Why is this generator expression function slower than the loop version?

Question

I have been operating under the theory that generator expressions tend to be more efficient than normal loops. But then I ran into the following example: write a function which given a number, N, and some factors, ps, returns the sum of all the numbers under N that are a multiple of at least one factor.

Here is a loop version and a shorter generator expression version:

def loops(N, ps):
    total_sum = 0 
    for i in xrange(N):
        for p in ps: 
            if i%p == 0:
                total_sum += i
                break
    return total_sum

def genexp(N, ps):
    return sum(i for i in xrange(N)
               if any(i%p == 0 for p in ps))

I'd expect the two to perform roughly equal, with maybe the comprehension version a little faster, but what I didn't expect was this:

for func in ('loops', 'genexp'):
    print func, timeit.timeit('%s(100000, [3,5,7])' % func, 
                              number=100, 
                              setup='from __main__ import %s' % func)


loops 2.82878184319
genexp 10.1663100719

4x slower isn't even close! Why? What am I misunderstanding?

Answer 1

First of all: generator expressions are memory efficient, not necessarily speed efficient.

Your compact genexp() version is slower for two reasons:

• Generator expressions are implemented using a new scope (like a new function). You are producing N new scopes, one for for each any() test. Creating a new scope and tearing it down again is relatively expensive, certainly when done in a loop and then compared with code that doesn't do this.

• The sum() and any() names are additional globals to be looked up. In the case of any(), that's an additional N global lookups per test. Globals must be looked up in a dictionary, versus locals which are looked up by index in a C-array (which is very fast).

The latter is but a small component, most of the cost lies in creating and destroying frames (scopes); if you create a version where _any and _sum are locals to the function you get but a small improvement in performance:

>>> def genexp_locals(N, ps, _any=any, _sum=sum):
...     return _sum(i for i in xrange(N)
...                if _any(i%p == 0 for p in ps))
... 
>>> for func in ('loops', 'genexp', 'genexp_locals'):
...     print func, timeit.timeit('%s(100000, [3,5,7])' % func, 
...                               number=100, 
...                               setup='from __main__ import %s' % func)
... 
loops 2.00835800171
genexp 6.45241594315
genexp_locals 6.23843789101

I didn't create a local for xrange to keep that aspect the same. Technically speaking, the _any name is looked up as a closure, not a local, by the generator expression code object, which are not as slow as global lookups but not quite as speedy as a local lookup either.