

def 					__lowercase      (     _A						,    _A = 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 > 3317044064679887385961981 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
      SCREAMING_SNAKE_CASE :      Any       =   [
          2047,
          1373653,
          25326001,
          3215031751,
          2152302898747,
          3474749660383,
          341550071728321,
          1,
          3825123056546413051,
          1,
          1,
          318665857834031151167461,
          3317044064679887385961981,
      ]

      SCREAMING_SNAKE_CASE :      int       =   [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
                  SCREAMING_SNAKE_CASE :      Dict       =   primes[:idx]
                  break
      SCREAMING_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:
            SCREAMING_SNAKE_CASE :      List[Any]       =   False
            for r in range(_A			):
                  SCREAMING_SNAKE_CASE :      Optional[int]       =   pow(_A						,    d * 2**r						,    _A			)
                  # see article for analysis explanation for m
                  if (r == 0 and m == 1) or ((m + 1) % n == 0):
                        SCREAMING_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 					__lowercase      (     )     ->						None:
      assert not miller_rabin(561			)
      assert miller_rabin(563			)
      # 2047

      assert not miller_rabin(838201			)
      assert miller_rabin(838207			)
      # 1_373_653

      assert not miller_rabin(17316001			)
      assert miller_rabin(17316017			)
      # 25_326_001

      assert not miller_rabin(3078386641			)
      assert miller_rabin(3078386653			)
      # 3_215_031_751

      assert not miller_rabin(1713045574801			)
      assert miller_rabin(1713045574819			)
      # 2_152_302_898_747

      assert not miller_rabin(2779799728307			)
      assert miller_rabin(2779799728327			)
      # 3_474_749_660_383

      assert not miller_rabin(113850023909441			)
      assert miller_rabin(113850023909527			)
      # 341_550_071_728_321

      assert not miller_rabin(1275041018848804351			)
      assert miller_rabin(1275041018848804391			)
      # 3_825_123_056_546_413_051

      assert not miller_rabin(79666464458507787791867			)
      assert miller_rabin(79666464458507787791951			)
      # 318_665_857_834_031_151_167_461

      assert not miller_rabin(552840677446647897660333			)
      assert miller_rabin(552840677446647897660359			)
      # 3_317_044_064_679_887_385_961_981
      # upper limit for probabilistic test


if __name__ == "__main__":
  test_miller_rabin()







import sys
import tempfile
import unittest
import unittest.mock as mock
from pathlib import Path

from huggingface_hub import HfFolder, delete_repo
from requests.exceptions import HTTPError

from transformers import AutoFeatureExtractor, WavaVecaFeatureExtractor
from transformers.testing_utils import TOKEN, USER, get_tests_dir, is_staging_test


sys.path.append(str(Path(__file__).parent.parent / """utils"""))

from test_module.custom_feature_extraction import CustomFeatureExtractor  # noqa E402


UpperCAmelCase__ :     int				    =    get_tests_dir("""fixtures""")







class        a__       (   unittest.TestCase       ):







  """simple docstring"""




  def  _lowercase      (			self    : Dict		)					->Any:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      Dict       =   mock.Mock()
        SCREAMING_SNAKE_CASE :      Optional[int]       =   5_0_0
        SCREAMING_SNAKE_CASE :      List[str]       =   {}
        SCREAMING_SNAKE_CASE :      List[Any]       =   HTTPError
        SCREAMING_SNAKE_CASE :      int       =   {}

        # Download this model to make sure it's in the cache.
        SCREAMING_SNAKE_CASE :      List[Any]       =   WavaVecaFeatureExtractor.from_pretrained("""hf-internal-testing/tiny-random-wav2vec2"""		)
        # Under the mock environment we get a 500 error when trying to reach the model.
        with mock.patch("""requests.Session.request"""				,				return_value=UpperCAmelCase__		) as mock_head:
              SCREAMING_SNAKE_CASE :      Optional[int]       =   WavaVecaFeatureExtractor.from_pretrained("""hf-internal-testing/tiny-random-wav2vec2"""		)
              # This check we did call the fake head request
              mock_head.assert_called()




  def  _lowercase      (			self    : Optional[Any]		)					->int:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      str       =   WavaVecaFeatureExtractor.from_pretrained(
            """https://huggingface.co/hf-internal-testing/tiny-random-wav2vec2/resolve/main/preprocessor_config.json"""		)







@is_staging_test
class        a__       (   unittest.TestCase       ):







  """simple docstring"""




  @classmethod
  def  _lowercase      (			cls    : List[str]		)					->Dict:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      int       =   TOKEN
        HfFolder.save_token(UpperCAmelCase__		)


  @classmethod
  def  _lowercase      (			cls    : List[str]		)					->Optional[int]:
        """simple docstring"""







        try:
              delete_repo(token=cls._token				,				repo_id="""test-feature-extractor"""		)
        except HTTPError:
              pass

        try:
              delete_repo(token=cls._token				,				repo_id="""valid_org/test-feature-extractor-org"""		)
        except HTTPError:
              pass

        try:
              delete_repo(token=cls._token				,				repo_id="""test-dynamic-feature-extractor"""		)
        except HTTPError:
              pass


  def  _lowercase      (			self    : int		)					->Optional[int]:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      int       =   WavaVecaFeatureExtractor.from_pretrained(UpperCAmelCase__		)
        feature_extractor.push_to_hub("""test-feature-extractor"""				,				use_auth_token=self._token		)

        SCREAMING_SNAKE_CASE :      Any       =   WavaVecaFeatureExtractor.from_pretrained(f"{USER}/test-feature-extractor"		)
        for k, v in feature_extractor.__dict__.items():
              self.assertEqual(UpperCAmelCase__				,				getattr(UpperCAmelCase__				,				UpperCAmelCase__		)		)

        # Reset repo
        delete_repo(token=self._token				,				repo_id="""test-feature-extractor"""		)

        # Push to hub via save_pretrained
        with tempfile.TemporaryDirectory() as tmp_dir:
              feature_extractor.save_pretrained(
                  UpperCAmelCase__				,				repo_id="""test-feature-extractor"""				,				push_to_hub=UpperCAmelCase__				,				use_auth_token=self._token		)

        SCREAMING_SNAKE_CASE :      List[str]       =   WavaVecaFeatureExtractor.from_pretrained(f"{USER}/test-feature-extractor"		)
        for k, v in feature_extractor.__dict__.items():
              self.assertEqual(UpperCAmelCase__				,				getattr(UpperCAmelCase__				,				UpperCAmelCase__		)		)


  def  _lowercase      (			self    : List[Any]		)					->List[Any]:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      List[str]       =   WavaVecaFeatureExtractor.from_pretrained(UpperCAmelCase__		)
        feature_extractor.push_to_hub("""valid_org/test-feature-extractor"""				,				use_auth_token=self._token		)

        SCREAMING_SNAKE_CASE :      Optional[Any]       =   WavaVecaFeatureExtractor.from_pretrained("""valid_org/test-feature-extractor"""		)
        for k, v in feature_extractor.__dict__.items():
              self.assertEqual(UpperCAmelCase__				,				getattr(UpperCAmelCase__				,				UpperCAmelCase__		)		)

        # Reset repo
        delete_repo(token=self._token				,				repo_id="""valid_org/test-feature-extractor"""		)

        # Push to hub via save_pretrained
        with tempfile.TemporaryDirectory() as tmp_dir:
              feature_extractor.save_pretrained(
                  UpperCAmelCase__				,				repo_id="""valid_org/test-feature-extractor-org"""				,				push_to_hub=UpperCAmelCase__				,				use_auth_token=self._token		)

        SCREAMING_SNAKE_CASE :      List[Any]       =   WavaVecaFeatureExtractor.from_pretrained("""valid_org/test-feature-extractor-org"""		)
        for k, v in feature_extractor.__dict__.items():
              self.assertEqual(UpperCAmelCase__				,				getattr(UpperCAmelCase__				,				UpperCAmelCase__		)		)




  def  _lowercase      (			self    : Optional[Any]		)					->Optional[int]:
        """simple docstring"""







        CustomFeatureExtractor.register_for_auto_class()
        SCREAMING_SNAKE_CASE :      Any       =   CustomFeatureExtractor.from_pretrained(UpperCAmelCase__		)

        feature_extractor.push_to_hub("""test-dynamic-feature-extractor"""				,				use_auth_token=self._token		)

        # This has added the proper auto_map field to the config
        self.assertDictEqual(
            feature_extractor.auto_map				,				{"""AutoFeatureExtractor""": """custom_feature_extraction.CustomFeatureExtractor"""}				,				)

        SCREAMING_SNAKE_CASE :      Any       =   AutoFeatureExtractor.from_pretrained(
            f"{USER}/test-dynamic-feature-extractor"				,				trust_remote_code=UpperCAmelCase__		)
        # Can't make an isinstance check because the new_feature_extractor is from the CustomFeatureExtractor class of a dynamic module
        self.assertEqual(new_feature_extractor.__class__.__name__				,				"""CustomFeatureExtractor"""		)




