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[Skip Montanaro]

> But I was really wondering if there was a simple solution that worked
> without people having to add libraries to their basic Python installations.

I think installing numpy is approximately

    pip install numpy

assuming you have write access to your site-packages directory.  If
not, install using --prefix and set PYTHONPATH accordingly.

I forgot that Python also has an array module.  With numpy available,
mature, and well-supported, I imagine it doesn't get much love these
days though.  Still, I gave it a whirl:

#######################################
import random
import array
from timeit import Timer

import numpy

stuff = [random.random() < 0.5 for i in range(10**7)]
sieve1 = numpy.array(stuff, dtype=bool)
sieve2 = array.array('B', stuff)

setup = """from __main__ import sieve1, sieve2
from itertools import islice
hi = 7*10**6
"""

t1 = Timer("(True == sieve1[:hi]).sum()", setup)
t2 = Timer("sieve2[:hi].count(True)", setup)
# t3 = Timer("sum(islice(sieve, hi))", setup)
# t4 = Timer("sum(x for x in islice(sieve, hi) if x)", setup)
# t5 = Timer("sum(x for x in islice(sieve, hi) if x is True)", setup)
# t6 = Timer("sum(1 for x in islice(sieve, hi) if x is True)", setup)
# t7 = Timer("len(list(filter(None, islice(sieve, hi))))", setup)

print(min(t1.repeat(number=10)))
print(min(t2.repeat(number=10)))
# for t in (t1, t2, t3, t4, t5, t6, t7):
#     print( min(t.repeat(number=10)) )
#######################################

Performance was not all that impressive:

0.340315103531
5.42102503777

Still, you might fiddle around with it a bit.  Perhaps unsigned ints
instead of unsigned bytes will provide more efficient counting...

Skip