def test_next(self):
# Test basic use of next.
next = compat23.next
it = iter([1, 'a'])
self.assertEqual(next(it), 1)
self.assertEqual(next(it), 'a')
self.assertRaises(StopIteration, next, it)
def test_next(self):
# Test basic use of next.
next = compat23.next
it = iter([1, 'a'])
self.assertEqual(next(it), 1)
self.assertEqual(next(it), 'a')
self.assertRaises(StopIteration, next, it)
def primes(strategy, start=None, end=None):
"""Yield primes using the given strategy function.
See this module's docstring for specifications for the ``strategy``
function.
If the optional arguments ``start`` and ``end`` are given, they must be
either None or an integer. Only primes in the half-open range ``start``
(inclusive) to ``end`` (exclusive) are yielded. If ``start`` is None,
the range begins at the lowest prime (namely 2), if ``end`` is None,
the range has no upper limit.
>>> from pyprimes.awful import turner
>>> list(primes(turner, 6, 30))
[7, 11, 13, 17, 19, 23, 29]
"""
#return filter_between(gen(), start, end)
it = strategy()
p = next(it)
if start is not None:
# Drop the primes below start as fast as possible, then yield.
while p < start:
p = next(it)
assert start is None or p >= start
if end is not None:
while p < end:
yield p
p = next(it)
else:
while True:
yield p
p = next(it)
def test_next_default(self):
# Test next with a default argument.
next = compat23.next
it = iter([2, 'b'])
self.assertEqual(next(it, -99), 2)
self.assertEqual(next(it, -99), 'b')
self.assertEqual(next(it, -99), -99)
self.assertRaises(TypeError, next, it, -1, -2)
def test_next_default(self):
# Test next with a default argument.
next = compat23.next
it = iter([2, 'b'])
self.assertEqual(next(it, -99), 2)
self.assertEqual(next(it, -99), 'b')
self.assertEqual(next(it, -99), -99)
self.assertRaises(TypeError, next, it, -1, -2)
def test_moderate_composites(self):
# Test is_probable_prime with moderate-sized composites.
for i in range(10):
# We should not run out of primes here. If we do, it's a bug
# in the test.
p, q = next(self.primes), next(self.primes)
n = p*q
assert n < 2**60, "n not in deterministic range for i_p_p"
self.assertEqual(probabilistic.is_probable_prime(n), 0)
def test_moderate_composites(self):
# Test is_probable_prime with moderate-sized composites.
for i in range(10):
# We should not run out of primes here. If we do, it's a bug
# in the test.
p, q = next(self.primes), next(self.primes)
n = p * q
assert n < 2**60, "n not in deterministic range for i_p_p"
self.assertEqual(probabilistic.is_probable_prime(n), 0)
def test_prime_sum(self):
# Test the prime_sum function by comparing it to prime_partial_sums.
it = pyprimes.prime_partial_sums()
for i in range(100):
expected = next(it)
actual = pyprimes.prime_sum(i)
self.assertEqual(actual, expected)
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 sieve():
"""Yield prime integers using the Sieve of Eratosthenes.
This recursive algorithm is modified to generate the primes lazily
rather than the traditional version which operates on a fixed size
array of integers.
"""
# This is based on a paper by Melissa E. O'Neill, with an implementation
# given by Gerald Britton:
# http://mail.python.org/pipermail/python-list/2009-January/1188529.html
innersieve = sieve()
prevsq = 1
table = {}
i = 2
while True:
# This explicit test is slightly faster than using
# prime = table.pop(i, None) and testing for None.
if i in table:
prime = table[i]
del table[i]
nxt = i + prime
while nxt in table:
nxt += prime
table[nxt] = prime
else:
yield i
if i > prevsq:
j = next(innersieve)
prevsq = j**2
table[prevsq] = j
i += 1
def test_prime_sum(self):
# Test the prime_sum function by comparing it to prime_partial_sums.
it = pyprimes.prime_partial_sums()
for i in range(100):
expected = next(it)
actual = pyprimes.prime_sum(i)
self.assertEqual(actual, expected)
def sieve():
"""Yield prime integers using the Sieve of Eratosthenes.
This recursive algorithm is modified to generate the primes lazily
rather than the traditional version which operates on a fixed size
array of integers.
"""
# This is based on a paper by Melissa E. O'Neill, with an implementation
# given by Gerald Britton:
# http://mail.python.org/pipermail/python-list/2009-January/1188529.html
innersieve = sieve()
prevsq = 1
table = {}
i = 2
while True:
# This explicit test is slightly faster than using
# prime = table.pop(i, None) and testing for None.
if i in table:
prime = table[i]
del table[i]
nxt = i + prime
while nxt in table:
nxt += prime
table[nxt] = prime
else:
yield i
if i > prevsq:
j = next(innersieve)
prevsq = j**2
table[prevsq] = j
i += 1
def test_primes_start(self):
# Test the prime generator with start argument only.
expected = [211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283, 293]
assert len(expected) == 16
it = pyprimes.primes(200)
values = [next(it) for _ in range(16)]
self.assertEqual(values, expected)
def test_primes_start(self):
# Test the prime generator with start argument only.
expected = [
211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277,
281, 283, 293
]
assert len(expected) == 16
it = pyprimes.primes(200)
values = [next(it) for _ in range(16)]
self.assertEqual(values, expected)
def trial(generator, count, repeat=1):
timer = Stopwatch()
best = YEAR100
for i in range(repeat):
it = generator()
timer.reset()
timer.start()
# Go to the count-th prime as fast as possible.
p = next(islice(it, count - 1, count))
timer.stop()
best = min(best, timer.elapsed)
return best
def test_prime_partial_sums(self):
it = pyprimes.prime_partial_sums()
self.assertTrue(it is iter(it))
# Table of values from http://oeis.org/A007504
expected = [
0, 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328,
381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161, 1264,
1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427, 2584, 2747,
2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227, 4438, 4661, 4888
]
actual = [next(it) for _ in range(len(expected))]
self.assertEqual(actual, expected)
def trial(generator, count, repeat=1):
timer = Stopwatch()
best = YEAR100
for i in range(repeat):
it = generator()
timer.reset()
timer.start()
# Go to the count-th prime as fast as possible.
p = next(islice(it, count-1, count))
timer.stop()
best = min(best, timer.elapsed)
return best
def test_prime_partial_sums(self):
it = pyprimes.prime_partial_sums()
self.assertTrue(it is iter(it))
# Table of values from http://oeis.org/A007504
expected = [
0, 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281,
328, 381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161,
1264, 1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427,
2584, 2747, 2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227,
4438, 4661, 4888]
actual = [next(it) for _ in range(len(expected))]
self.assertEqual(actual, expected)
def nth_prime(n):
"""nth_prime(n) -> int
Return the nth prime number, starting counting from 1. Equivalent to
p[n] (p subscript n) in standard maths notation.
>>> nth_prime(1) # First prime is 2.
2
>>> nth_prime(5)
11
>>> nth_prime(50)
229
"""
# http://oeis.org/A000040
if n < 1:
raise ValueError('argument must be a positive integer')
return next(itertools.islice(primes(), n-1, n))
def test_primes_end_none(self):
# Check that None is allowed as an end argument.
it = pyprimes.primes(end=None)
self.assertEqual(next(it), 2)
def test_primes_start_is_inclusive(self):
# Start argument to primes() is inclusive.
n = 211
assert pyprimes.is_prime(n)
it = pyprimes.primes(start=n)
self.assertEqual(next(it), n)
def check_against_known_prime_list(self, prime_maker):
"""Check that generator produces the first 100 primes."""
it = prime_maker()
primes = [next(it) for _ in range(100)]
self.assertEqual(primes, PRIMES)
def check_against_known_prime_list(self, prime_maker):
"""Check that generator produces the first 100 primes."""
it = prime_maker()
primes = [next(it) for _ in range(100)]
self.assertEqual(primes, PRIMES)
def test_primes_end_none(self):
# Check that None is allowed as an end argument.
it = pyprimes.primes(end=None)
self.assertEqual(next(it), 2)
def test_primes_start_is_inclusive(self):
# Start argument to primes() is inclusive.
n = 211
assert pyprimes.is_prime(n)
it = pyprimes.primes(start=n)
self.assertEqual(next(it), n)
