




"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tensorflow_text_available, is_torch_available


A   =       {
    """configuration_ernie""": ["""ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """ErnieConfig""", """ErnieOnnxConfig"""],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					A   =       [
					    """ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """ErnieForCausalLM""",
					    """ErnieForMaskedLM""",
					    """ErnieForMultipleChoice""",
					    """ErnieForNextSentencePrediction""",
					    """ErnieForPreTraining""",
					    """ErnieForQuestionAnswering""",
					    """ErnieForSequenceClassification""",
					    """ErnieForTokenClassification""",
					    """ErnieModel""",
					    """ErniePreTrainedModel""",
					]

if TYPE_CHECKING:
					from .configuration_ernie import ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP, ErnieConfig, ErnieOnnxConfig

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_ernie import (
										    ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST,
										    ErnieForCausalLM,
										    ErnieForMaskedLM,
										    ErnieForMultipleChoice,
										    ErnieForNextSentencePrediction,
										    ErnieForPreTraining,
										    ErnieForQuestionAnswering,
										    ErnieForSequenceClassification,
										    ErnieForTokenClassification,
										    ErnieModel,
										    ErniePreTrainedModel,
										)

else:
					import sys

					A   =       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)








"""simple docstring"""





def 					_UpperCamelCase    (			UpperCamelCase				,       UpperCamelCase = False							)			->			bool:


			"""simple docstring"""
			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_3170_4406_4679_8873_8596_1981 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
			__UpperCAmelCase	: List[str]		=					[
			    2047,
			    137_3653,
			    2532_6001,
			    32_1503_1751,
			    2_1523_0289_8747,
			    3_4747_4966_0383,
			    341_5500_7172_8321,
			    1,
			    382_5123_0565_4641_3051,
			    1,
			    1,
			    3186_6585_7834_0311_5116_7461,
			    3_3170_4406_4679_8873_8596_1981,
			]

			__UpperCAmelCase	: Tuple		=					[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
			for idx, _p in enumerate(UpperCamelCase				,       1							):
						if n < _p:
									# then we have our last prime to check
									__UpperCAmelCase	: Tuple		=					primes[:idx]
									break
			__UpperCAmelCase	,     __UpperCAmelCase	: List[str]		=					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:
						__UpperCAmelCase	: Optional[int]		=					False
						for r in range(UpperCamelCase							):
									__UpperCAmelCase	: Dict		=					pow(UpperCamelCase				,       d * 2**r				,       UpperCamelCase							)
									# see article for analysis explanation for m
									if (r == 0 and m == 1) or ((m + 1) % n == 0):
												__UpperCAmelCase	: Optional[int]		=					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 					_UpperCamelCase    (			)			->			None:


			"""simple docstring"""
			assert not miller_rabin(561							)
			assert miller_rabin(563							)
			# 2047

			assert not miller_rabin(83_8201							)
			assert miller_rabin(83_8207							)
			# 1_373_653

			assert not miller_rabin(1731_6001							)
			assert miller_rabin(1731_6017							)
			# 25_326_001

			assert not miller_rabin(30_7838_6641							)
			assert miller_rabin(30_7838_6653							)
			# 3_215_031_751

			assert not miller_rabin(1_7130_4557_4801							)
			assert miller_rabin(1_7130_4557_4819							)
			# 2_152_302_898_747

			assert not miller_rabin(2_7797_9972_8307							)
			assert miller_rabin(2_7797_9972_8327							)
			# 3_474_749_660_383

			assert not miller_rabin(113_8500_2390_9441							)
			assert miller_rabin(113_8500_2390_9527							)
			# 341_550_071_728_321

			assert not miller_rabin(127_5041_0188_4880_4351							)
			assert miller_rabin(127_5041_0188_4880_4391							)
			# 3_825_123_056_546_413_051

			assert not miller_rabin(796_6646_4458_5077_8779_1867							)
			assert miller_rabin(796_6646_4458_5077_8779_1951							)
			# 318_665_857_834_031_151_167_461

			assert not miller_rabin(5528_4067_7446_6478_9766_0333							)
			assert miller_rabin(5528_4067_7446_6478_9766_0359							)
			# 3_317_044_064_679_887_385_961_981
			# upper limit for probabilistic test


if __name__ == "__main__":
					test_miller_rabin()


