


"""simple docstring"""


def   snake_case		(     UpperCamelCase__       :						int			,				UpperCamelCase__       :						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 > 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
      lowerCamelCase					:					Tuple        =	[
          2047,
          1373653,
          25326001,
          3215031751,
          2152302898747,
          3474749660383,
          341550071728321,
          1,
          3825123056546413051,
          1,
          1,
          318665857834031151167461,
          3317044064679887385961981,
      ]

      lowerCamelCase					:					str        =	[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
                  lowerCamelCase					:					List[str]        =	primes[:idx]
                  break
      lowerCamelCase     ,			lowerCamelCase					:					List[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:
            lowerCamelCase					:					List[str]        =	False
            for r in range(UpperCamelCase__    ):
                  lowerCamelCase					:					Union[str, Any]        =	pow(UpperCamelCase__			,				d * 2**r			,				UpperCamelCase__    )
                  # see article for analysis explanation for m
                  if (r == 0 and m == 1) or ((m + 1) % n == 0):
                        lowerCamelCase					:					Any        =	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   snake_case		(     )   ->      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()








"""simple docstring"""


from ...configuration_utils import PretrainedConfig
from ...utils import logging


__lowerCamelCase      :Optional[int]	    =		logging.get_logger(__name__)

__lowerCamelCase      :List[str]	    =		{
    'google/realm-cc-news-pretrained-embedder': (
        'https://huggingface.co/google/realm-cc-news-pretrained-embedder/resolve/main/config.json'
    ),
    'google/realm-cc-news-pretrained-encoder': (
        'https://huggingface.co/google/realm-cc-news-pretrained-encoder/resolve/main/config.json'
    ),
    'google/realm-cc-news-pretrained-scorer': (
        'https://huggingface.co/google/realm-cc-news-pretrained-scorer/resolve/main/config.json'
    ),
    'google/realm-cc-news-pretrained-openqa': (
        'https://huggingface.co/google/realm-cc-news-pretrained-openqa/aresolve/main/config.json'
    ),
    'google/realm-orqa-nq-openqa': 'https://huggingface.co/google/realm-orqa-nq-openqa/resolve/main/config.json',
    'google/realm-orqa-nq-reader': 'https://huggingface.co/google/realm-orqa-nq-reader/resolve/main/config.json',
    'google/realm-orqa-wq-openqa': 'https://huggingface.co/google/realm-orqa-wq-openqa/resolve/main/config.json',
    'google/realm-orqa-wq-reader': 'https://huggingface.co/google/realm-orqa-wq-reader/resolve/main/config.json',
    # See all REALM models at https://huggingface.co/models?filter=realm
}


class 			A__	(						__lowercase):


     """simple docstring"""
     snake_case__	:					Optional[Any]													='''realm'''

     def __init__(	self:						Union[str, Any]     ,		__a:						List[Any]=30_522     ,		__a:						List[Any]=768     ,		__a:						List[Any]=128     ,		__a:						Union[str, Any]=12     ,		__a:						Union[str, Any]=12     ,		__a:						Optional[Any]=8     ,		__a:						Dict=3_072     ,		__a:						List[Any]="gelu_new"     ,		__a:						List[Any]=0.1     ,		__a:						Tuple=0.1     ,		__a:						Optional[Any]=512     ,		__a:						Optional[int]=2     ,		__a:						str=0.02     ,		__a:						int=1e-1_2     ,		__a:						Optional[Any]=256     ,		__a:						Any=10     ,		__a:						Dict=1e-3     ,		__a:						Optional[Any]=5     ,		__a:						Dict=320     ,		__a:						Tuple=13_353_718     ,		__a:						List[Any]=5_000     ,		__a:						Dict=1     ,		__a:						int=0     ,		__a:						Dict=2     ,		**__a:						List[str]     ,		)->    Any:
           super().__init__(pad_token_id=__a     ,		bos_token_id=__a     ,		eos_token_id=__a     ,		**__a	)

           # Common config
           lowerCamelCase					:					Optional[Any]        =	vocab_size
           lowerCamelCase					:					str        =	max_position_embeddings
           lowerCamelCase					:					Dict        =	hidden_size
           lowerCamelCase					:					Dict        =	retriever_proj_size
           lowerCamelCase					:					Optional[Any]        =	num_hidden_layers
           lowerCamelCase					:					List[str]        =	num_attention_heads
           lowerCamelCase					:					Tuple        =	num_candidates
           lowerCamelCase					:					int        =	intermediate_size
           lowerCamelCase					:					Dict        =	hidden_act
           lowerCamelCase					:					List[str]        =	hidden_dropout_prob
           lowerCamelCase					:					Dict        =	attention_probs_dropout_prob
           lowerCamelCase					:					Optional[int]        =	initializer_range
           lowerCamelCase					:					Dict        =	type_vocab_size
           lowerCamelCase					:					Optional[Any]        =	layer_norm_eps

           # Reader config
           lowerCamelCase					:					List[str]        =	span_hidden_size
           lowerCamelCase					:					Dict        =	max_span_width
           lowerCamelCase					:					Optional[Any]        =	reader_layer_norm_eps
           lowerCamelCase					:					Optional[int]        =	reader_beam_size
           lowerCamelCase					:					List[Any]        =	reader_seq_len

           # Retrieval config
           lowerCamelCase					:					int        =	num_block_records
           lowerCamelCase					:					Dict        =	searcher_beam_size




