Python Operators

In this part of the Python programming tutorial, we will talk about operators.
An operator is a special symbol which indicates a certain process is carried out. Operators in programming languages are taken from mathematics. Programmers work with data. The operators are used to process data.
In Python programming language, we have several types of operators:

• Arithmetic operators
• Boolean operators
• Relational operators
• Bitwise operators

An operator may have one or two operands. An operand is one of the inputs (arguments) of an operator. Those operators that work with only one operand are called unary operators. Those who work with two operands are called binary operators.
+ and - signs can be addition and substraction operators as well as unary sign operators. It depends on the situation.

>>> 2
2
>>> +2
2
>>> 

The plus sign can be used to indicate that we have a positive nubmer. But it is mostly not used. The minus sign changes the sign of a value.

>>> a = 1
>>> -a
-1
>>> -(-a)
1

Multiplication and addition operators are examples of binary operators. They are used with two operands.

>>> 3 * 3
9
>>> 3 + 3
6

The assignment operator

The assignment operator = assigns a value to a variable. In mathematics, the = operator has a different meaning. In an equation, the = operator is an equality operator. The left side of the equation is equal to the right one.

>>> x = 1
>>> x
1

Here we assign a number to an x variable.

>>> x = x + 1
>>> x
2

The previous expression does not make sense in mathematics. But it is legal in programming. The expression means that we add 1 to the x variable. The right side is equal to 2 and 2 is assigned to x.

>>> a = b = c = 4
>>> print a, b, c
4 4 4

It is possible to assign a value to multiple variables.

>>> 3 = y
  File "<stdin>", line 1
SyntaxError: can't assign to literal

This code example results in syntax error. We cannot assign a value to a literal.

Arithmetic operators

The following is a table of arithmentic operators in Python programming language.

Symbol	Name
+	Addition
-	Subtraction
*	Multiplication
/	Division
//	Floor division
%	Modulo
**	Power

The following example shows arithmetic operations.

#!/usr/bin/python

# arithmetic.py

a = 10
b = 11
c = 12

add = a + b + c
sub = c - a
mult = a * b
div = c / 3

pow = a ** 2

print add, sub, mult, div
print pow

All these are known operators from mathematics.

$ ./arithmetic.py 
33 2 110 4
100

The division operations in Python may be surprising for beginners. It is because by default, the division operator / performs integer division. This means that we get an integer as a result. If we want to get a more exact result, we use at least one floating point number as an operand.

#!/usr/bin/python

# division.py

print 9 / 3
print 9 / 4
print 9 / 4.0
print 9 // 4.0
print 9 % 4

The example demonstrates division operators.

print 9 / 4

This results in 2. The division operator works differently for integers and for floating point numbers. Integer division gives an integer result. The fraction part is truncated. Hence we get: 9 / 4 = 2

print 9 / 4.0

Here we get the expected value: 2.25. One of the operands is a floating point number, so the result is a floating point too.

print 9 // 4.0

Python has also a special floor division operator. The result is the floor of the value returned by true division.

print 9 % 4

The % operator is called the modulo operator. It finds the remainder of division of one number by another. 9 % 4, 9 modulo 4 is 1, because 4 goes into 9 twice with a remainder of 1.

$ ./division.py 
3
2
2.25
2.0
1

>>> 'return' + 'of' + 'the' + 'king'
'returnoftheking'

The addition operator can be used to concatenate strings as well.

>>> 3 + ' apples'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unsupported operand type(s) for +: 'int' and 'str'

We cannot add integers and strings. This results in a TypeError.

>>> str(3) + ' apples'
'3 apples'

For the example to work, we must convert the number to a string using the str() function.
On the other hand, the multiplication operator can be used with a string and a number.

>>> 'dollar ' * 5
'dollar dollar dollar dollar dollar '

Boolean operators

In Python, we have and, or and not boolean operators. With boolean operators we perform logical operations. These are most often used with if and while keywords.

#!/usr/bin/python

# andop.py

print True and True
print True and False
print False and True
print False and False

This example shows the logical and operator. The logical and operator evaluates to True only if both operands are True.

$ ./andop.py 
True
False
False
False

The logical or operator evaluates to True, if either of the operands is True.

#!/usr/bin/python

# orop.py

print True or True
print True or False
print False or True
print False or False

If one of the sides of the operator is True, the outcome of the operation is True.

$ ./orop.py 
True
True
True
False

The negation operator not makes True False and False True.

#!/usr/bin/python

# negation.py

print not False
print not True
print not ( 4 < 3 )

The example shows the not operator in action.

$ ./negation.py 
True
False
True

And, or operators are short circuit evaluated. Short circuit evaluation means that the second argument is only evaluated if the first argument does not suffice to determine the value of the expression: when the first argument of and evaluates to false, the overall value must be false; and when the first argument of or evaluates to true, the overall value must be true. (wikipedia)
A typical example follows.

#!/usr/bin/python

# shortcircuit.py

x = 10
y = 0

if (y != 0 and x/y < 100):
      print "a small value"

The first part of the expression evaluates to False. The second part of the expression is not evaluated. Otherwise, we would get a ZeroDivisionError.

Relational Operators

Relational operators are used to compare values. These operators always result in a boolean value.

Symbol	Meaning
<	strictly less than
<=	less than or equal to
>	greater than
>=	greater than or equal to
==	equal to
!= or <>	not equal to
is	object identity
is not	negated object identity

The above table shows Python relational operators.

>>> 3 < 4
True
>>> 4 == 3
False
>>> 4 >= 3
True

As we already mentioned, the relational operators return boolean values. True or False.
Notice that the relational operators are not limited to numbers. We can use them for other objects as well. Although they might not always be meaningful.

>>> "six" == "six"
True
>>> "a" > 6
True
>>> 'a' < 'b'
True

We can compare string objects too. We can use relational operators for different object types. In our case we compare a string with a number.

>>> 'a' < 'b'

What exactly happens here? Computers do not know characters or strings. For them, everything is just a number. Characters are special numbers stored in specific tables. Like ASCII.

#!/usr/bin/python

# compare.py


print 'a' < 'b'

print "a is:", ord('a')
print "b is:", ord('b')

Internally, the a and b characters are numbers. So when we compare two characters, we compare their stored numbers. The built-in ord() function returns the ASCII value of a single character.

$ ./compare.py 
True
a is: 97
b is: 98

In fact, we compare two numbers. 97 with 98.

>>> "ab" > "aa"
True

Say we have a string with more characters. If the first characters are equal, we compare the next ones. In our case, the b character at the second position has a greater value than the a character. That is why "ab" string is greater than "aa" string. Comparing strings in such a way does not make much sense, of course. But it is technically possible.

#!/usr/bin/python

# objects.py

print None == None
print None is None

print True is True

print [] == []
print [] is []

print "Python" is "Python"

The == operator tests for equality The is keyword tests for object identity. Whether we are talking about the same object. Note, that more variables may refer to the same object.

$ ./objects.py 
True
True
True
True
False
True

The output might be surprising for you. In Python language, there is only one None and one True object. That's why True is equal and also identical to True. There is only one truth out there, anyway. The empty list [] is equal to another empty list []. But they are not identical. Python has put them into two different memory locations. They are two distinct objects. Hence the is keyword returns False. On the other hand, "Python" is "Python" returns True. This is because of optimalisation. If two string literals are equal, they have been put to same memory location. A string is an immutable entity. No harm can be done.

Bitwise operators

Decimal numbers are natural to humans. Binary numbers are native to comptuters. Binary, octal, decimal or hexadecimal symbols are only notations of the same number. Bitwise operators work with bits of a binary number. We have binary logical operators and shift operators. Bitwise operators are seldom used in higher level languages like Python.

Symbol	Meaning
~	bitwise negation
^	bitwise exclusive or
&	bitwise and
|	bitwise or
<<	left shift
>>	right shift

The bitwise negation operator changes each 1 to 0 and 0 to 1.

>>> ~7
-8
>>> ~-8
7

The operator reverts all bits of a number 7. One of the bits also determines, whether the number is negative or not. If we negate all the bits one more time, we get number 7 again.
The bitwise and operator performs bit-by-bit comparison between two nubmers. The result for a bit position is 1 only if both corresponding bits in the operands are 1.

     00110
  &  00011
   = 00010

The first number is a binary notation of 6. The second is 3. The result is 2.

>>> 6 & 3
2
>>> 3 & 6
2

The bitwise or operator performs bit-by-bit comparison between two nubmers. The result for a bit position is 1 if either of the corresponding bits in the operands is 1.

     00110
  |  00011
   = 00111

The result is 00110 or decimal 7.

>>> 6 | 3
7

The bitwise exclusive or operator performs bit-by-bit comparison between two nubmers. The result for a bit position is 1 if one or the other (but not both) of the corresponding bits in the operands is 1.

     00110
  ^  00011
   = 00101

The result is 00101 or decimal 5.

>>> 6 ^ 3
5

As we mentioned, bitwise operators are seldom used in Python and other high level languages. Yet there are some situations, where they are used. One example is a mask. A mask is a specific bit pattern. It determines whether some property is set or not.
Let's have an example from GUI programming.

#!/usr/bin/python

# nominimizebox.py

import wx

app = wx.App()
window = wx.Frame(None, style=wx.MAXIMIZE_BOX | wx.RESIZE_BORDER 
	| wx.SYSTEM_MENU | wx.CAPTION |	 wx.CLOSE_BOX)
window.Show(True)

app.MainLoop()

This is a small example of a wxPython code. wx.MAXIMIZE_BOX, wx.RESIZE_BORDER, wx.SYSTEM_MENU, wx.CAPTION and wx.CLOSE_BOX are constants. The bitwise or operator adds all these constants to the mask. In our case, all these properties are set using the bitwise or operator and applied to the wx.Frame widget.
Finally, we also have bitwise shift operators. The bitwise shift operators shift bits to the right or left.

number << n : multiply number 2 to the nth power
number >> n : divide number by 2 to the nth power

These operators are also called arithmetic shift.

     00110
  >>  00001
   = 00011

We shift each of the bits of number six to the right. It is equal to dividing the six by 2. The result is 00011 or decimal 3.

>>> 6 >> 1
3

     00110
  << 00001
   = 01100

We shift each of the bits of number six to the left. It is equal to muliplying the number six by 2. The result is 01100 or decimal 12.

>>> 6 << 1
12

Compound assignment operators

The compound assignment operators consist of two operators. They are shorthand operators.

>>> i = 1
>>> i = i + 1
>>> i
2
>>> i += 1
>>> i
3

The += compound operator is one of these shorthand operators. They are less readable than the full expressions but experienced programmers often use them.
Other compound operators are:

-=   *=   /=   //=   %=   **=   &=   |=   ^=   >>=   <<=

Operator precedence

The operator precedence tells us which operators are evaluated first. The precedence level is necessary to avoid ambiguity in expressions.
What is the outcome of the following expression? 28 or 40?

3 + 5 * 5

Like in mathematics, the multiplication operator has a higher precedence than addition operator. So the outcome is 28.

(3 + 5) * 5

To change the order of evaluation, we can use square brackets. Expressions inside square brackets are always evaluated first.
The following list shows operator precedence in Python.

   unary +  -  ~
   **
   *  /  %
   +  -
   >>  <<
   &
   ^
   |
   <  <=  ==  >=  >  !=  <>  is
   not
   and 
   or

The operators on the same row have the same level of precedence. The precedence grows from bottom to top.

#!/usr/bin/python

# precedence.py


print 3 + 5 * 5
print (3 + 5) * 5

print 2 ** 3 * 5
print not True or True
print not (True or True)

In this code example, we show some common expressions. The outcome of each expression is dependent on the precedence level.

print 2 ** 3 * 5

The power operator has higher precedence than the multiplication operator. First, the 2 ** 3 is evaluated, which returns 8. Than the outcome is multiplied by 5. 8 * 5. And the result is 40.

print not True or True

In this case, the not operator has a higher precedence. First, the first True value is negated to False, that the or operator combines False and True, which gives True in the end.

$ ./precedence.py 
28
40
40
True
False

The relational operators have a higher precedence than logical operators.

#!/usr/bin/python

# positive.py

a = 1
b = 2

if (a > 0 and b > 0):
   print "a and b are positive integers"

The and operator awaits two boolean values. If one of the operands would not be a boolean value, we would get a syntax error. In Python, the relational operators are evaluated first. The logical operator then.

$ ./positive.py 
a and b are positive integers

Associativity

Sometimes the precedence is not satisfactory to determine the outcome of an expression. There is another rule called associativity. The associativity of operators determines the order of evaluation of operators with the sameprecedence level.

9 / 3 * 3

What is the outcome of this expression? 9 or 1? The multiplication, deletion and the modulo operator are left to right associated. So the expression is evaluated this way: (9 / 3) * 3 and the result is 9.
Arithmetic, boolean, relational and bitwise operators are all left to right associated.
On the other hand, the assignment operator is right associated.

>>> a = b = c = d = 0
>>> a, b, c, d
(0, 0, 0, 0)

If the association was left to right, the previous expression would not be possible.
The compound assignment operators are right to left associated.

>>> j = 0
>>> j *= 3 + 1
>>> j
0

You might expect the result to be 1. But the actual result is 0. Because of the associativity. The expression on the right is evaluated first and than the compound assignment operator is applied.
In this chapter, we have talked about operators in Python.