





'''simple docstring'''






def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase = 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
			__snake_case					:      List[Any]							      =     [
			    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,
			]

			__snake_case					:      str							      =     [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
			for idx, _p in enumerate(_lowerCamelCase    ,	1 ):
						if n < _p:
									# then we have our last prime to check
									__snake_case					:      Tuple							      =     primes[:idx]
									break
			__snake_case      ,     __snake_case					:      Union[str, Any]							      =     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					:      Tuple							      =     False
						for r in range(_lowerCamelCase ):
									__snake_case					:      Tuple							      =     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					:      List[str]							      =     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 					_a						(       ) ->				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()









'''simple docstring'''






import warnings

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding




class  _A (					__lowercase		):
		lowercase__:   Any				     =   ['''image_processor''', '''tokenizer''']
		lowercase__:   Any				     =   '''CLIPImageProcessor'''
		lowercase__:   Optional[Any]				     =   ('''CLIPTokenizer''', '''CLIPTokenizerFast''')

		def __init__(   self					:   int  ,      __magic_name__					:   Dict=None  ,      __magic_name__					:   Dict=None  ,      **__magic_name__					:   Union[str, Any]			)					->    Any:


					"""simple docstring"""

					__snake_case					:      Optional[Any]							      =     None
					if "feature_extractor" in kwargs:
								warnings.warn(
								    """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
								    """ instead."""  ,      __magic_name__  ,      )
								__snake_case					:      List[Any]							      =     kwargs.pop("""feature_extractor"""			)

					__snake_case					:      List[str]							      =     image_processor if image_processor is not None else feature_extractor
					if image_processor is None:
								raise ValueError("""You need to specify an `image_processor`."""			)
					if tokenizer is None:
								raise ValueError("""You need to specify a `tokenizer`."""			)

					super().__init__(__magic_name__  ,      __magic_name__			)

		def __call__(   self					:   int  ,      __magic_name__					:   List[str]=None  ,      __magic_name__					:   Tuple=None  ,      __magic_name__					:   Any=None  ,      **__magic_name__					:   Union[str, Any]			)					->    Optional[int]:


					"""simple docstring"""

					if text is None and images is None:
								raise ValueError("""You have to specify either text or images. Both cannot be none."""			)

					if text is not None:
								__snake_case					:      int							      =     self.tokenizer(__magic_name__  ,      return_tensors=__magic_name__  ,      **__magic_name__			)

					if images is not None:
								__snake_case					:      str							      =     self.image_processor(__magic_name__  ,      return_tensors=__magic_name__  ,      **__magic_name__			)

					if text is not None and images is not None:
								__snake_case					:      Union[str, Any]							      =     image_features.pixel_values
								return encoding
					elif text is not None:
								return encoding
					else:
								return BatchEncoding(data=dict(**__magic_name__			)  ,      tensor_type=__magic_name__			)

		def 	lowercase__     (   self					:   Optional[int]  ,      *__magic_name__					:   List[Any]  ,      **__magic_name__					:   Any			)					->    Optional[Any]:


					"""simple docstring"""

					return self.tokenizer.batch_decode(*__magic_name__  ,      **__magic_name__			)

		def 	lowercase__     (   self					:   List[str]  ,      *__magic_name__					:   Tuple  ,      **__magic_name__					:   List[Any]			)					->    int:


					"""simple docstring"""

					return self.tokenizer.decode(*__magic_name__  ,      **__magic_name__			)

		@property
		def 	lowercase__     (   self					:   List[Any]			)					->    Optional[Any]:


					"""simple docstring"""

					__snake_case					:      Dict							      =     self.tokenizer.model_input_names
					__snake_case					:      str							      =     self.image_processor.model_input_names
					return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names			)			)

		@property
		def 	lowercase__     (   self					:   int			)					->    List[str]:


					"""simple docstring"""

					warnings.warn(
					    """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""  ,      __magic_name__  ,      )
					return self.image_processor_class

		@property
		def 	lowercase__     (   self					:   Union[str, Any]			)					->    Dict:


					"""simple docstring"""

					warnings.warn(
					    """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""  ,      __magic_name__  ,      )
					return self.image_processor


