


'''simple docstring'''





def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase = False			):
							if n == 2:
														return True
							if not n % 2 or n < 2:
														return False
							if n > 5 and n % 1_0 not in (1, 3, 7, 9):  # can quickly check last digit
														return False
							if n > 3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1 and not allow_probable:
														raise ValueError(
														    "Warning: upper bound of deterministic test is exceeded. "
														    "Pass allow_probable=True to allow probabilistic test. "
														    "A return value of True indicates a probable prime."			)
							# array bounds provided by analysis
							__snake_case	:    Any											=     [
							    2_0_4_7,
							    1_3_7_3_6_5_3,
							    2_5_3_2_6_0_0_1,
							    3_2_1_5_0_3_1_7_5_1,
							    2_1_5_2_3_0_2_8_9_8_7_4_7,
							    3_4_7_4_7_4_9_6_6_0_3_8_3,
							    3_4_1_5_5_0_0_7_1_7_2_8_3_2_1,
							    1,
							    3_8_2_5_1_2_3_0_5_6_5_4_6_4_1_3_0_5_1,
							    1,
							    1,
							    3_1_8_6_6_5_8_5_7_8_3_4_0_3_1_1_5_1_1_6_7_4_6_1,
							    3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1,
							]

							__snake_case	:    List[str]											=     [2, 3, 5, 7, 1_1, 1_3, 1_7, 1_9, 2_3, 2_9, 3_1, 3_7, 4_1]
							for idx, _p in enumerate(__lowerCamelCase							,			1			):
														if n < _p:
																					# then we have our last prime to check
																					__snake_case	:    Union[str, Any]											=     primes[:idx]
																					break
							__snake_case	:    int											=     n - 1, 0
							# break up n -1 into a power of 2 (s) and
							# remaining odd component
							# essentially, solve for d * 2 ** s == n - 1
							while d % 2 == 0:
														d //= 2
														s += 1
							for prime in plist:
														__snake_case	:    List[Any]											=     False
														for r in range(__lowerCamelCase			):
																					__snake_case	:    str											=     pow(__lowerCamelCase							,			d * 2**r							,			__lowerCamelCase			)
																					# see article for analysis explanation for m
																					if (r == 0 and m == 1) or ((m + 1) % n == 0):
																												__snake_case	:    Union[str, Any]											=     True
																												# this loop will not determine compositeness
																												break
														if pr:
																					continue
														# if pr is False, then the above loop never evaluated to true,
														# and the n MUST be composite
														return False
							return True







def        lowerCAmelCase_  (      ):
							assert not miller_rabin(5_6_1			)
							assert miller_rabin(5_6_3			)
							# 2047

							assert not miller_rabin(8_3_8_2_0_1			)
							assert miller_rabin(8_3_8_2_0_7			)
							# 1_373_653

							assert not miller_rabin(1_7_3_1_6_0_0_1			)
							assert miller_rabin(1_7_3_1_6_0_1_7			)
							# 25_326_001

							assert not miller_rabin(3_0_7_8_3_8_6_6_4_1			)
							assert miller_rabin(3_0_7_8_3_8_6_6_5_3			)
							# 3_215_031_751

							assert not miller_rabin(1_7_1_3_0_4_5_5_7_4_8_0_1			)
							assert miller_rabin(1_7_1_3_0_4_5_5_7_4_8_1_9			)
							# 2_152_302_898_747

							assert not miller_rabin(2_7_7_9_7_9_9_7_2_8_3_0_7			)
							assert miller_rabin(2_7_7_9_7_9_9_7_2_8_3_2_7			)
							# 3_474_749_660_383

							assert not miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_4_4_1			)
							assert miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_5_2_7			)
							# 341_550_071_728_321

							assert not miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_5_1			)
							assert miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_9_1			)
							# 3_825_123_056_546_413_051

							assert not miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_8_6_7			)
							assert miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_9_5_1			)
							# 318_665_857_834_031_151_167_461

							assert not miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_3_3			)
							assert miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_5_9			)
							# 3_317_044_064_679_887_385_961_981
							# upper limit for probabilistic test


if __name__ == "__main__":
			test_miller_rabin()





import warnings

from ...utils import logging
from .image_processing_poolformer import PoolFormerImageProcessor


_snake_case  :	List[str]			      =       logging.get_logger(__name__)

class        a	(_lowerCAmelCase   ):




							"""simple docstring"""


							def __init__(							self :						int					,			*lowerCamelCase :						Any					,			**lowerCamelCase :						Union[str, Any]       )			->					None:
														warnings.warn(
														    "The class PoolFormerFeatureExtractor is deprecated and will be removed in version 5 of Transformers."
														    " Please use PoolFormerImageProcessor instead."					,			lowerCamelCase					,			)
														super().__init__(*lowerCamelCase					,			**lowerCamelCase       )

