Maximum value for long integer

Solution 1:

Long integers:

There is no explicitly defined limit. The amount of available address space forms a practical limit.
(Taken from this site). See the docs on Numeric Types where you'll see that Long integers have unlimited precision. In Python 2, Integers will automatically switch to longs when they grow beyond their limit:

>>> import sys
>>> type(sys.maxsize)
<type 'int'>
>>> type(sys.maxsize+1)
<type 'long'>

for integers we have

maxint and maxsize:

The maximum value of an int can be found in Python 2.x with sys.maxint. It was removed in Python 3, but sys.maxsize can often be used instead. From the changelog:

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).

and, for anyone interested in the difference (Python 2.x):

sys.maxint The largest positive integer supported by Python’s regular integer type. This is at least 2**31-1. The largest negative integer is -maxint-1 — the asymmetry results from the use of 2’s complement binary arithmetic.

sys.maxsize The largest positive integer supported by the platform’s Py_ssize_t type, and thus the maximum size lists, strings, dicts, and many other containers can have.

and for completeness, here's the Python 3 version:

sys.maxsize An integer giving the maximum value a variable of type Py_ssize_t can take. It’s usually 2^31 - 1 on a 32-bit platform and 2^63 - 1 on a 64-bit platform.

floats:

There's float("inf") and float("-inf"). These can be compared to other numeric types:

>>> import sys
>>> float("inf") > sys.maxsize
True

Solution 2:

Python long can be arbitrarily large. If you need a value that's greater than any other value, you can use float('inf'), since Python has no trouble comparing numeric values of different types. Similarly, for a value lesser than any other value, you can use float('-inf').

Solution 3:

Direct answer to title question:

Integers are unlimited in size and have no maximum value in Python.

Answer which addresses stated underlying use case:

According to your comment of what you're trying to do, you are currently thinking something along the lines of

minval = MAXINT;
for (i = 1; i < num_elems; i++)
    if a[i] < a[i-1]
        minval = a[i];

That's not how to think in Python. A better translation to Python (but still not the best) would be

minval = a[0]  # Just use the first value
for i in range(1, len(a)):
    minval = min(a[i], a[i - 1])

Note that the above doesn't use MAXINT at all. That part of the solution applies to any programming language: You don't need to know the highest possible value just to find the smallest value in a collection.

But anyway, what you really do in Python is just

minval = min(a)

That is, you don't write a loop at all. The built-in min() function gets the minimum of the whole collection.

Solution 4:

long type in Python 2.x uses arbitrary precision arithmetic and has no such thing as maximum possible value. It is limited by the available memory. Python 3.x has no special type for values that cannot be represented by the native machine integer — everything is int and conversion is handled behind the scenes.