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# Copyright (c) 2021 SUSE Linux GmbH. All rights reserved.
#
# This file is part of kiwi.
#
# kiwi is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# kiwi is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with kiwi. If not, see <http://www.gnu.org/licenses/>
#
import math
from typing import List, Iterator
# initial list of prime numbers which will be extended as much as required
# and reused in next calls
_primes: List[int] = [2, 3, 5, 7, 11, 13, 17]
def _update_primes(n: int) -> None:
"""
Extend the list of prime numbers if required.
"""
global _primes
if n <= _primes[-1]:
return
_n = int(math.ceil(n**0.5))
_update_primes(_n)
start = _primes[-1] + 1
for i in range(start, n + 1):
if all(i % p for p in primes(_n)):
_primes.append(i)
def primes(number: int) -> Iterator[int]:
"""
Get prime numbers no greater than given number.
:param int number: highest possible number to return.
:rtype: int generator
"""
global _primes
_update_primes(number)
for p in _primes:
if p <= number:
yield p
else:
break
def factors(number: int, max_factor: int = None) -> Iterator[int]:
_max = int(math.ceil(number**0.5))
_max = min(_max, max_factor or _max)
_number = number
for i in primes(_max):
while _number % i == 0 and i <= _max:
_number = _number // i
_max = min(_max, int(math.ceil(_number**0.5)))
yield i
if _number != 1:
if not max_factor or _number <= max_factor:
yield _number
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