Why do Python's math.ceil() and math.floor() operations return floats instead of integers?

Can someone explain this (straight from the docs- emphasis mine):

math.ceil(x) Return the ceiling of x as a float, the smallest integer value greater than or equal to x.

math.floor(x) Return the floor of x as a float, the largest integer value less than or equal to x.

Why would .ceil and .floor return floats when they are by definition supposed to calculate integers?

EDIT:

Well this got some very good arguments as to why they should return floats, and I was just getting used to the idea, when @jcollado pointed out that they in fact do return ints in Python 3...

Solution 1:

As pointed out by other answers, in python they return floats probably because of historical reasons to prevent overflow problems. However, they return integers in python 3.

>>> import math
>>> type(math.floor(3.1))
<class 'int'>
>>> type(math.ceil(3.1))
<class 'int'>

You can find more information in PEP 3141.

Solution 2:

The range of floating point numbers usually exceeds the range of integers. By returning a floating point value, the functions can return a sensible value for input values that lie outside the representable range of integers.

Consider: If floor() returned an integer, what should floor(1.0e30) return?

Now, while Python's integers are now arbitrary precision, it wasn't always this way. The standard library functions are thin wrappers around the equivalent C library functions.

Solution 3:

Because python's math library is a thin wrapper around the C math library which returns floats.

Solution 4:

The source of your confusion is evident in your comment:

The whole point of ceil/floor operations is to convert floats to integers!

The point of the ceil and floor operations is to round floating-point data to integral values. Not to do a type conversion. Users who need to get integer values can do an explicit conversion following the operation.

Note that it would not be possible to implement a round to integral value as trivially if all you had available were a ceil or float operation that returned an integer. You would need to first check that the input is within the representable integer range, then call the function; you would need to handle NaN and infinities in a separate code path.

Additionally, you must have versions of ceil and floor which return floating-point numbers if you want to conform to IEEE 754.

Solution 5:

Before Python 2.4, an integer couldn't hold the full range of truncated real numbers.

http://docs.python.org/whatsnew/2.4.html#pep-237-unifying-long-integers-and-integers