






"""simple docstring"""




def 						_SCREAMING_SNAKE_CASE							( UpperCamelCase     :	int		,				UpperCamelCase     :	int = 1000    ):
  if (not isinstance(UpperCamelCase		,				UpperCamelCase    )) or (digit_position <= 0):
    raise ValueError("""Digit position must be a positive integer"""    )
  elif (not isinstance(UpperCamelCase		,				UpperCamelCase    )) 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
  A__											=							(
      4 * _subsum(UpperCamelCase		,				1		,				UpperCamelCase    )
      - 2 * _subsum(UpperCamelCase		,				4		,				UpperCamelCase    )
      - _subsum(UpperCamelCase		,				5		,				UpperCamelCase    )
      - _subsum(UpperCamelCase		,				6		,				UpperCamelCase    )
  )

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






def 						_SCREAMING_SNAKE_CASE							( UpperCamelCase     :	int		,				UpperCamelCase     :	int		,				UpperCamelCase     :	int    ):
  A__											=							0.0
  for sum_index in range(digit_pos_to_extract + precision    ):
    A__											=							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
      A__											=							pow(
          16		,				digit_pos_to_extract - 1 - sum_index		,				UpperCamelCase    )
    else:
      A__											=							pow(16		,				digit_pos_to_extract - 1 - sum_index    )
    total += exponential_term / denominator
  return total


if __name__ == "__main__":
      import doctest

      doctest.testmod()












"""simple docstring"""




from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime







class 					_UpperCamelCase		( __snake_case):






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


      """simple docstring"""
      super().__init__(*lowerCamelCase__						,      **lowerCamelCase__   )






    def  A    (self						,      lowerCamelCase__						,      lowerCamelCase__   ):


      """simple docstring"""
      A__											=							(
          next_prime(value % self.size_table   )
          if not is_prime(value % self.size_table   )
          else value % self.size_table
      )  # gt = bigger than
      return next_prime_gt - (data % next_prime_gt)






    def  A    (self						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__   ):


      """simple docstring"""
      return (increment * self.__hash_function_a(lowerCamelCase__						,      lowerCamelCase__   )) % self.size_table






    def  A    (self						,      lowerCamelCase__						,      lowerCamelCase__=None   ):


      """simple docstring"""
      A__											=							1
      A__											=							self.hash_function(lowerCamelCase__   )

      while self.values[new_key] is not None and self.values[new_key] != key:
        A__											=							(
            self.__hash_double_function(lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__   )
            if self.balanced_factor() >= self.lim_charge
            else None
        )
        if new_key is None:
          break
        else:
          i += 1

      return new_key




