Python/maths/odd_sieve.py
2024-04-02 21:18:47 +02:00

43 lines
1.0 KiB
Python

from itertools import compress, repeat
from math import ceil, sqrt
def odd_sieve(num: int) -> list[int]:
"""
Returns the prime numbers < `num`. The prime numbers are calculated using an
odd sieve implementation of the Sieve of Eratosthenes algorithm
(see for reference https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes).
>>> odd_sieve(2)
[]
>>> odd_sieve(3)
[2]
>>> odd_sieve(10)
[2, 3, 5, 7]
>>> odd_sieve(20)
[2, 3, 5, 7, 11, 13, 17, 19]
"""
if num <= 2:
return []
if num == 3:
return [2]
# Odd sieve for numbers in range [3, num - 1]
sieve = bytearray(b"\x01") * ((num >> 1) - 1)
for i in range(3, int(sqrt(num)) + 1, 2):
if sieve[(i >> 1) - 1]:
i_squared = i**2
sieve[(i_squared >> 1) - 1 :: i] = repeat(
0, ceil((num - i_squared) / (i << 1))
)
return [2, *list(compress(range(3, num, 2), sieve))]
if __name__ == "__main__":
import doctest
doctest.testmod()