Operator Overloading, Non-member Operator Functions

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CS201 Introduction to Programming

Lecture Handout

Introduction to Programming

Lecture No. 31

Reading Material

Deitel & Deitel - C++ How to Program

Chapter 8

8.2, 8.3, 8.4, 8.6, 8.7

Summary

Lecture Overview

What is Operator Overloading and Why is it Required

Where is it Relevant to Apply

Operators to Overload

Restrictions on Operator Overloading

Examples of Operator Overloading

Non-member Operator Functions

Example Program 1

Example Program 2

Tips

Lecture Overview

The topic of this lecture is Operator Overloading. In previous lectures, we discussed

about it a bit while discussing about references. So we will see in detail what is operator

overloading, how to overload operators, where it is relevant to apply and what are the

restrictions on it.

What is Operator Overloading and Why is it Required?

Operator overloading is to allow the same operator to be bound to more than one

implementation, depending on the types of the operands.

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As you know that there are standard arithmetic operators in C/C++ for addition ( + ),

subtraction ( - ), multiplication ( * ) and division ( / ). We should only use these operators

for their specific purposes. If we want to add two ints, say i and j, the addition will take

place in the following manner i.e. i + j. To add two double numbers, we use the same

operator and write d1 + d2. We may add two floats with the help of the same operator as

f1 + f2. Similarly other operations of -, * and / on the primitive types (sometimes called

as native or built-in types) can be employed. In other words, these operators are already

overloaded for primitive types in C++. But these C++ operators cannot be used for

classes and their objects. We have to write our own operator functions that can work with

objects.

Let's take an example of complex numbers. There are two parts of a complex number i.e.

real and imaginary. As complex numbers are part of mathematical vocabulary, so the

mathematical manipulations are done on them like addition, subtraction and

multiplication. Suppose, we write our own class for complex numbers named Complex,

but we can't add two complex numbers c1 and c2 as c1 + c2 because until now we don't

know how to write it. Although, we are able to write a function say cadd() to serve this

purpose.

Complex cadd ( Complex c1, Complex c2 ) ;

It accepts two complex numbers as parameters and returns back the resultant complex

number. But the usage of this function to add two complex numbers is generally clumsy.

It gets more cumbersome and complex if we want to carry out cascading operations like

i + j + k. It is better to use the standard operators of +, -, * and / as they are more readable

and elegant.

Where is it Relevant to Apply?

Firstly, the operator overloading gets relevant whenever there is the application of the

mathematical functions of addition, subtraction, multiplication and division. Complex

number is one example of it. As discussed earlier, in case of Date class, the operators can

be effectively used to get the future or past dates.

Secondly, the operators are also used sometimes in case of non-mathematical

manipulation. The example of String class to manipulate strings help us understand it in

a better way. The operator + can be used to concatenate two strings. Previously, we used

strcat() function declared inside string.h header file to concatenate two strings. As

compared to strcat(), the use of + to concatenate two strings is definitely easier and

more readable. But there is a little bit cost associated with this process of operators

overloading.

The cost is involved whenever we overload an operator. We have to write a function and

make use of the operator semantics correctly while implementing the function. This

means that the function written to overload + operator should do addition or

concatenation of strings in case of String objects.

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Operators to Overload

There are two types of operators to overload:

1. Unary

2. Binary

Unary operators are the ones that require only one operator to work. Unary operators are

applied to the left of the operand. For example, ^, &, ~ and !.

Binary operators require two operands on both sides of the operator. +, -, *, /, %, =, <

and > are examples of binary operators.

The complete list of C++ operators that can be overloaded is as follows:

>>= <<= ==

&& | |

-> * ,

[ ]

()

new new[ ] delete delete[ ]

The following operators can't be overloaded.

sizeof

Let's start with operator overloading mechanism. Consider an object date of the Date

class. The data member day can be accessed as follows:

date.day = 2;

In this statement, the day data member of the date object is accessed and assigned value

2. This expression (date.day) is driven by the object name at left.

Similarly, while using operators, the statement like a + b is driven by the object at the

left. In this case, + operator function for the object a will be called and b object is passed

explicitly to the + operator function as an argument. The rules of function overloading are

applied to the operator overloading. We cannot write two + operator functions with

exactly identical parameters. Following the overloading rules, the two operator functions

have to be different by the type or number of arguments.

The syntax of the prototype of the overloaded operator function is:

return-type operator operator-symbol (parameter-list);

operator is the keyword here. An example of this will be as follows:

Complex operator + (Complex & );

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We sometimes write only operator to refer to the operator function in our discussion.

Restrictions on Operator Overloading

There are some restrictions on operator overloading.

- The operator overloading functions for overloading (), [], -> or the assignment (=)

Operators must be declared as class members.

- The arity (number of operands) cannot be changed. If you are overloading an operator

that requires two operands e.g. *. It cannot be used as a unary operator that requires

one operand.

- No new operators can be created. Like in Fortran language, we have ** as `raise to

the power (exponent) operator' but this operator does not exist in C++. Therefore, it

can't be overloaded. Hence, only existing operators of C++ are used.

- Overloading can't be performed for the built-in (sometimes called primitive or native)

data types. For example, we cannot change how two ints are added. That means that

operators are overloaded to use with defined data types like classes.

- Precedence of an operator cannot be changed. For example, the * has higher

precedence than +. This precedence cannot be changed.

- Associativity of an operator cannot be changed. If some operator is right associative,

it cannot be changed to be left associative.

Examples of Operator Overloading

Let's take the complex number's class Complex and define a + operator function.

We know that when we write the following line:

x = y + z;

y and z operands are take part in the addition operation but there is no change in them due

to this operation. This is the + operator's functionality. The resultant is being assigned to

the variable x. This is assignment operator's functionality.

Now we will discuss a little bit about the assignment operator as well. Let's say we write

the following statement for two complex numbers c1 and c2.

c1 = c2 ;

Here c2 is being assigned to c1. Will this assignment work when we have not written any

assignment operator function for complex number? Apparently, it looks that the

statement will produce a compilation error (as there is assignment operator defined by us)

but this is not true. Whenever, we write our own class and compile it, the compiler

automatically generates a default assignment operator. The default assignment operator

makes a member to member assignment. This works fine unless there is a pointer data

member inside our class and that pointer is pointing to some data inside memory. For that

case (when there is a pointer data member) we have to write our own assignment operator

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otherwise the default assignment operator works fine for us. That will be discussed in the

subsequent lectures.

By definition of addition of complex numbers, we know that whenever two complex

numbers are added, the real part of one number is added into the real part of other

number. Similarly, the imaginary part of one number is added to the imaginary part of the

other number. We also know that when a complex number is added to another complex

number, the resultant is also a complex number consisting of real and imaginary parts.

This addition of real, imaginary parts and return of resultant complex number is the

functionality of the + operator function we are going to write.

Another thing to decide for this + operator is whether this operator will be a member

operator or a friend operator. Normally, operators are member operators but there are

situations when they cannot be member operators. In case of member operator, following

is the syntax of its prototype:

Complex operator + (parameter-list);

For member operator, the object on the left side of the + operator is driving this +

operation. Therefore, the driving object on the left is available by this pointer to +

operator function. But the object on the right is passed explicitly to the + operator as an

argument.

We can define a member operator as under:

Complex Complex :: operator + (Complex c)

{

Complex temp ;

temp.real = real + c.real ;

temp.imag = imag + c.imag ;

return temp ;

}

Let's see this code line by line.

Line 1 indicates that the return type is Complex, it is an operator + function and it is

accepting a Complex object by value as an argument.

In line 3, a local Complex object is declared, called temp.

In line 4, real part of the calling object (that is the one, driving) on the left of the +

operator is being added to the real part of the object c, where c is passed as an argument.

In line 5, imag part of the calling object (that is the one, driving) on the left of the +

operator is being added to the imag part of the object c, where c is passed as an argument.

In line 6, the Complex object temp containing the resultant of + operation is being

returned by value.

In our code, we can write something as:

Complex c1, c2, c3 ;

...

c3 = c1 + c2 ;

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In the above statement ( c3 = c1 + c2; ), c1 is the object that is calling or driving the

+ operator. c2 object is being passed as an argument to the + operator. So c1 and c2

objects are added by the + operator and resultant Complex object containing the addition

of these two numbers is returned back. That returned Complex object is assigned to the

c3 Complex object using the default assignment operator (that is created by the C++

compiler automatically).

What happens if we want to add a double number to a complex number (a instance of

Complex)? Like the following:

c3 = c1 + d ;

This + operation is driven by the c1 object of Complex while double number d of type

double is passed as argument. Therefore, our above written + operator is not useable for

this operation of addition. We need to overload + operator for accepting a parameter of

type double, i.e. we need to write another operator function. The definition of this newly

overloaded + operator is:

Complex Complex :: operator + (double d)

{

Complex temp ;

temp.real = real + d ;

// d is added into the real part

temp.imag = imag ;

return temp ;

}

By now, you should have noticed that operator overloading and function overloading are

quite similar.

When we write the following statement:

c3 = d + c1;

The operand on the left of + operator is a double number d. Therefore, this + operation

should be driven by (called by) the double number. Until now, we have not written such

an operator. Our previously written two + operators were driven by the Complex object.

Operator functions, not driven by the class type objects, are kept as friends to the class.

friend is the keyword used to declare such functions. A friend function to a class also

has access to the private members of that class.

friend Complex operator + (double d, Complex c)

{

Complex temp;

temp.real = d + c.real; // d is added into the real part of c

temp.imag = c.imag;

return temp;

}

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You might have noticed that all the three overloaded + operator functions are accepting

and returning variables by value. To make these functions better, we can also use

references. So our first member + operator's prototype can be rewritten as:

Complex& operator + (Complex& c);

Now this operator function is accepting a complex number Complex by reference and

returning a reference to the resultant complex number.

As discussed above, in case of assignment, the default assignment operator is used

because we have not implemented (overloaded) our own assignment operator (`=').

But in case, we want to perform the following operation where the two operands are

added and the resultant is assigned to one of them as:

c1 = c1 + c2;

There is one operator (+=) that can be used to do both the operations of addition and

assignment instead of doing these operations separately within operator + and operator

=. So we can overload this one operator (+=) here to make the code more efficient and

reduce our work. Therefore, instead of writing:

c1 = c1 + c2;

We will write:

c1 += c2;

We will write our operator += as:

void Complex :: operator += ( Complex& c )

{

real += c.real;

imag += c.imag;

}

Non-member Operator Functions

Now we are much clear that when an operator function is implemented as a member

function, the leftmost operator must be a class object or reference to a class object of the

operator's class.

When an operator function is implemented as a non-member function, the left-most

operand may be an object of the operator's class, an object of a different class, or a built-

in type. Now we discuss it in a detailed manner.

We can always write our operators as non-member functions. As a non-member

functions, the binary operators like + gets both the operands as arguments. One thing to

take care of while writing non-member functions that they cannot access the private

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members of classes. Actually, this is just to this reason that we make those non-member

functions as friends to the classes whose private data members are required to be

accessed. But the question arises, can we write a non-member operator function without

making it a friend of a class. The answer to this question is yes; If there are public

member functions to access the private data members of the class then they serve the

purpose. In this case of Complex class, let's say we have two public member functions:

double real( );

double imaginary( );

to access the private data members real and imag respectively. Then we can write non-

member operator + function as:

Complex operator + (Complex& c1, Complex& c2)

{

Complex temp;

temp.real ( c1.real() + c2.real() );

temp.imaginary ( c1.imaginary() + c2.imaginary() );

return temp;

}

But this non-member operation functions without declaring a friend of the class is

definitely slower than the member function or a friend one. The reason for this is obvious

from the code that it is making three additional function calls of real() and imaginary()

for each private data member. Also it is not easy to write as compared to member

functions. Therefore, it is recommended to write the member functions for operators

instead of non-members.

Let's take an example where the operators are performing a non-arithmetical operation.

We are writing a class String for strings manipulation as:

class String

{

private :

char string [ 30 ] ;

public :

String ( )

{

strcpy ( string , "" ) ;

}

void getString ( )

{

cout << "Enter the String : " ;

cin >> string ;

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}

void displayString ( )

{

cout << "The String Is : " << string << endl ;

}

// Declaration (prototype) of overloaded sum operator

String operator + ( String & s ) ;

};

We want to write + operator to concatenate two strings. Firstly, we will see the operator's

behavior in ordinary context (behavior with primitive variables for example) and try to

implement the same behavior for this class. We want to concatenate two strings (two

String objects) and then assign the resultant string to a new String object. Here is how

we will write + operator function.

String String :: operator + ( String &s )

{

String temp;

// Declared object temp of String type

strcpy ( temp.string , "" );

// Initialized the temp with empty string

strcat ( temp.string , string );

// Concatenated the driving object's string to

// temp object

strcat ( temp.string , s.string );

// Concatenated the argument's string to the

// temp object

return temp;

// Returned the temp object

}

As you might have guessed already, the String object on the left will be the one to drive

this + operation and the second String object on the left of + will be passed as an

argument to this function. Note that we are not doing the error checking here, the size of

the resultant string temp may increase the array size 30 ( the array size defined in the

class).

Example Program 1

Rudimentary implementation of a class named Complex class to cater complex numbers.

A + operator function has been implemented to add two complex numbers.

/* This program implements the basic class for complex numbers and demonstrates +

operator function */

#include <iostream.h>

class Complex

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{

private :

double real ; // Real Part

double imag ; // Imaginary Part

public :

/* Parameterless Constructor */

Complex ( )

{

cout << "\n Parameterless Constructor called ..." ;

}

/* Parameterized Constructor */

Complex ( double r, double i )

{

cout << "\n Parameterized Constructor called ...";

real = r ;

imag = i ;

}

/* Setter of real data member */

void real ( double r)

{

real = r ;

}

/* Getter of the real data member */

double real ( )

{

return real ;

}

/* Setter of the imag data member */

void imaginary ( double i )

{

imag = i ;

}

/* Getter of the imag data member */

double imaginary ( )

{

return imag ;

}

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/* A Function to display parts of a Complex object */

void display ( )

{

cout << "\n\n Displaying parts of complex number ...";

cout << "\n Real Part : " << real << endl ;

cout << " Imaginary Part : " << imag << endl ;

}

/* Declaration (prototype) of overloaded sum operator */

Complex operator + ( Complex & c2 ) ;

};

Complex Complex :: operator + ( Complex & c1 )

{

cout << "\n Operator + called ...";

Complex temp ;

temp.real = real + c1.real ;

temp.imag = imag + c1.imag ;

return temp ;

}

void main ( )

{

Complex c1 ( 1 , 2 ) ; // Consturct an object using the parameterized constructor

Complex c2 ( 2 , 3 ) ; // Consturct another object using the parameterized

// constructor

Complex result ; // Construct an object using a parameterless constructor

result = c1 + c2 ; // Call the Operator + to add two complex numbers (c1 & c2)

// and then assign the result to 'result' object

result.display ( ) ; // Display the result object contents

}

The output of the program is as follows:

Parameterized Constructor called ...

Parameterless Constructor called ...

Operator + called ...

Parameterless Constructor called ...

Displaying parts of complex number ...

Real Part : 3

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Imaginary Part : 5

The + operator function can be enhanced to return reference of Complex object. We can

also implement += operator. += operator and the enhanced operator + are implemented

as:

Complex & Complex :: operator + ( Complex & c1 )

{

real = real + c1.real ;

imag = imag + c1.imag ;

return *this;

}

// Declaration (prototype) of overloaded sum assignment operator definition

Complex & Complex :: operator += ( Complex & c2 )

{

real += c2.real ;

imag += c2.imag ;

return *this;

}

Example Program 2

Rudimentary Implementation of String class to manipulate strings. It uses + operator to

concatenate strings.

/* This program implements the basic class for strings and demonstrates + operator

function to concatenate two strings*/

#include <iostream.h>

#include <string.h>

class String

{

private :

char string [ 30 ] ; // Array to store string

public :

/* Parameterless Constructor */

String ( )

{

strcpy ( string , "" ) ;

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}

/* Getter function of string */

void getString ( )

{

cout << "Enter the String: " ;

cin >> string ;

}

/* Function to display string */

void displayString ( )

{

cout << "The String is : " << string << endl ;

}

// Declaration (prototype) of overloaded sum operator

String operator + ( String & s ) ;

};

String String :: operator + ( String &s )

{

String temp ;

strcpy ( temp.string , "" ) ;

strcat ( temp.string , string );

strcat ( temp.string , s.string );

return temp;

}

void main ( )

{

String string1 , string2 ;

// Declared two String objects

string1.getString ( ) ;

// Get string for string1 object

string2.getString ( ) ;

// Get string for string2 object

String hold = string1 + string2 ;

// Concatenate string1 and string2 and store the

// result in hold object

hold.displayString ( ) ;

// Display the string

}

The output of the above program is as follows:

Enter the String: Operator

Enter the String: Overloading

The String is : OperatorOverloading

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Tips

Operator Overloading is quite similar to Function Overloading.

There are two types of operators to overload: unary and binary.

C++ built-in operators work for built-in (primitve) types but for user defined data

types, user has to write his/her own operators.

There are some restriction while performing Operator Overloading. For example,

only existing C++ operators are overloaded without creating a new one in the

language. Also, it should not impact the type, semantics (behavior), arity (number of

operands required), precedence and associativity of the operator.

For binary member operators, operands on the left drives (calls) the operation.

Operator functions written as non-members but friends of the class, get both the

operands as their arguments.

Operators can be written as non-members and even without making them friends. But

this is tedious and less efficient way, therefore, it is not recommended.

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