No, but you can use upside-down floor division:¹
def ceildiv(a, b):
return -(a // -b)
This works because Python's division operator does floor division (unlike in C, where integer division truncates the fractional part).
Here's a demonstration:
>>> from __future__ import division # for Python 2.x compatibility
>>> import math
>>> def ceildiv(a, b):
... return -(a // -b)
...
>>> b = 3
>>> for a in range(-7, 8):
... q1 = math.ceil(a / b) # a/b is float division
... q2 = ceildiv(a, b)
... print("%2d/%d %2d %2d" % (a, b, q1, q2))
...
-7/3 -2 -2
-6/3 -2 -2
-5/3 -1 -1
-4/3 -1 -1
-3/3 -1 -1
-2/3 0 0
-1/3 0 0
0/3 0 0
1/3 1 1
2/3 1 1
3/3 1 1
4/3 2 2
5/3 2 2
6/3 2 2
7/3 3 3
Why this instead of math.ceil?
math.ceil(a / b) can quietly produce incorrect results, because it introduces floating-point error. For example:
>>> from __future__ import division # Python 2.x compat
>>> import math
>>> def ceildiv(a, b):
... return -(a // -b)
...
>>> x = 2**64
>>> y = 2**48
>>> ceildiv(x, y)
65536
>>> ceildiv(x + 1, y)
65537 # Correct
>>> math.ceil(x / y)
65536
>>> math.ceil((x + 1) / y)
65536 # Incorrect!
In general, it's considered good practice to avoid floating-point arithmetic altogether unless you specifically need it. Floating-point math has several tricky edge cases, which tends to introduce bugs if you're not paying close attention. It can also be computationally expensive on small/low-power devices that do not have a hardware FPU.
¹In a previous version of this answer, ceildiv was implemented as return -(-a // b) but it was changed to return -(a // -b) after commenters reported that the latter performs slightly better in benchmarks. That makes sense, because the dividend (a) is typically larger than the divisor (b). Since Python uses arbitrary-precision arithmetic to perform these calculations, computing the unary negation -a would almost always involve equal-or-more work than computing -b.
Hello, Can someone please explain the me the difference between those two arithmetic signs because am new to programming python:)
Videos
When should I use floor division instead of regular division in Python?
What is the floor division of 5 and 2?
How does floor division work with negative numbers?
No, but you can use upside-down floor division:¹
def ceildiv(a, b):
return -(a // -b)
This works because Python's division operator does floor division (unlike in C, where integer division truncates the fractional part).
Here's a demonstration:
>>> from __future__ import division # for Python 2.x compatibility
>>> import math
>>> def ceildiv(a, b):
... return -(a // -b)
...
>>> b = 3
>>> for a in range(-7, 8):
... q1 = math.ceil(a / b) # a/b is float division
... q2 = ceildiv(a, b)
... print("%2d/%d %2d %2d" % (a, b, q1, q2))
...
-7/3 -2 -2
-6/3 -2 -2
-5/3 -1 -1
-4/3 -1 -1
-3/3 -1 -1
-2/3 0 0
-1/3 0 0
0/3 0 0
1/3 1 1
2/3 1 1
3/3 1 1
4/3 2 2
5/3 2 2
6/3 2 2
7/3 3 3
Why this instead of math.ceil?
math.ceil(a / b) can quietly produce incorrect results, because it introduces floating-point error. For example:
>>> from __future__ import division # Python 2.x compat
>>> import math
>>> def ceildiv(a, b):
... return -(a // -b)
...
>>> x = 2**64
>>> y = 2**48
>>> ceildiv(x, y)
65536
>>> ceildiv(x + 1, y)
65537 # Correct
>>> math.ceil(x / y)
65536
>>> math.ceil((x + 1) / y)
65536 # Incorrect!
In general, it's considered good practice to avoid floating-point arithmetic altogether unless you specifically need it. Floating-point math has several tricky edge cases, which tends to introduce bugs if you're not paying close attention. It can also be computationally expensive on small/low-power devices that do not have a hardware FPU.
¹In a previous version of this answer, ceildiv was implemented as return -(-a // b) but it was changed to return -(a // -b) after commenters reported that the latter performs slightly better in benchmarks. That makes sense, because the dividend (a) is typically larger than the divisor (b). Since Python uses arbitrary-precision arithmetic to perform these calculations, computing the unary negation -a would almost always involve equal-or-more work than computing -b.
Solution 1: Convert floor to ceiling with negation
def ceiling_division(n, d):
return -(n // -d)
Reminiscent of the Penn & Teller levitation trick, this "turns the world upside down (with negation), uses plain floor division (where the ceiling and floor have been swapped), and then turns the world right-side up (with negation again)"
Solution 2: Let divmod() do the work
def ceiling_division(n, d):
q, r = divmod(n, d)
return q + bool(r)
The divmod() function gives (a // b, a % b) for integers (this may be less reliable with floats due to round-off error). The step with bool(r) adds one to the quotient whenever there is a non-zero remainder.
Solution 3: Adjust the numerator before the division
def ceiling_division(n, d):
return (n + d - 1) // d
Translate the numerator upwards so that floor division rounds down to the intended ceiling. Note, this only works for integers.
Solution 4: Convert to floats to use math.ceil()
def ceiling_division(n, d):
return math.ceil(n / d)
The math.ceil() code is easy to understand, but it converts from ints to floats and back. This isn't very fast and it may have rounding issues. Also, it relies on Python 3 semantics where "true division" produces a float and where the ceil() function returns an integer.
In Python 3.x, 5 / 2 will return 2.5 and 5 // 2 will return 2. The former is floating point division, and the latter is floor division, sometimes also called integer division.
In Python 2.2 or later in the 2.x line, there is no difference for integers unless you perform a from __future__ import division, which causes Python 2.x to adopt the 3.x behavior.
Regardless of the future import, 5.0 // 2 will return 2.0 since that's the floor division result of the operation.
You can find a detailed description at PEP 238: Changing the Division Operator.
Python 2.x Clarification:
To clarify for the Python 2.x line, / is neither floor division nor true division.
/ is floor division when both args are int, but is true division when either of the args are float.
Like this:
int(5/2) 5//2
Is there ever a case where these are different.
You can expand the operator to be more than a single character. For example you could do /int~ and /float~ to disambiguate which division operation to use. It's pretty verbose but if you can find a shorter term to signify which operation you can use that.
This can then be expanded to other operations to for example ensure that overflow behavior is specified for integer addition +sat32~.
Some options that don't involve namespaces:
- Python:
a // b - Visual Basic:
a \ b - Pascal:
a div b
Normal division is a / b in all the cases.