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Improve the sieve() recipe in the itertools docs (gh-109199)

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Lazier sieve
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Raymond Hettinger 2023-09-09 17:50:04 -05:00 • committed by GitHub
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11
Doc/library/itertools.rst
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@ -1030,13 +1030,16 @@ The following recipes have a more mathematical flavor:
def sieve(n): def sieve(n):
"Primes less than n." "Primes less than n."
# sieve(30) --> 2 3 5 7 11 13 17 19 23 29 # sieve(30) --> 2 3 5 7 11 13 17 19 23 29
if n > 2:
yield 2
start = 3
data = bytearray((0, 1)) * (n // 2) data = bytearray((0, 1)) * (n // 2)
data[:3] = 0, 0, 0
limit = math.isqrt(n) + 1 limit = math.isqrt(n) + 1
for p in compress(range(limit), data): for p in iter_index(data, 1, start, limit):
yield from iter_index(data, 1, start, p*p)
data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p))) data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
data[2] = 1 start = p*p
return iter_index(data, 1) if n > 2 else iter([]) yield from iter_index(data, 1, start)
def factor(n): def factor(n):
"Prime factors of n." "Prime factors of n."