
"""simple docstring"""







def 			A_			(					lowercase						, lowercase = 1000      )     ->							str:


     """simple docstring"""







     if (not isinstance(lowercase						, lowercase      )) or (digit_position <= 0):
          raise ValueError("""Digit position must be a positive integer"""      )
     elif (not isinstance(lowercase						, lowercase      )) or (precision < 0):
          raise ValueError("""Precision must be a nonnegative integer"""      )

     # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
     # accurate
     UpperCAmelCase_						:    Union[str, Any]    					=  (
         4 * _subsum(lowercase						, 1						, lowercase      )
         - 2 * _subsum(lowercase						, 4						, lowercase      )
         - _subsum(lowercase						, 5						, lowercase      )
         - _subsum(lowercase						, 6						, lowercase      )
     )

     # return the first hex digit of the fractional part of the result
     return hex(int((sum_result % 1) * 16      )      )[2:]




def 			A_			(					lowercase						, lowercase						, lowercase      )     ->							float:


     """simple docstring"""







     UpperCAmelCase_						:    List[str]    					=  0.0
     for sum_index in range(digit_pos_to_extract + precision      ):
          UpperCAmelCase_						:    Optional[Any]    					=  8 * sum_index + denominator_addend
          if sum_index < digit_pos_to_extract:
               # if the exponential term is an integer and we mod it by the denominator
               # before dividing, only the integer part of the sum will change;
               # the fractional part will not
               UpperCAmelCase_						:    Optional[Any]    					=  pow(
                   16						, digit_pos_to_extract - 1 - sum_index						, lowercase      )
          else:
               UpperCAmelCase_						:    Dict    					=  pow(16						, digit_pos_to_extract - 1 - sum_index      )
          total += exponential_term / denominator
     return total


if __name__ == "__main__":
       import doctest

       doctest.testmod()



"""simple docstring"""







import warnings

from .generation import FlaxGenerationMixin



class 		UpperCAmelCase_	(lowerCamelCase_						):
 """simple docstring"""




 warnings.warn(
     """Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will """
     """be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead."""  , lowerCamelCase_  , )

