



"""simple docstring"""
def        lowerCAmelCase_(   lowercase_     :							int						,   lowercase_     :							bool = False							)	->       bool:
				if n == 2:
								return True
				if not n % 2 or n < 2:
								return False
				if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
								return False
				if n > 3_31_70_44_06_46_79_88_73_85_96_19_81 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
				_lowerCamelCase        =				[
				    20_47,
				    1_37_36_53,
				    25_32_60_01,
				    32_15_03_17_51,
				    2_15_23_02_89_87_47,
				    3_47_47_49_66_03_83,
				    3_41_55_00_71_72_83_21,
				    1,
				    3_82_51_23_05_65_46_41_30_51,
				    1,
				    1,
				    31_86_65_85_78_34_03_11_51_16_74_61,
				    3_31_70_44_06_46_79_88_73_85_96_19_81,
				]

				_lowerCamelCase        =				[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
				for idx, _p in enumerate(lowercase_						,   1							):
								if n < _p:
												# then we have our last prime to check
												_lowerCamelCase        =				primes[:idx]
												break
				_lowerCamelCase  ,     _lowerCamelCase        =				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:
								_lowerCamelCase        =				False
								for r in range(lowercase_							):
												_lowerCamelCase        =				pow(lowercase_						,   d * 2**r						,   lowercase_							)
												# see article for analysis explanation for m
												if (r == 0 and m == 1) or ((m + 1) % n == 0):
																_lowerCamelCase        =				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_(   )	->       None:
				assert not miller_rabin(5_61							)
				assert miller_rabin(5_63							)
				# 2047

				assert not miller_rabin(83_82_01							)
				assert miller_rabin(83_82_07							)
				# 1_373_653

				assert not miller_rabin(17_31_60_01							)
				assert miller_rabin(17_31_60_17							)
				# 25_326_001

				assert not miller_rabin(30_78_38_66_41							)
				assert miller_rabin(30_78_38_66_53							)
				# 3_215_031_751

				assert not miller_rabin(1_71_30_45_57_48_01							)
				assert miller_rabin(1_71_30_45_57_48_19							)
				# 2_152_302_898_747

				assert not miller_rabin(2_77_97_99_72_83_07							)
				assert miller_rabin(2_77_97_99_72_83_27							)
				# 3_474_749_660_383

				assert not miller_rabin(1_13_85_00_23_90_94_41							)
				assert miller_rabin(1_13_85_00_23_90_95_27							)
				# 341_550_071_728_321

				assert not miller_rabin(1_27_50_41_01_88_48_80_43_51							)
				assert miller_rabin(1_27_50_41_01_88_48_80_43_91							)
				# 3_825_123_056_546_413_051

				assert not miller_rabin(7_96_66_46_44_58_50_77_87_79_18_67							)
				assert miller_rabin(7_96_66_46_44_58_50_77_87_79_19_51							)
				# 318_665_857_834_031_151_167_461

				assert not miller_rabin(55_28_40_67_74_46_64_78_97_66_03_33							)
				assert miller_rabin(55_28_40_67_74_46_64_78_97_66_03_59							)
				# 3_317_044_064_679_887_385_961_981
				# upper limit for probabilistic test


if __name__ == "__main__":
			test_miller_rabin()





"""simple docstring"""
import warnings

from .generation import TFGenerationMixin


class 							lowerCamelCase_(   A__    ):





					'''simple docstring'''



					warnings.warn(
					    'Importing `TFGenerationMixin` from `src/transformers/generation_tf_utils.py` is deprecated and will '
					    'be removed in Transformers v5. Import as `from transformers import TFGenerationMixin` instead.',				A__,				)
