






'''simple docstring'''


import random




class 							lowerCAmelCase					:







   """simple docstring"""







   def __init__( self   ,   _A   ,   _A			)    ->   None:
    __a    :	str									=						x
    __a    :	Dict									=						y



   def    __magic_name__    ( self			)    ->   bool:
    return (self.x**2 + self.y**2) <= 1



   @classmethod
   def    __magic_name__    ( cls			)    ->   Any:
    return cls(x=random.random()   ,   y=random.random()			)






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 if number_of_simulations < 1:
  raise ValueError('At least one simulation is necessary to estimate PI.'		)

 __a    :	Tuple									=						0
 for _ in range(SCREAMING_SNAKE_CASE__		):
  __a    :	Any									=						Point.random_unit_square()

  if random_point.is_in_unit_circle():
   number_in_unit_circle += 1

 return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
  # import doctest

  # doctest.testmod()
  from math import pi

  SCREAMING_SNAKE_CASE_				      =							"Please enter the desired number of Monte Carlo simulations: "
  SCREAMING_SNAKE_CASE_				      =							estimate_pi(int(input(prompt).strip()))
  print(F"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")












'''simple docstring'''


import math
from timeit import timeit






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 __a    :	Any									=						0
 __a    :	List[Any]									=						abs(SCREAMING_SNAKE_CASE__		)
 while True:
  __a    :	int									=						n // 10
  digits += 1
  if n == 0:
   break
 return digits






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 return 1 if n == 0 else math.floor(math.log(abs(SCREAMING_SNAKE_CASE__		)       ,		10		) + 1		)






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 return len(str(abs(SCREAMING_SNAKE_CASE__		)		)		)






def   lowerCAmelCase__			(					):
 from collections.abc import Callable

 def benchmark_a_function(SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__		) -> None:
  __a    :	Tuple									=						f'''{func.__name__}({value})'''
  __a    :	List[Any]									=						timeit(f'''__main__.{call}'''       ,		setup='import __main__'		)
  print(f'''{call}: {func(SCREAMING_SNAKE_CASE__		)} -- {timing} seconds'''		)

 for value in (262144, 1125899906842624, 1267650600228229401496703205376):
  for func in (num_digits, num_digits_fast, num_digits_faster):
   benchmark_a_function(SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__		)
  print()


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()




