operators.md

Operators

An operator is a special symbol which indicates a certain process is carried out.
Operators in programming languages are taken from mathematics.
Applications work with data. The operators are used to process data.

In Python, 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.

The + and - signs can be addition and subtraction 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 number. 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

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 arithmetic operators:

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

The following example shows arithmetic operations.

# arithmetic.py

a = 10
b = 11
c = 12

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

power = a ** 2

print(add, sub, mult, div)
print(power)

All these are known operators from mathematics.

$ ./arithmetic.py
33 2 110 4.0
100

There are three operators dealing with division.

# division.py

print(9 / 3)
print(9 / 4)
print(9 // 4)
print(9 % 4)

The example demonstrates division operators.

print(9 / 4)

This results in 2.25. The / operator returns a decimal number.

print(9 // 4)

The // operator is an integer operator.

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
3.0
2.25
2
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.

# 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.

# 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.

# 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.

The following example demonstrates the short curcuit evaluation.

# short_circuit.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
!=	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' < 'b'
True

We can compare string objects, too.

>>> '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.

>>> 'a' > 6
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unorderable types: str() > int()

It is not possible to use relational operators on different data types. This code leads to a TypeError.

# 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 and 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.

Object identity operators

The object identity operators, is and not is, check if its operatos are the same object.

# object_identity.py

print(None == None)
print(None is None)

print(True is True)

print([] == [])
print([] is [])

print("Python" is "Python")

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

$ ./object_identity.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 operator returns False.

On the other hand, "Python" is "Python" returns True. This is because of optimization: if two string
literals are equal, they have been put to same memory location. Since a string is an immutable entity,
no harm can be done.

Membership operators

The membership operators, in and not in, test for membership in a sequence, such as strings, lists, or tuples.

# membership.py

items = ("coin", "book", "pencil", "spoon", "paper")

if "coin" in items:
    print("There is a coin in the tuple")
else:
    print("There is no coin in the tuple")

if "bowl" not in items:
    print("There is no bowl in the tuple")
else:
    print("There is a bowl in the tuple")

With the membership operators, we test if a item is present in a tuple.

if "coin" in items:

With the in operator, we check if "coin" is present in the items tuple.

if "bowl" not in items:

With the not in operator, we check if "bowl" is not present in the items tuple.

$ ./membership.py
There is a coin in the tuple
There is no bowl in the tuple

Ternary operator

A ternary operator is a simple terse conditional assignment statement.

exp1 if condition else exp2

If condition is true, exp1 is evaluated and the result is returned. If the condition
is false, exp2 is evaluated and its result is returned.

# ternary.py

age = 31

adult = True if age >= 18 else False

print("Adult: {0}".format(adult))

In many countries the adulthood is based on your age. You are adult if you are older
than a certain age. This is a situation for a ternary operator.

adult = True if age >= 18 else False

First the condition is evaluated. If the age is greater or equal to 18, True is returned.
If not, the value following the else keyword is returned. The returned value is then
assigned to the adult variable.

$ ./ternary.py
Adult: True

A 31 years old person is adult.

Bitwise operators

Decimal numbers are natural to humans. Binary numbers are native to computers. 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. 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 numbers. 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 and the final result is 2.

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

The bitwise or operator performs bit-by-bit comparison between two numbers. 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 numbers.
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.

# bitwise_or.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. The 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 multiplying 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.

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.

# 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. Then the outcome is multiplied by 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, then 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.

# 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 before the logical and.

$ ./positive.py
a and b are positive integers
Python associativity rule

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 same precedence 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 then the compound assignment operator is applied.