
'''simple docstring'''







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				= 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=_SCREAMING_SNAKE_CASE	,			default=1	,			help="Number of TPU cores to use (1 or 8)."  )

						# positional
						parser.add_argument(
						    "training_script"	,			type=_SCREAMING_SNAKE_CASE	,			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=_SCREAMING_SNAKE_CASE  )

						return parser.parse_args()



def 			_a		(	):
						_SCREAMING_SNAKE_CASE				= parse_args()

						# Import training_script as a module.
						_SCREAMING_SNAKE_CASE				= Path(args.training_script  )
						sys.path.append(str(script_fpath.parent.resolve()  )  )
						_SCREAMING_SNAKE_CASE				= script_fpath.stem
						_SCREAMING_SNAKE_CASE				= importlib.import_module(_SCREAMING_SNAKE_CASE  )

						# Patch sys.argv
						_SCREAMING_SNAKE_CASE				= [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()

'''simple docstring'''







from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int  ):

						# A local function to see if a dot lands in the circle.
						def is_in_circle(_SCREAMING_SNAKE_CASE		:   float	,			_SCREAMING_SNAKE_CASE		:   float  ) -> bool:
												_SCREAMING_SNAKE_CASE				= sqrt((x**2) + (y**2)  )
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						_SCREAMING_SNAKE_CASE				= mean(
						    int(is_in_circle(uniform(-1.0	,			1.0  )	,			uniform(-1.0	,			1.0  )  )  )
						    for _ in range(_SCREAMING_SNAKE_CASE  )  )
						# The ratio of the area for circle to square is pi/4.
						_SCREAMING_SNAKE_CASE				= proportion * 4
						print(F'The estimated value of pi is {pi_estimate}'  )
						print(F'The numpy value of pi is {pi}'  )
						print(F'The total error is {abs(pi - pi_estimate  )}'  )



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int	,			_SCREAMING_SNAKE_CASE		:   Callable[[float], float]	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 1.0	,			):
						return mean(
						    function_to_integrate(uniform(_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )  ) for _ in range(_SCREAMING_SNAKE_CASE  )  ) * (max_value - min_value)



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 1.0  ):

						def identity_function(_SCREAMING_SNAKE_CASE		:   float  ) -> float:
												return x

						_SCREAMING_SNAKE_CASE				= area_under_curve_estimator(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )
						_SCREAMING_SNAKE_CASE				= (max_value * max_value - min_value * min_value) / 2

						print("******************"  )
						print(F'Estimating area under y=x where x varies from {min_value} to {max_value}'  )
						print(F'Estimated value is {estimated_value}'  )
						print(F'Expected value is {expected_value}'  )
						print(F'Total error is {abs(estimated_value - expected_value  )}'  )
						print("******************"  )



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int  ):

						def function_to_integrate(_SCREAMING_SNAKE_CASE		:   float  ) -> float:
												return sqrt(4.0 - x * x  )

						_SCREAMING_SNAKE_CASE				= area_under_curve_estimator(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			0.0	,			2.0  )

						print("******************"  )
						print("Estimating pi using area_under_curve_estimator"  )
						print(F'Estimated value is {estimated_value}'  )
						print(F'Expected value is {pi}'  )
						print(F'Total error is {abs(estimated_value - pi  )}'  )
						print("******************"  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()