



'''simple docstring'''





def lowerCAmelCase    (__A    ,      __A = False):



     """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_317_044_064_679_887_385_961_981 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
     _a           =    [
         2_047,
         1_373_653,
         25_326_001,
         3_215_031_751,
         2_152_302_898_747,
         3_474_749_660_383,
         341_550_071_728_321,
         1,
         3_825_123_056_546_413_051,
         1,
         1,
         318_665_857_834_031_151_167_461,
         3_317_044_064_679_887_385_961_981,
     ]

     _a           =    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
     for idx, _p in enumerate(__A    ,      1):
          if n < _p:
               # then we have our last prime to check
               _a           =    primes[:idx]
               break
     _a    ,       _a           =    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:
          _a           =    False
          for r in range(__A):
               _a           =    pow(__A    ,      d * 2**r    ,      __A)
               # see article for analysis explanation for m
               if (r == 0 and m == 1) or ((m + 1) % n == 0):
                    _a           =    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    ():



     """simple docstring"""



     assert not miller_rabin(561)
     assert miller_rabin(563)
     # 2047

     assert not miller_rabin(838_201)
     assert miller_rabin(838_207)
     # 1_373_653

     assert not miller_rabin(17_316_001)
     assert miller_rabin(17_316_017)
     # 25_326_001

     assert not miller_rabin(3_078_386_641)
     assert miller_rabin(3_078_386_653)
     # 3_215_031_751

     assert not miller_rabin(1_713_045_574_801)
     assert miller_rabin(1_713_045_574_819)
     # 2_152_302_898_747

     assert not miller_rabin(2_779_799_728_307)
     assert miller_rabin(2_779_799_728_327)
     # 3_474_749_660_383

     assert not miller_rabin(113_850_023_909_441)
     assert miller_rabin(113_850_023_909_527)
     # 341_550_071_728_321

     assert not miller_rabin(1_275_041_018_848_804_351)
     assert miller_rabin(1_275_041_018_848_804_391)
     # 3_825_123_056_546_413_051

     assert not miller_rabin(79_666_464_458_507_787_791_867)
     assert miller_rabin(79_666_464_458_507_787_791_951)
     # 318_665_857_834_031_151_167_461

     assert not miller_rabin(552_840_677_446_647_897_660_333)
     assert miller_rabin(552_840_677_446_647_897_660_359)
     # 3_317_044_064_679_887_385_961_981
     # upper limit for probabilistic test


if __name__ == "__main__":
  test_miller_rabin()










"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


a		:					Optional[Any]	      =     {
    '''configuration_owlvit''': [
        '''OWLVIT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''OwlViTConfig''',
        '''OwlViTOnnxConfig''',
        '''OwlViTTextConfig''',
        '''OwlViTVisionConfig''',
    ],
    '''processing_owlvit''': ['''OwlViTProcessor'''],
}


try:
		if not is_vision_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a		:					str	      =     ['''OwlViTFeatureExtractor''']
		a		:					List[Any]	      =     ['''OwlViTImageProcessor''']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a		:					List[Any]	      =     [
		    '''OWLVIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''OwlViTModel''',
		    '''OwlViTPreTrainedModel''',
		    '''OwlViTTextModel''',
		    '''OwlViTVisionModel''',
		    '''OwlViTForObjectDetection''',
		]

if TYPE_CHECKING:
		from .configuration_owlvit import (
		    OWLVIT_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    OwlViTConfig,
		    OwlViTOnnxConfig,
		    OwlViTTextConfig,
		    OwlViTVisionConfig,
		)
		from .processing_owlvit import OwlViTProcessor

		try:
				if not is_vision_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .feature_extraction_owlvit import OwlViTFeatureExtractor
				from .image_processing_owlvit import OwlViTImageProcessor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_owlvit import (
				    OWLVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
				    OwlViTForObjectDetection,
				    OwlViTModel,
				    OwlViTPreTrainedModel,
				    OwlViTTextModel,
				    OwlViTVisionModel,
				)

else:
		import sys

		a		:					List[str]	      =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


