def turner():
"""Generate prime numbers very slowly using Euler's sieve.
>>> p = turner()
>>> [next(p) for _ in range(10)]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
The function is named for David Turner, who developed this implementation
in a paper in 1975. Due to its simplicity, it has become very popular,
particularly in Haskell circles where it is usually implemented as some
variation of::
primes = sieve [2..]
sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]
This algorithm is sometimes wrongly described as the Sieve of
Eratosthenes, but it is not, it is a version of Euler's Sieve.
Although simple, it is extremely slow and inefficient, with
asymptotic behaviour of O(N**2/(log N)**2) which is worse than
trial division, and only marginally better than ``primes0``.
In her paper http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf
O'Neill calls this the "Sleight on Eratosthenes".
"""
# See also:
# http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
# http://en.literateprograms.org/Sieve_of_Eratosthenes_(Haskell)
# http://www.haskell.org/haskellwiki/Prime_numbers
nums = itertools.count(2)
while True:
prime = next(nums)
yield prime
nums = filter(lambda v, p=prime: (v % p) != 0, nums)
def test_filter(self):
self.check_returns_iterator(compat23.filter, None, [1, 2, 3])
result = compat23.filter(lambda x: x > 100, [1, 2, 101, 102, 3, 103])
self.assertEqual(list(result), [101, 102, 103])
def test_filter(self):
self.check_returns_iterator(compat23.filter, None, [1, 2, 3])
result = compat23.filter(lambda x: x > 100, [1, 2, 101, 102, 3, 103])
self.assertEqual(list(result), [101, 102, 103])
