


'''simple docstring'''
import math
from collections.abc import Callable


def 			_lowercase       (				UpperCamelCase__       :					Callable[[float], float],				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 __A  :		float       =			xa
 __A  :		float       =			xa
 while True:
  if x_n == x_na or function(UpperCamelCase__			) == function(UpperCamelCase__			):
   raise ZeroDivisionError('float division by zero, could not find root'			)
  __A  :		float       =			x_na - (
      function(UpperCamelCase__			) / ((function(UpperCamelCase__			) - function(UpperCamelCase__			)) / (x_na - x_n))
  )
  if abs(x_na - x_na			) < 10**-5:
   return x_na
  __A  :		Any       =			x_na
  __A  :		str       =			x_na


def 			_lowercase       (				UpperCamelCase__       :					float			):
 return math.pow(UpperCamelCase__,				3			) - (2 * x) - 5


if __name__ == "__main__":
 print(intersection(f, 3, 3.5))










'''simple docstring'''
from __future__ import annotations

class 						_lowerCamelCase					:




 '''simple docstring'''


 def __init__(      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Dict       =			order

  # a_{0} ... a_{k}
  __A  :		str       =			[1.0] + [0.0] * order
  # b_{0} ... b_{k}
  __A  :		Any       =			[1.0] + [0.0] * order

  # x[n-1] ... x[n-k]
  __A  :		Optional[int]       =			[0.0] * self.order
  # y[n-1] ... y[n-k]
  __A  :		Dict       =			[0.0] * self.order


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase						):

  """simple docstring"""







  if len(__lowercase						) < self.order:
   __A  :		List[Any]       =			[1.0, *a_coeffs]

  if len(__lowercase						) != self.order + 1:
   __A  :		Tuple       =			(
       F"""Expected a_coeffs to have {self.order + 1} elements """
       F"""for {self.order}-order filter, got {len(__lowercase						)}"""
   )
   raise ValueError(__lowercase						)

  if len(__lowercase						) != self.order + 1:
   __A  :		List[Any]       =			(
       F"""Expected b_coeffs to have {self.order + 1} elements """
       F"""for {self.order}-order filter, got {len(__lowercase						)}"""
   )
   raise ValueError(__lowercase						)

  __A  :		Optional[int]       =			a_coeffs
  __A  :		Optional[int]       =			b_coeffs







 def  snake_case__   (      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Union[str, Any]       =			0.0

  # Start at index 1 and do index 0 at the end.
  for i in range(1      ,      self.order + 1						):
   result += (
       self.b_coeffs[i] * self.input_history[i - 1]
       - self.a_coeffs[i] * self.output_history[i - 1]
   )

  __A  :		Optional[int]       =			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

  __A  :		List[str]       =			self.input_history[:-1]
  __A  :		Optional[int]       =			self.output_history[:-1]

  __A  :		Optional[int]       =			sample
  __A  :		Dict       =			result

  return result






