Why do Python s math ceil and math floor operations return floats instead of integers

Question

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

User · Accepted Answer

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.

User · Answer

This totally caught me off guard recently   This is because I ve programmed in C since the 1970 s and I m only now learning the fine details of Python   Like this curious behavior of math floor    The math library of Python is how you access the C standard math library   And the C standard math library is a collection of floating point numerical functions  like sin    and cos    sqrt     The floor   function in the context of numerical calculations has ALWAYS returned a float  For 50 YEARS now  It s part of the standards for numerical computation  For those of us familiar with the math library of C  we don t understand it to be just  quot math functions quot   We understand it to be a collection of floating-point algorithms  It would be better named something like NFPAL - Numerical Floating Point Algorithms Libary     Those of us that understand the history instantly see the python math module as just a wrapper for the long-established C floating-point library  So we expect without a second thought  that math floor   is the same function as the C standard library floor   which takes a float argument and returns a float value  The use of floor   as a numerical math concept goes back to 1798 per the Wikipedia page on the subject  https   en wikipedia org wiki Floor and ceiling functions Notation It never has been a computer science covert floating-point to integer storage format function even though logically it s a similar concept  The floor   function in this context has always been a floating-point numerical calculation as all most  the functions in the math library   Floating-point goes beyond what integers can do   They include the special values of  inf  -inf  and Nan  not a number  which are all well defined as to how they propagate through floating-point numerical calculations   Floor   has always CORRECTLY preserved values like Nan and  inf and -inf in numerical calculations   If Floor returns an int  it totally breaks the entire concept of what the numerical floor   function was meant to do  math floor float  quot nan quot    must return  quot nan quot  if it is to be a true floating-point numerical floor   function  When I recently saw a Python education video telling us to use  i   math floor 12 34 3   to get an integer I laughed to myself at how clueless the instructor was   But before writing a snarkish comment  I did some testing and to my shock  I found the numerical algorithms library in Python was returning an int   And even stranger  what I thought was the obvious answer to getting an int from a divide  was to use  i   12 34    3  Why not use the built-in integer divide to get the integer you are looking for  From my C background  it was the obvious right answer  But low and behold  integer divide in Python returns a FLOAT in this case  Wow  What a strange upside-down world Python can be  A better answer in Python is that if you really NEED an int type  you should just be explicit and ask for int in python  i   int 12 34 3   Keeping in mind however that floor   rounds towards negative infinity and int   rounds towards zero so they give different answers for negative numbers  So if negative values are possible  you must use the function that gives the results you need for your application  Python however is a different beast for good reasons   It s trying to address a different problem set than C   The static typing of Python is great for fast prototyping and development  but it can create some very complex and hard to find bugs when code that was tested with one type of objects  like floats  fails in subtle and hard to find ways when passed an int argument   And because of this  a lot of interesting choices were made for Python that put the need to minimize surprise errors above other historic norms  Changing the divide to always return a float  or some form of non int  was a move in the right direction for this   And in this same light  it s logical to make    be a floor a b  function  and not an  quot int divide quot   Making float divide by zero a fatal error instead of returning float  quot inf quot   is likewise wise because  in MOST python code  a divide by zero is not a numerical calculation but a programming bug where the math is wrong or there is an off by one error  It s more important for average Python code to catch that bug when it happens  instead of propagating a hidden error in the form of an  quot inf quot  which causes a blow-up miles away from the actual bug  And as long as the rest of the language is doing a good job of casting ints to floats when needed  such as in divide  or math sqrt    it s logical to have math floor   return an int  because if it is needed as a float later  it will be converted correctly back to a float   And if the programmer needed an int  well then the function gave them what they needed  math floor a b  and a  b should act the same way  but the fact that they don t I guess is just a matter of history not yet adjusted for consistency  And maybe too hard to  quot fix quot  due to backward compatibility issues  And maybe not that important    In Python  if you want to write hard-core numerical algorithms  the correct answer is to use NumPy and SciPy  not the built-in Python math module  import numpy as np  nan   np float64 0 0    0 0      gives a warning and returns float64 nan  nan   np floor nan               returns float64 nan  Python is different  for good reasons  and it takes a bit of time to understand it   And we can see in this case  the OP  who didn t understand the history of the numerical floor   function  needed and expected it to return an int from their thinking about mathematical integers and reals  Now Python is doing what our mathematical  vs computer science  training implies  Which makes it more likely to do what a beginner expects it to do while still covering all the more complex needs of advanced numerical algorithms with NumPy and SciPy   I m constantly impressed with how Python has evolved  even if at times I m totally caught off guard

User · Answer

Because the range for floats is greater than that of integers -- returning an integer could overflow

User · Answer

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    gt  gt  gt  import math  gt  gt  gt  type math floor 3 1    lt class  int  gt   gt  gt  gt  type math ceil 3 1    lt class  int  gt    You can find more information in PEP 3141

User · Answer

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

User · Answer

Maybe because other languages do this as well  so it is generally-accepted behavior   For good reasons  as shown in the other answers

User · Answer

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

User · Answer

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

User · Answer

This is a very interesting question  As a float requires some bits to store the exponent   bits for exponent  any floating point number greater than 2   float size - bits for exponent  will always be an integral value  At the other extreme a float with a negative exponent will give one of 1  0 or -1  This makes the discussion of integer range versus float range moot because these functions will simply return the original number whenever the number is outside the range of the integer type   The python functions are wrappers of the C function and so this is really a deficiency of the C functions where they should have returned an integer and forced the programer to do the range NaN Inf check before calling ceil floor   Thus the logical answer is the only time these functions are useful they would return a value within integer range and so the fact they return a float is a mistake and you are very smart for realizing this

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

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