Computer Programming (II/2546) 23 Arithmetic Operations (Cont.) Math: a = bc/de C++: a = (b*c)/(d*e) Is b*c/d*e == (b*c)/(d*e)? Is b*c*d*e == (b*c)*(d*e)? Math: m = C++: m = (y-b)/(x-a) Is y-b/x-a == (y-b)/(x-a)? Is y-b-x-a == (y-b)-(x-a)?

178110: Computer Programming (II/2546) 24 Arithmetic Operations (Cont.) -34*32 = ? Choice a: (-34)*32 Choice b: -(34*32) 7 – 2 % 3 = ? Choice a: (7-2)% 3 Choice b: 7 – (2 %3) / 4 = ? Choice a: 3 + (2/4) Choice b: (3 + 2)/ 4

178110: Computer Programming (II/2546) 25 Arithmetic Operations (Cont.) #include using namespace std; int main() { // tests operators +, -, *, /, and %: int m=54; int n=20; cout << "m = " << m << " and n = " << n << endl; cout << "m+n = " << m+n << endl; // = 74 cout << "m-n = " << m-n << endl; // = 34 cout << "m*n = " << m*n << endl; // 54*20 = 1080 cout << "m/n = " << m/n << endl; // 54/20 = 2 cout << "m%n = " << m%n << endl; // 54%20 = 14 return 0; }

178110: Computer Programming (II/2546) 26 Increment & Decrement Operators The values of integral objects can be incremented by one with the ++ operator and decremented by one with the – operator Each of “++” and “--” operator has two versions: A “pre” version A “post” version

178110: Computer Programming (II/2546) & -- Operators The “pre” version performs the operation on the object before the resulting value is used in its context Example: n = ++m  m= m + 1, n = m The “post” version performs the operation on the operation after the object’s current value ahs been used Example: n = m++  n = m, m = m + 1

178110: Computer Programming (II/2546) & -- Operators (Cont.) int main() { // shows the difference between m++ and ++m m = 44; n = ++m; cout << “m = “ << m << “, n = “ << n << endl; m = 44; n = m++; cout << “m = “ << m << “, n = “ << n << endl; }

178110: Computer Programming (II/2546) 29 Composite Assignment Operators The standard assignment operator in C++ is the equal sign ‘=‘ C++ also includes the composite assignment operators: ‘+=‘, ‘-=‘, ‘*=‘, ‘/=‘, and ‘%=‘ Examples: A += B;  A = A + B; A *= B;  A = A * B;

178110: Computer Programming (II/2546) 30 Composite Assignment Operators #include using namespace std; int main() { // tests arithmetic assignment operators: int n=22; cout << "n = " << n << endl; n += 9; // adds 9 to n cout << "After n += 9, n = " << n << endl; n %= 7; // mod n with 7 cout << "After n %= 7, n = " << n << endl; }

178110: Computer Programming (II/2546) 31 Floating-Point Types C++ has three types for storing values with floating-point float: use 4 bytes double: use 8 bytes long double: use 8, 10, 12, or 16 bytes On most systems, double uses twice as many bytes as float

178110: Computer Programming (II/2546) 32 Floating-Point Arithmetic int main() { double x = 54.0; double y = 20.0; cout << “x*y = “ << x*y << endl; // 1080 cout << “x/y = “ << x/y << endl; // 2.7 } If x and y have type ‘int’, what is the value of x/y? 2

178110: Computer Programming (II/2546) 33 Using the sizeof Operator The programs use the sizeof operator which returns the size in bytes of the type specified Examples: cout << “size of integer is “ << sizeof(int) << endl; cout << “size of float is “ << sizeof(float) << endl; Output: size of integer is 4 size of float is 4

178110: Computer Programming (II/2546) 34 Type Conversions int n = 22; float x = ; n += x; x += n; cout << “n is “ << n << endl; cout << “x is “ << x << endl; What are the values of n and x? n is 25 x is

178110: Computer Programming (II/2546) 35 Type Conversions (Cont.) If T is one type and v is a v value of another type, then the expression T(v) converts v to type T This process is called type casting Example: double v = ; int n = (int) v; cout << “n is “ << n endl; What is the value of n? n is 1234

178110: Computer Programming (II/2546) 36 Numeric Overflow Computers are finite, so the range of any type must also be finite But in mathematics, there are infinitely many integers Consequently, computers are manifestly prone to error when their numeric values become too large This kind of error is called numeric overflow

178110: Computer Programming (II/2546) 37 Numeric Overflow (Cont.) int main() { // print n until it overflows int n = 10000; cout << “sizeof(int) is “ << sizeof(int) << endl; cout << “n is “ << n << endl; n *= 10000; cout << “n is “ << n << endl; n *= 10000; cout << “n is “ << n << endl; return 0; } What is the maximum n can be?

178110: Computer Programming (II/2546) 38 Integer Overflow (Cont.) What is the size of an integer in bits? 32 bits 2 32 = 4,294,967,296 What is the maximum value of a variable with type ‘int’? 2,147,483,647 ((2 32 )/2) - 1 What is the minimum value of a variable with type ‘int’? -(2 32 )/2

178110: Computer Programming (II/2546) 39 Floating-Point Overflow #include using namespace std; int main() { // prints x until it overflows: float x=1000.0; cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; }

178110: Computer Programming (II/2546) 40 Floating-Point Overflow (Cont.) Output x = x = 1e+08 x = 1e+16 x = 1e+32 x = inf Integer overflow “wrap around” to negative integers Floating-point overflow “sinks” into the abstract notion of infinity

178110: Computer Programming (II/2546) 41 Round-off Error Round-off error is another kind of error that often occurs when computers do arithmetic on rational numbers Example: The number 1/3 might be stored as , which is not exactly equal to 1/3 The difference is called round-off error In some cases, these errors can cause serious problems

178110: Computer Programming (II/2546) 42 Round-Off Error (Cont.) // Example 2.14 on page 28 // Round-off Error #include using namespace std; int main() { // illustrates round-off error:: double x = 1000/3.0; cout << "x = " << x << endl; // x = 1000/3 double y = x ; cout << "y = " << y << endl; // y = 1/3 double z = 3*y - 1.0; cout << "z = " << z << endl; // z = 3(1/3) - 1 if (z == 0) cout << "z == 0.\n"; else cout << "z does not equal 0.\n"; // z != 0 }

178110: Computer Programming (II/2546) 43 Round-Off Error (Cont.) Program output x = 1000/3 = // x = 1000/3 y = x – 333 = // y = 1/3 z = 3*y – 1.0 = e-14// z = 3(1/3) - 1 z does not equal 0. // z != 0 It is better to avoid tests for equality with floating-point types Overflow and round-off errors are run-time errrors

178110: Computer Programming (II/2546) 44 E-Format for Floating-Point Values When input or output, floating-point values may be specified in either of two formats: Fixed-point format Example: , 0.1 Scientific format Example: x = e-14

178110: Computer Programming (II/2546) 45 E-Format (Cont.) Letter e stands for “exponent on 10” Thus, e-14 means The scientific format is thus usually used to express very small or very large numbers You can use either e or E in the scientific format

178110: Computer Programming (II/2546) 46 Scope The scope of an identifier is that part of the program where it can be used Variables cannot be used before they are declared The scope of a variable extends from the point where it is declared to the end of the internal block within which it is declared { int a = 2; // a can be used from this point } a cannot be used here

178110: Computer Programming (II/2546) 47 Scope (Cont.) #include using namespace std; int main() { // illustrates the scope of variables: x = 11; // Is this line OK? int x; { x = 22; // Is this line OK? y = 33; // Is this line OK? int y; y = 11; // Is this line OK? } x = 66; // Is this line OK? y = 77; // Is this line OK? }

178110: Computer Programming (II/2546) 48 Scope (Cont.) int x = 11; int main() { int x = 22; { int x = 33; cout << “In block inside main(): x = “ << x << endl; } cout << “In main(): x = “ << x << endl; cout << “In main(): ::x = “ << ::x << endl; } The scope resolution operator :: is to access the global x that is otherwise hidden in main()