


import math as m
def        UpperCAmelCase_      (							__snake_case  ,		__snake_case  ,		__snake_case=0.0_01		)  ->    Optional[int]:







 """simple docstring"""


 return (f(a + h		) - f(a - h		)) / (2 * h)
def        UpperCAmelCase_      (							__snake_case  ,		__snake_case=0  ,		__snake_case=100  ,		__snake_case=0.00_01  ,		__snake_case=1e-6  ,		__snake_case=False		)  ->    Any:







 """simple docstring"""


 _lowercase							   =xa  # set the initial guess
 _lowercase							   =[a]
 _lowercase							   =abs(f(__snake_case		)		)
 _lowercase							   =lambda __snake_case		: calc_derivative(__snake_case  ,		__snake_case  ,		h=__snake_case		)  # noqa: E731  Derivative of f(x)
 for _ in range(__snake_case		):
  if fa(__snake_case		) == 0:
   raise ValueError('''No converging solution found'''		)
  _lowercase							   =a - f(__snake_case		) / fa(__snake_case		)  # Calculate the next estimate
  if logsteps:
   steps.append(__snake_case		)
  if error < maxerror:
   break
 else:
  raise ValueError('''Iteration limit reached, no converging solution found'''		)
 if logsteps:
  # If logstep is true, then log intermediate steps
  return a, error, steps
 return a, error


if __name__ == "__main__":
  from matplotlib import pyplot as plt

  UpperCAmelCase__     			=							lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
  UpperCAmelCase__			,UpperCAmelCase__			,UpperCAmelCase__     			=							newton_raphson(
      f, xa=10, maxiter=1000, step=1e-6, logsteps=True
  )
  plt.plot([abs(f(x)) for x in steps])
  plt.xlabel('''step''')
  plt.ylabel('''error''')
  plt.show()
  print(f'''solution = {{{solution:f}}}, error = {{{error:f}}}''')





UpperCAmelCase__     			=							[0.33, 0.44, 0.55, 0.44, 0.33]
UpperCAmelCase__     			=							3
UpperCAmelCase__     			=							5

# Buffer Space (with Parameters Space)
UpperCAmelCase__     			=							[]
UpperCAmelCase__     			=							[]

# Machine Time
UpperCAmelCase__     			=							0
def        UpperCAmelCase_      (							__snake_case		)  ->    Tuple:







 """simple docstring"""


 global buffer_space, params_space, machine_time, K, m, t

 # Choosing Dynamical Systems (All)
 for key, value in enumerate(__snake_case		):
  # Evolution Parameter
  _lowercase							   =float(seed / value		)

  # Control Theory: Orbit Change
  _lowercase							   =(buffer_space[(key + 1) % m] + e) % 1

  # Control Theory: Trajectory Change
  _lowercase							   =(params_space[key] + e) % 1 + 3

  # Modification (Transition Function) - Jumps
  _lowercase							   =round(float(r * value * (1 - value)		)  ,		10		)
  _lowercase							   =r  # Saving to Parameters Space

 # Logistic Map
 assert max(__snake_case		) < 1
 assert max(__snake_case		) < 4

 # Machine Time
 machine_time += 1
def        UpperCAmelCase_      (							)  ->    Union[str, Any]:







 """simple docstring"""


 global buffer_space, params_space, machine_time, K, m, t

 # PRNG (Xorshift by George Marsaglia)
 def xorshift(__snake_case  ,		__snake_case		):
  x ^= y >> 13
  y ^= x << 17
  x ^= y >> 5
  return x

 # Choosing Dynamical Systems (Increment)
 _lowercase							   =machine_time % m

 # Evolution (Time Length)
 for _ in range(0  ,		__snake_case		):
  # Variables (Position + Parameters)
  _lowercase							   =params_space[key]
  _lowercase							   =buffer_space[key]

  # Modification (Transition Function) - Flow
  _lowercase							   =round(float(r * value * (1 - value)		)  ,		10		)
  _lowercase							   =(machine_time * 0.01 + r * 1.01) % 1 + 3

 # Choosing Chaotic Data
 _lowercase							   =int(buffer_space[(key + 2) % m] * (10**10)		)
 _lowercase							   =int(buffer_space[(key - 2) % m] * (10**10)		)

 # Machine Time
 machine_time += 1

 return xorshift(__snake_case  ,		__snake_case		) % 0XF_F_F_F_F_F_F_F
def        UpperCAmelCase_      (							)  ->    int:







 """simple docstring"""


 global buffer_space, params_space, machine_time, K, m, t

 _lowercase							   =K
 _lowercase							   =[0] * m
 _lowercase							   =0


if __name__ == "__main__":
  # Initialization
  reset()

  # Pushing Data (Input)
  import random

  UpperCAmelCase__     			=							random.sample(range(0xffff_ffff), 100)
  for chunk in message:
    push(chunk)

  # for controlling
  UpperCAmelCase__     			=							''''''

  # Pulling Data (Output)
  while inp in ("e", "E"):
    print(f'''{format(pull(), '#04x')}''')
    print(buffer_space)
    print(params_space)
    UpperCAmelCase__     			=							input('''(e)exit? ''').strip()

