

import random



class 						__lowercase       :




			"""simple docstring"""







			def __init__(				self						:  List[str]     ,		lowerCAmelCase__						:  float     ,		lowerCAmelCase__						:  float):
									SCREAMING_SNAKE_CASE_:				Dict							= x
									SCREAMING_SNAKE_CASE_:				Tuple							= y



			def  _SCREAMING_SNAKE_CASE    (				self						:  Optional[Any]):
									return (self.x**2 + self.y**2) <= 1




			@classmethod
			def  _SCREAMING_SNAKE_CASE    (				cls						:  int):
									return cls(x=random.random()     ,		y=random.random())







def     A_   (					_UpperCAmelCase					):







						if number_of_simulations < 1:
												raise ValueError("At least one simulation is necessary to estimate PI."					)

						SCREAMING_SNAKE_CASE_:				Optional[int]							= 0
						for _ in range(_UpperCAmelCase					):
												SCREAMING_SNAKE_CASE_:				Dict							= 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

	lowerCAmelCase							:						Optional[Any]     			=		"""Please enter the desired number of Monte Carlo simulations: """
	lowerCAmelCase							:						Dict     			=		estimate_pi(int(input(prompt).strip()))
	print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')









import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp







def     A_   (					):
						SCREAMING_SNAKE_CASE_:				Tuple							= ArgumentParser(
						    description=(
						        "PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"
						    )					)

						# Optional arguments for the launch helper
						parser.add_argument("--num_cores"       ,			type=_UpperCAmelCase       ,			default=1       ,			help="Number of TPU cores to use (1 or 8)."					)

						# positional
						parser.add_argument(
						    "training_script"       ,			type=_UpperCAmelCase       ,			help=(
						        "The full path to the single TPU training "
						        "program/script to be launched in parallel, "
						        "followed by all the arguments for the "
						        "training script"
						    )       ,			)

						# rest from the training program
						parser.add_argument("training_script_args"       ,			nargs=_UpperCAmelCase					)

						return parser.parse_args()







def     A_   (					):
						SCREAMING_SNAKE_CASE_:				List[str]							= parse_args()

						# Import training_script as a module.
						SCREAMING_SNAKE_CASE_:				Tuple							= Path(args.training_script					)
						sys.path.append(str(script_fpath.parent.resolve()					)					)
						SCREAMING_SNAKE_CASE_:				Union[str, Any]							= script_fpath.stem
						SCREAMING_SNAKE_CASE_:				Optional[Any]							= importlib.import_module(_UpperCAmelCase					)

						# Patch sys.argv
						SCREAMING_SNAKE_CASE_:				int							= [args.training_script] + args.training_script_args + ["--tpu_num_cores", str(args.num_cores					)]

						xmp.spawn(mod._mp_fn       ,			args=()       ,			nprocs=args.num_cores					)


if __name__ == "__main__":
						main()






