Is divmod() faster than using the % and // operators?

Question

I remember from assembly that integer division instructions yield both the quotient and remainder. So, in python will the built-in divmod() function be better performance-wise than using the % and // operators (suppose of course one needs both the quotient and the remainder)?

q, r = divmod(n, d)
q, r = (n // d, n % d)

Answer 1

To measure is to know (all timings on a Macbook Pro 2.8Ghz i7):

>>> import sys, timeit
>>> sys.version_info
sys.version_info(major=2, minor=7, micro=12, releaselevel='final', serial=0)
>>> timeit.timeit('divmod(n, d)', 'n, d = 42, 7')
0.1473848819732666
>>> timeit.timeit('n // d, n % d', 'n, d = 42, 7')
0.10324406623840332

The divmod() function is at a disadvantage here because you need to look up the global each time. Binding it to a local (all variables in a timeit time trial are local) improves performance a little:

>>> timeit.timeit('dm(n, d)', 'n, d = 42, 7; dm = divmod')
0.13460898399353027

but the operators still win because they don't have to preserve the current frame while a function call to divmod() is executed:

>>> import dis
>>> dis.dis(compile('divmod(n, d)', '', 'exec'))
  1           0 LOAD_NAME                0 (divmod)
              3 LOAD_NAME                1 (n)
              6 LOAD_NAME                2 (d)
              9 CALL_FUNCTION            2
             12 POP_TOP             
             13 LOAD_CONST               0 (None)
             16 RETURN_VALUE        
>>> dis.dis(compile('(n // d, n % d)', '', 'exec'))
  1           0 LOAD_NAME                0 (n)
              3 LOAD_NAME                1 (d)
              6 BINARY_FLOOR_DIVIDE 
              7 LOAD_NAME                0 (n)
             10 LOAD_NAME                1 (d)
             13 BINARY_MODULO       
             14 BUILD_TUPLE              2
             17 POP_TOP             
             18 LOAD_CONST               0 (None)
             21 RETURN_VALUE        

The // and % variant uses more opcodes, but the CALL_FUNCTION bytecode is a bear, performance wise.

---

In PyPy, for small integers there isn't really much of a difference; the small speed advantage the opcodes have melts away under the sheer speed of C integer arithmetic:

>>>> import platform, sys, timeit
>>>> platform.python_implementation(), sys.version_info
('PyPy', (major=2, minor=7, micro=10, releaselevel='final', serial=42))
>>>> timeit.timeit('divmod(n, d)', 'n, d = 42, 7', number=10**9)
0.5659301280975342
>>>> timeit.timeit('n // d, n % d', 'n, d = 42, 7', number=10**9)
0.5471200942993164

(I had to crank the number of repetitions up to 1 billion to show how small the difference really is, PyPy is blazingly fast here).

However, when the numbers get large, divmod() wins by a country mile:

>>>> timeit.timeit('divmod(n, d)', 'n, d = 2**74207281 - 1, 26', number=100)
17.620037078857422
>>>> timeit.timeit('n // d, n % d', 'n, d = 2**74207281 - 1, 26', number=100)
34.44323515892029

(I now had to tune down the number of repetitions by a factor of 10 compared to hobbs' numbers, just to get a result in a reasonable amount of time).

This is because PyPy no longer can unbox those integers as C integers; you can see the striking difference in timings between using sys.maxint and sys.maxint + 1:

>>>> timeit.timeit('divmod(n, d)', 'import sys; n, d = sys.maxint, 26', number=10**7)
0.008622884750366211
>>>> timeit.timeit('n // d, n % d', 'import sys; n, d = sys.maxint, 26', number=10**7)
0.007693052291870117
>>>> timeit.timeit('divmod(n, d)', 'import sys; n, d = sys.maxint + 1, 26', number=10**7)
0.8396248817443848
>>>> timeit.timeit('n // d, n % d', 'import sys; n, d = sys.maxint + 1, 26', number=10**7)
1.0117690563201904

Answer 2

Martijn's answer is correct if you're using "small" native integers, where arithmetic operations are very fast compared to function calls. However, with bigints, it's a whole different story:

>>> import timeit
>>> timeit.timeit('divmod(n, d)', 'n, d = 2**74207281 - 1, 26', number=1000)
24.22666597366333
>>> timeit.timeit('n // d, n % d', 'n, d = 2**74207281 - 1, 26', number=1000)
49.517399072647095

when dividing a 22-million-digit number, divmod is almost exactly twice as fast as doing the division and modulus separately, as you might expect.

On my machine, the crossover occurs somewhere around 2^63, but don't take my word for it. As Martijn says, measure! When performance really matters, don't assume that what held true in one place will still be true in another.