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

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.

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