


'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


__UpperCamelCase      :       str      			=      {
    '''configuration_mvp''': ['''MVP_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MvpConfig''', '''MvpOnnxConfig'''],
    '''tokenization_mvp''': ['''MvpTokenizer'''],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __UpperCamelCase      :       str      			=      ['''MvpTokenizerFast''']

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __UpperCamelCase      :       List[str]      			=      [
     '''MVP_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''MvpForCausalLM''',
     '''MvpForConditionalGeneration''',
     '''MvpForQuestionAnswering''',
     '''MvpForSequenceClassification''',
     '''MvpModel''',
     '''MvpPreTrainedModel''',
 ]

if TYPE_CHECKING:
 from .configuration_mvp import MVP_PRETRAINED_CONFIG_ARCHIVE_MAP, MvpConfig, MvpOnnxConfig
 from .tokenization_mvp import MvpTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_mvp_fast import MvpTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_mvp import (
      MVP_PRETRAINED_MODEL_ARCHIVE_LIST,
      MvpForCausalLM,
      MvpForConditionalGeneration,
      MvpForQuestionAnswering,
      MvpForSequenceClassification,
      MvpModel,
      MvpPreTrainedModel,
  )

else:
 import sys

 __UpperCamelCase      :       Optional[Any]      			=      _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)







'''simple docstring'''



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	int,					SCREAMING_SNAKE_CASE__:	bool = 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
   __a				     =    [
       2047,
       1373653,
       25326001,
       3215031751,
       2152302898747,
       3474749660383,
       341550071728321,
       1,
       3825123056546413051,
       1,
       1,
       318665857834031151167461,
       3317044064679887385961981,
   ]

   __a				     =    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
   for idx, _p in enumerate(SCREAMING_SNAKE_CASE__,					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(SCREAMING_SNAKE_CASE__    ):
         __a				     =    pow(SCREAMING_SNAKE_CASE__,					d * 2**r,					SCREAMING_SNAKE_CASE__    )
         # 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    __UpperCAmelCase	(				)  ->			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()