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