



'''simple docstring'''





def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase = 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       :       str           = [
      2047,
      1373653,
      25326001,
      3215031751,
      2152302898747,
      3474749660383,
      341550071728321,
      1,
      3825123056546413051,
      1,
      1,
      318665857834031151167461,
      3317044064679887385961981,
  ]

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





import argparse
from pathlib import Path

from transformers import AutoConfig, AutoTokenizer, RagConfig, RagSequenceForGeneration, RagTokenForGeneration

def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase = None       ,_lowerCAmelCase = None       ,_lowerCAmelCase = None       ,)      ->      Optional[int]:
  if config_name_or_path is None:
    __lowerCamelCase       :       List[Any]           = 'facebook/rag-token-base' if model_type == 'rag_token' else 'facebook/rag-sequence-base'

  if generator_tokenizer_name_or_path is None:
    __lowerCamelCase       :       Optional[int]           = generator_name_or_path

  if question_encoder_tokenizer_name_or_path is None:
    __lowerCamelCase       :       Tuple           = question_encoder_name_or_path

  __lowerCamelCase       :       Union[str, Any]           = RagTokenForGeneration if model_type == 'rag_token' else RagSequenceForGeneration

  # Save model.
  __lowerCamelCase       :       Tuple           = RagConfig.from_pretrained(_lowerCAmelCase       )
  __lowerCamelCase       :       List[Any]           = AutoConfig.from_pretrained(_lowerCAmelCase       )
  __lowerCamelCase       :       Union[str, Any]           = AutoConfig.from_pretrained(_lowerCAmelCase       )

  __lowerCamelCase       :       Tuple           = gen_config
  __lowerCamelCase       :       List[Any]           = question_encoder_config

  __lowerCamelCase       :       str           = model_class.from_pretrained_question_encoder_generator(
      _lowerCAmelCase       ,_lowerCAmelCase       ,config=_lowerCAmelCase       )
  rag_model.save_pretrained(_lowerCAmelCase       )

  # Sanity check.
  model_class.from_pretrained(_lowerCAmelCase       )

  # Save tokenizers.
  __lowerCamelCase       :       List[str]           = AutoTokenizer.from_pretrained(_lowerCAmelCase       )
  gen_tokenizer.save_pretrained(dest_dir / 'generator_tokenizer/'       )
  __lowerCamelCase       :       Optional[int]           = AutoTokenizer.from_pretrained(_lowerCAmelCase       )
  question_encoder_tokenizer.save_pretrained(dest_dir / 'question_encoder_tokenizer/'       )


if __name__ == "__main__":
   _UpperCamelCase											=						argparse.ArgumentParser()
   parser.add_argument(
       '--model_type',
       choices=['rag_sequence', 'rag_token'],
       required=True,
       type=str,
       help='RAG model type: rag_sequence, rag_token',
   )
   parser.add_argument('--dest', type=str, required=True, help='Path to the output checkpoint directory.')
   parser.add_argument('--generator_name_or_path', type=str, required=True, help='Generator model identifier')
   parser.add_argument(
       '--question_encoder_name_or_path', type=str, required=True, help='Question encoder model identifier'
   )

   parser.add_argument(
       '--generator_tokenizer_name_or_path',
       type=str,
       help='Generator tokenizer identifier, if not specified, resolves to ``generator_name_or_path``',
   )
   parser.add_argument(
       '--question_encoder_tokenizer_name_or_path',
       type=str,
       help='Question encoder tokenizer identifier, if not specified, resolves to ``question_encoder_name_or_path``',
   )
   parser.add_argument(
       '--config_name_or_path',
       type=str,
       help=(
           'Identifier of the model config to use, if not provided, resolves to a base config for a given'
           ' ``model_type``'
       ),
   )

   _UpperCamelCase											=						parser.parse_args()

   _UpperCamelCase											=						Path(args.dest)
   dest_dir.mkdir(exist_ok=True)

   consolidate(
       args.model_type,
       args.generator_name_or_path,
       args.question_encoder_name_or_path,
       dest_dir,
       args.config_name_or_path,
       args.generator_tokenizer_name_or_path,
       args.question_encoder_tokenizer_name_or_path,
   )






