

"""simple docstring"""

def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__ = False   )			->						bool:
 if n == 2:
  return True
 if not n % 2 or n < 2:
  return False
 if n > 5 and n % 1_0 not in (1, 3, 7, 9):  # can quickly check last digit
  return False
 if n > 3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1 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 			=				[
     2_0_4_7,
     1_3_7_3_6_5_3,
     2_5_3_2_6_0_0_1,
     3_2_1_5_0_3_1_7_5_1,
     2_1_5_2_3_0_2_8_9_8_7_4_7,
     3_4_7_4_7_4_9_6_6_0_3_8_3,
     3_4_1_5_5_0_0_7_1_7_2_8_3_2_1,
     1,
     3_8_2_5_1_2_3_0_5_6_5_4_6_4_1_3_0_5_1,
     1,
     1,
     3_1_8_6_6_5_8_5_7_8_3_4_0_3_1_1_5_1_1_6_7_4_6_1,
     3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1,
 ]

 lowerCAmelCase__   :				Dict 			=				[2, 3, 5, 7, 1_1, 1_3, 1_7, 1_9, 2_3, 2_9, 3_1, 3_7, 4_1]
 for idx, _p in enumerate(lowercase__					,					1   ):
  if n < _p:
   # then we have our last prime to check
   lowerCAmelCase__   :				List[str] 			=				primes[:idx]
   break
 lowerCAmelCase__			,						lowerCAmelCase__   :				Union[str, 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__   :				Optional[Any] 			=				False
  for r in range(lowercase__   ):
   lowerCAmelCase__   :				Any 			=				pow(lowercase__					,					d * 2**r					,					lowercase__   )
   # see article for analysis explanation for m
   if (r == 0 and m == 1) or ((m + 1) % n == 0):
    lowerCAmelCase__   :				Optional[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       SCREAMING_SNAKE_CASE							( )			->						None:
 assert not miller_rabin(5_6_1   )
 assert miller_rabin(5_6_3   )
 # 2047

 assert not miller_rabin(8_3_8_2_0_1   )
 assert miller_rabin(8_3_8_2_0_7   )
 # 1_373_653

 assert not miller_rabin(1_7_3_1_6_0_0_1   )
 assert miller_rabin(1_7_3_1_6_0_1_7   )
 # 25_326_001

 assert not miller_rabin(3_0_7_8_3_8_6_6_4_1   )
 assert miller_rabin(3_0_7_8_3_8_6_6_5_3   )
 # 3_215_031_751

 assert not miller_rabin(1_7_1_3_0_4_5_5_7_4_8_0_1   )
 assert miller_rabin(1_7_1_3_0_4_5_5_7_4_8_1_9   )
 # 2_152_302_898_747

 assert not miller_rabin(2_7_7_9_7_9_9_7_2_8_3_0_7   )
 assert miller_rabin(2_7_7_9_7_9_9_7_2_8_3_2_7   )
 # 3_474_749_660_383

 assert not miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_4_4_1   )
 assert miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_5_2_7   )
 # 341_550_071_728_321

 assert not miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_5_1   )
 assert miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_9_1   )
 # 3_825_123_056_546_413_051

 assert not miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_8_6_7   )
 assert miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_9_5_1   )
 # 318_665_857_834_031_151_167_461

 assert not miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_3_3   )
 assert miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_5_9   )
 # 3_317_044_064_679_887_385_961_981
 # upper limit for probabilistic test


if __name__ == "__main__":
    test_miller_rabin()









"""simple docstring"""

from typing import Union

from ..utils import add_end_docstrings, is_torch_available, is_vision_available, logging
from .base import PIPELINE_INIT_ARGS, Pipeline


if is_vision_available():
    from PIL import Image

    from ..image_utils import load_image

if is_torch_available():
    from ..models.auto.modeling_auto import MODEL_FOR_VISUAL_QUESTION_ANSWERING_MAPPING

_UpperCamelCase		     =    logging.get_logger(__name__)






@add_end_docstrings(__magic_name__       )
class 			__a					(						__magic_name__       ):





       """simple docstring"""


       def __init__(   self			,					*snake_case			,					**snake_case   ):





        """simple docstring"""

        super().__init__(*snake_case			,					**snake_case   )
        self.check_model_type(snake_case   )






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case=None			,					snake_case=None			,					snake_case=None			,					**snake_case   ):





        """simple docstring"""

        lowerCAmelCase__			,						lowerCAmelCase__   :				List[Any] 			=				{}, {}
        if padding is not None:
         lowerCAmelCase__   :				Dict 			=				padding
        if truncation is not None:
         lowerCAmelCase__   :				Tuple 			=				truncation
        if top_k is not None:
         lowerCAmelCase__   :				str 			=				top_k
        return preprocess_params, {}, postprocess_params






       def __call__(   self			,					snake_case			,					snake_case = None			,					**snake_case   ):





        """simple docstring"""

        if isinstance(snake_case			,					(Image.Image, str)   ) and isinstance(snake_case			,					snake_case   ):
         lowerCAmelCase__   :				int 			=				{"image": image, "question": question}
        else:
         lowerCAmelCase__   :				Optional[int] 			=				image
        lowerCAmelCase__   :				Optional[Any] 			=				super().__call__(snake_case			,					**snake_case   )
        return results






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case			,					snake_case=False			,					snake_case=False   ):





        """simple docstring"""

        lowerCAmelCase__   :				Union[str, Any] 			=				load_image(inputs["image"]   )
        lowerCAmelCase__   :				str 			=				self.tokenizer(
            inputs["question"]			,					return_tensors=self.framework			,					padding=snake_case			,					truncation=snake_case   )
        lowerCAmelCase__   :				int 			=				self.image_processor(images=snake_case			,					return_tensors=self.framework   )
        model_inputs.update(snake_case   )
        return model_inputs






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case   ):





        """simple docstring"""

        lowerCAmelCase__   :				Optional[int] 			=				self.model(**snake_case   )
        return model_outputs






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case			,					snake_case=5   ):





        """simple docstring"""

        if top_k > self.model.config.num_labels:
         lowerCAmelCase__   :				List[Any] 			=				self.model.config.num_labels

        if self.framework == "pt":
         lowerCAmelCase__   :				Optional[int] 			=				model_outputs.logits.sigmoid()[0]
         lowerCAmelCase__			,						lowerCAmelCase__   :				Optional[int] 			=				probs.topk(snake_case   )
        else:
         raise ValueError(F"""Unsupported framework: {self.framework}"""   )

        lowerCAmelCase__   :				int 			=				scores.tolist()
        lowerCAmelCase__   :				str 			=				ids.tolist()
        return [{"score": score, "answer": self.model.config.idalabel[_id]} for score, _id in zip(snake_case			,					snake_case   )]






