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Python Integers |
The theoretical domain for integers in python is negative infinity to infinity. In practice, integer values are limited by the amount of available memory.
In Python 2, there was a distinction between int
, numbers that fit in a 32 or 64 bit C long, and long
, numbers limited by available memory. Python 3 unified the two types into just int
, more info in PEP 237.
int
creation using integer literals
Integer objects can be created using using integer literals. Unadorned numbers without decimals are integer literals:
>>> 1234567890 # Unadorned numbers are integer literals
1234567890
>>> type(1234567890)
<class 'int'>
Numeric literals do not contain a sign, however creating negative integer objects is possible by prefixing with a unary -
(minus) operator with no space before the literal:
>>> -1234567890
-1234567890
>>> type(-1234567890)
<class 'int'>
Likewise, positive integer objects can be created by prefixing a unary +
(plus) operator with no space before the digits. Usually +
is ommited:
>>> +1234
1234
Binary (base 2, prefix: 0b
or 0B
), octal (base 8, prefix: 0o
or 0O
), and hexadecimal (base 16, prefix: 0x
or 0X
) integers can also be created using integer literals:
>>> 0b1, 0b10, 0b11
(1, 2, 3)
>>> 0o1, 0o10, 0o11
(1, 8, 9)
>>> 0x1, 0x10, 0x11
(1, 16, 17)
Note that leading 0's for non-zero integer literals are not allowed:
>>> 0 # Zero by itself is okay.
0
>>> 01 # Leading zero(s) cause SyntaxError.
File "<stdin>", line 1
01
^
SyntaxError: invalid token
The int
constructor is another way to create integer objects.
class int(x=0)
class int(x, base=10)
Creating integer objects with integer literals is preferred when possible:
>>> a = 1 # Prefer integer literal when possible.
>>> type(a)
<class 'int'>
>>> b = int(1) # Works but unnecessary.
>>> type(b)
<class 'int'>
However, the constructor allows for creating integer objects from other number types:
>>> a = 1.123
>>> type(a)
<class 'float'>
>>> print(a)
1.123
>>> b = int(1.123)
>>> type(b)
<class 'int'>
>>> print(b)
1
Using the int
constructor for floating point numbers will truncate the number towards zero:
>>> int(-1.23)
-1
>>> int(1.23)
1
The built-in boolean
constants are instances of the bool
class, and are subclasses of the int
class, making them a kind of numeric type:
>>> type(True)
<class 'bool'>
>>> issubclass(bool, int)
True
If that doesn't make sense to you, don't worry. For now just remember that calling the int constructor with boolean
objects will return integer objects:
>>> int(True)
1
>>> int(False)
0
The int
constructor will also make integer objects from strings:
>>> a = "10"
>>> type(a)
<class 'str'>
>>> b = int("10")
>>> type(b)
<class 'int'>
Strings for the int
constructor must represent an integer literal:
The second parameter of the int
constructor is to specify a base (default: 10). Valid bases are 0 and 2-36.
If an explicit base is provided the first argument must be a string.
>>> int("111", 2)
7
>>> int(111, 2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: int() can't convert non-string with explicit base
The string used for the int
constructor with an explicit base must be a valid integer literal for that base:
>>> int('11', 2)
3
>>> int('12', 2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: invalid literal for int() with base 2: '12'
Both prefixed and non-prefixed strings of integer literals can be used, however, if used, the prefix must match the provided base.
>>> int('1101', 2)
13
>>> int('0b1101', 2)
13
>>> int('0x1101', 2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: invalid literal for int() with base 2: '0x1101'
If a prefixed string and base 0 is used, the created integer object will use the base specified by the prefix. If no prefix is used, then the base is assumed 10
>>> int('100', 0)
100
>>> int('0b100', 0)
4
>>> int('0o100', 0)
64