How does Python manage int and long?

106

Does anybody know how Python manage internally int and long types?

  • Does it choose the right type dynamically?
  • What is the limit for an int?
  • I am using Python 2.6, Is is different with previous versions?

How should I understand the code below?

>>> print type(65535)
<type 'int'>
>>> print type(65536*65536)
<type 'long'>

Update:

>>> print type(0x7fffffff)
<type 'int'>
>>> print type(0x80000000)
<type 'long'>
python
integer
asked on Stack Overflow Jan 20, 2010 by luc • edited Oct 25, 2012 by ted

10 Answers

111

int and long were "unified" a few versions back. Before that it was possible to overflow an int through math ops.

3.x has further advanced this by eliminating long altogether and only having int.

  • Python 2: sys.maxint contains the maximum value a Python int can hold.
    • On a 64-bit Python 2.7, the size is 24 bytes. Check with sys.getsizeof().
  • Python 3: sys.maxsize contains the maximum size in bytes a Python int can be.
    • This will be gigabytes in 32 bits, and exabytes in 64 bits.
    • Such a large int would have a value similar to 8 to the power of sys.maxsize.
answered on Stack Overflow Jan 20, 2010 by Ignacio Vazquez-Abrams • edited Oct 31, 2019 by Cristian Ciupitu
15

This PEP should help.

Bottom line is that you really shouldn't have to worry about it in python versions > 2.4

answered on Stack Overflow Jan 20, 2010 by mluebke
5

On my machine:

>>> print type(1<<30)
<type 'int'>
>>> print type(1<<31)
<type 'long'>
>>> print type(0x7FFFFFFF)
<type 'int'>
>>> print type(0x7FFFFFFF+1)
<type 'long'>

Python uses ints (32 bit signed integers, I don't know if they are C ints under the hood or not) for values that fit into 32 bit, but automatically switches to longs (arbitrarily large number of bits - i.e. bignums) for anything larger. I'm guessing this speeds things up for smaller values while avoiding any overflows with a seamless transition to bignums.

answered on Stack Overflow Jan 20, 2010 by MAK
4

Interesting. On my 64-bit (i7 Ubuntu) box:

>>> print type(0x7FFFFFFF)
<type 'int'>
>>> print type(0x7FFFFFFF+1)
<type 'int'>

Guess it steps up to 64 bit ints on a larger machine.

answered on Stack Overflow Feb 22, 2011 by Gringo Suave
4

Python 2.7.9 auto promotes numbers. For a case where one is unsure to use int() or long().

>>> a = int("123")
>>> type(a)
<type 'int'>
>>> a = int("111111111111111111111111111111111111111111111111111")
>>> type(a)
<type 'long'>
answered on Stack Overflow Feb 17, 2017 by nvd
4

Python 2 will automatically set the type based on the size of the value. A guide of max values can be found below.

The Max value of the default Int in Python 2 is 65535, anything above that will be a long

For example:

>> print type(65535)
<type 'int'>
>>> print type(65536*65536)
<type 'long'>

In Python 3 the long datatype has been removed and all integer values are handled by the Int class. The default size of Int will depend on your CPU architecture.

For example:

  • 32 bit systems the default datatype for integers will be 'Int32'
  • 64 bit systems the default datatype for integers will be 'Int64'

The min/max values of each type can be found below:

  • Int8: [-128,127]
  • Int16: [-32768,32767]
  • Int32: [-2147483648,2147483647]
  • Int64: [-9223372036854775808,9223372036854775807]
  • Int128: [-170141183460469231731687303715884105728,170141183460469231731687303715884105727]
  • UInt8: [0,255]
  • UInt16: [0,65535]
  • UInt32: [0,4294967295]
  • UInt64: [0,18446744073709551615]
  • UInt128: [0,340282366920938463463374607431768211455]

If the size of your Int exceeds the limits mentioned above, python will automatically change it's type and allocate more memory to handle this increase in min/max values. Where in Python 2, it would convert into 'long', it now just converts into the next size of Int.

Example: If you are using a 32 bit operating system, your max value of an Int will be 2147483647 by default. If a value of 2147483648 or more is assigned, the type will be changed to Int64.

There are different ways to check the size of the int and it's memory allocation. Note: In Python 3, using the built-in type() method will always return <class 'int'> no matter what size Int you are using.

answered on Stack Overflow Sep 5, 2018 by James Lane
1

From python 3.x, the unified integer libries are even more smarter than older versions. On my (i7 Ubuntu) box I got the following,

>>> type(math.factorial(30))
<class 'int'>

For implementation details refer Include/longintrepr.h, Objects/longobject.c and Modules/mathmodule.c files. The last file is a dynamic module (compiled to an so file). The code is well commented to follow.

answered on Stack Overflow Jul 23, 2016 by Venki
1

Just to continue to all the answers that were given here, especially @James Lanes

the size of the integer type can be expressed by this formula:

total range = (2 ^ bit system)

lower limit = -(2 ^ bit system)*0.5 upper limit = ((2 ^ bit system)*0.5) - 1

answered on Stack Overflow Nov 16, 2018 by Nader Belal
0

It manages them because int and long are sibling class definitions. They have appropriate methods for +, -, *, /, etc., that will produce results of the appropriate class.

For example

>>> a=1<<30
>>> type(a)
<type 'int'>
>>> b=a*2
>>> type(b)
<type 'long'>

In this case, the class int has a __mul__ method (the one that implements *) which creates a long result when required.

answered on Stack Overflow Jan 20, 2010 by S.Lott
0

From Python 3.x all integer values are part of the Int class. Integers size in now dependent on the CPU architecture. enter image description here

answered on Stack Overflow May 3, 2019 by S Sourav

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