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Integer (int) has no max limit in Python 3

Modified: | Tags: Python, Numeric

In Python 3, the int type has no max limit. You can handle values as large as the available memory allows.

Python 2 has two integer types, int and long, whereas Python 3 has only int. The int in Python 3 is equivalent to the long in Python 2, with no max limit.

Contents

For information on the max and min float values, refer to the following article.

NumPy uses fixed-bit data types, such as int32 (32-bit integer) and int64 (64-bit integer).

int and long in Python 2

Python 2 has two integer types: int and long.

In Python 2, the max int value can be obtained using sys.maxint. The min int value, which is the largest negative number, is -sys.maxint - 1.

sys.maxint typically has a value of 2**31 - 1 in a 32-bit environment and 2**63 - 1 in a 64-bit environment.

The long type has no max or min limit.

int has no max limit in Python 3

The int type in Python 3, equivalent to the long type in Python 2, has no max or min limit.

The sys.maxint constant was removed, since there is no longer a limit to the value of integers. However, sys.maxsize can be used as an integer larger than any practical list or string index. It conforms to the implementation’s “natural” integer size and is typically the same as sys.maxint in previous releases on the same platform (assuming the same build options). What’s New In Python 3.0 — Python 3.12.1 documentation

In Python 3, sys.maxint has been removed, and sys.maxsize has been added.

sys.maxsize is 2**31 - 1 in a 32-bit environment and 2**63 - 1 in a 64-bit environment, similar to sys.maxint in Python 2.

import sys

print(sys.maxsize)
# 9223372036854775807

print(type(sys.maxsize))
# <class 'int'>

print(sys.maxsize == 2**63 - 1)
# True
source: sys_maxsize.py

When converted to binary and hexadecimal strings using bin() and hex(), sys.maxsize is expressed as follows.

print(bin(sys.maxsize))
# 0b111111111111111111111111111111111111111111111111111111111111111

print(hex(sys.maxsize))
# 0x7fffffffffffffff
source: sys_maxsize.py

sys.maxsize is not the max int value; you can handle larger values as long as there is sufficient available memory.

i = 10**100

print(i)
# 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

print(i > sys.maxsize)
# True
source: sys_maxsize.py

Comparison with float

sys.float_info.max provides the max float value.

print(sys.float_info.max)
# 1.7976931348623157e+308
source: sys_maxsize.py

With no max limit, int can handle values exceeding the max float value.

i_e309 = 10**309

print(type(i_e309))
# <class 'int'>

print(i_e309 > sys.float_info.max)
# True
source: sys_maxsize.py

Note that float represents infinity as inf, which is considered larger than any other numerical value.

print(float('inf'))
# inf

print(float('inf') > sys.float_info.max)
# True

print(float('inf') > i_e309)
# True
source: sys_maxsize.py

Converting inf to int results in an OverflowError.

# int(float('inf'))
# OverflowError: cannot convert float infinity to integer
source: sys_maxsize.py

For details about infinity (inf), refer to the following article.

Integer string conversion length limitation

In versions released after September 7, 2022 (Python 3.11, 3.10.7, 3.9.14, 3.8.14, 3.7.14, and later), integer-string conversion is limited to 4300 digits by default.

This limitation aims to prevent DoS attacks that exploit the O(n^2) complexity of integer-string conversions.

This limit applies only to conversion; int can still represent values larger than 4300 digits, and other operations remain unaffected.

Be aware that functions that internally convert integers to strings, such as print() or repr(), are also subject to this limit.

i = 10**10000
# print(i)
# ValueError: Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit
source: int_str_conversion_limit.py

For details on how to set the digit limit, refer to the following article.

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