





def 			_a		(       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 > 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__  :		List[str]     =				[
       2047,
       1373653,
       25326001,
       3215031751,
       2152302898747,
       3474749660383,
       341550071728321,
       1,
       3825123056546413051,
       1,
       1,
       318665857834031151167461,
       3317044064679887385961981,
   ]

   lowerCamelCase__  :		Optional[Any]     =				[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
         lowerCamelCase__  :		List[Any]     =				primes[:idx]
         break
   lowerCamelCase__  :		Tuple     =				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__  :		str     =				False
      for r in range(_A	):
         lowerCamelCase__  :		Any     =				pow(_A     ,    d * 2**r     ,    _A	)
         # 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 			_a		(       )							->							None:







   """simple docstring"""
   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"""







import os
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils import AddedToken
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
				from .tokenization_fnet import FNetTokenizer
else:
				_lowerCAmelCase            =	None

_lowerCAmelCase            =	logging.get_logger(__name__)
_lowerCAmelCase            =	{'vocab_file': 'spiece.model', 'tokenizer_file': 'tokenizer.json'}

_lowerCAmelCase            =	{
    'vocab_file': {
        'google/fnet-base': 'https://huggingface.co/google/fnet-base/resolve/main/spiece.model',
        'google/fnet-large': 'https://huggingface.co/google/fnet-large/resolve/main/spiece.model',
    },
    'tokenizer_file': {
        'google/fnet-base': 'https://huggingface.co/google/fnet-base/resolve/main/tokenizer.json',
        'google/fnet-large': 'https://huggingface.co/google/fnet-large/resolve/main/tokenizer.json',
    },
}

_lowerCAmelCase            =	{
    'google/fnet-base': 5_12,
    'google/fnet-large': 5_12,
}

_lowerCAmelCase            =	'▁'


class      UpperCamelCase		(__snake_case     ):
						_SCREAMING_SNAKE_CASE  : Dict												=		VOCAB_FILES_NAMES
						_SCREAMING_SNAKE_CASE  : Optional[Any]												=		PRETRAINED_VOCAB_FILES_MAP
						_SCREAMING_SNAKE_CASE  : Optional[Any]												=		PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
						_SCREAMING_SNAKE_CASE  : Optional[Any]												=		["""input_ids""", """token_type_ids"""]
						_SCREAMING_SNAKE_CASE  : Union[str, Any]												=		FNetTokenizer






						def __init__(		self  :Optional[Any]			, __magic_name__  :Union[str, Any]=None			, __magic_name__  :Any=None			, __magic_name__  :List[str]=False			, __magic_name__  :Any=True			, __magic_name__  :Any=True			, __magic_name__  :Union[str, Any]="<unk>"			, __magic_name__  :List[Any]="[SEP]"			, __magic_name__  :Union[str, Any]="<pad>"			, __magic_name__  :Tuple="[CLS]"			, __magic_name__  :Optional[int]="[MASK]"			, **__magic_name__  :Optional[int]			, )      ->Tuple:
										# Mask token behave like a normal word, i.e. include the space before it and
										# is included in the raw text, there should be a match in a non-normalized sentence.
										lowercase    :      Union[str, Any]       = (
										    AddedToken(__magic_name__			, lstrip=__magic_name__			, rstrip=__magic_name__			, normalized=__magic_name__				)
										    if isinstance(__magic_name__			, __magic_name__				)
										    else mask_token
										)

										super().__init__(
										    __magic_name__			, tokenizer_file=__magic_name__			, do_lower_case=__magic_name__			, remove_space=__magic_name__			, keep_accents=__magic_name__			, unk_token=__magic_name__			, sep_token=__magic_name__			, pad_token=__magic_name__			, cls_token=__magic_name__			, mask_token=__magic_name__			, **__magic_name__			, )

										lowercase    :      Tuple       = do_lower_case
										lowercase    :      Tuple       = remove_space
										lowercase    :      List[str]       = keep_accents
										lowercase    :      Union[str, Any]       = vocab_file
										lowercase    :      int       = False if not self.vocab_file else True






						def      __snake_case      (		self  :Any			, __magic_name__  :List[int]			, __magic_name__  :Optional[List[int]] = None				)      ->List[int]:
										lowercase    :      List[str]       = [self.sep_token_id]
										lowercase    :      Any       = [self.cls_token_id]
										if token_ids_a is None:
														return cls + token_ids_a + sep
										return cls + token_ids_a + sep + token_ids_a + sep






						def      __snake_case      (		self  :int			, __magic_name__  :List[int]			, __magic_name__  :Optional[List[int]] = None				)      ->List[int]:
										lowercase    :      Tuple       = [self.sep_token_id]
										lowercase    :      Union[str, Any]       = [self.cls_token_id]

										if token_ids_a is None:
														return len(cls + token_ids_a + sep				) * [0]
										return len(cls + token_ids_a + sep				) * [0] + len(token_ids_a + sep				) * [1]






						def      __snake_case      (		self  :int			, __magic_name__  :str			, __magic_name__  :Optional[str] = None				)      ->Tuple[str]:
										if not os.path.isdir(__magic_name__				):
														logger.error(f"""Vocabulary path ({save_directory}) should be a directory"""				)
														return
										lowercase    :      str       = os.path.join(
										    __magic_name__			, (filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""vocab_file"""]				)

										if os.path.abspath(self.vocab_file				) != os.path.abspath(__magic_name__				):
														copyfile(self.vocab_file			, __magic_name__				)

										return (out_vocab_file,)
