






"""simple docstring"""



from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def 						_SCREAMING_SNAKE_CASE (    __snake_case			:  int    ):





  '''simple docstring'''





  def is_in_circle(__snake_case			:  float		,					__snake_case			:  float    ) -> bool:
    lowercase							    =       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
  lowercase							    =       mean(
      int(is_in_circle(uniform(-1.0		,					1.0    )		,					uniform(-1.0		,					1.0    )    )    )
      for _ in range(__snake_case    )    )
  # The ratio of the area for circle to square is pi/4.
  lowercase							    =       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 						_SCREAMING_SNAKE_CASE (    __snake_case			:  int		,					__snake_case			:  Callable[[float], float]		,					__snake_case			:  float = 0.0		,					__snake_case			:  float = 1.0		,					):





  '''simple docstring'''





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





  '''simple docstring'''





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

  lowercase							    =       area_under_curve_estimator(
      __snake_case		,					__snake_case		,					__snake_case		,					__snake_case    )
  lowercase							    =       (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 						_SCREAMING_SNAKE_CASE (    __snake_case			:  int    ):





  '''simple docstring'''





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

  lowercase							    =       area_under_curve_estimator(
      __snake_case		,					__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()










"""simple docstring"""



import os
from argparse import ArgumentParser
from typing import List

import torch.utils.data

from datasets import Dataset, IterableDataset
from datasets.distributed import split_dataset_by_node


_UpperCamelCase		:  List[Any]						=		4
_UpperCamelCase		:  Optional[Any]						=		3

class        a     (   a_	):
    pass


def 						_SCREAMING_SNAKE_CASE (    __snake_case			:  List[str]    ):





  '''simple docstring'''





  for shard in shards:
    for i in range(__snake_case    ):
      yield {"i": i, "shard": shard}
def 						_SCREAMING_SNAKE_CASE (    ):





  '''simple docstring'''





  lowercase							    =       int(os.environ['RANK']    )
  lowercase							    =       int(os.environ['WORLD_SIZE']    )

  lowercase							    =       ArgumentParser()
  parser.add_argument('--streaming'		,					type=__snake_case    )
  parser.add_argument('--local_rank'		,					type=__snake_case    )
  parser.add_argument('--num_workers'		,					type=__snake_case		,					default=0    )
  lowercase							    =       parser.parse_args()
  lowercase							    =       args.streaming
  lowercase							    =       args.num_workers

  lowercase							    =       {'shards': [f'shard_{shard_idx}' for shard_idx in range(__snake_case    )]}
  lowercase							    =       IterableDataset.from_generator(__snake_case		,					gen_kwargs=__snake_case    )
  if not streaming:
    lowercase							    =       Dataset.from_list(list(__snake_case    )    )

  lowercase							    =       split_dataset_by_node(__snake_case		,					rank=__snake_case		,					world_size=__snake_case    )
  lowercase							    =       torch.utils.data.DataLoader(__snake_case		,					num_workers=__snake_case    )

  lowercase							    =       NUM_SHARDS * NUM_ITEMS_PER_SHARD
  lowercase							    =       full_size // world_size
  expected_local_size += int(rank < (full_size % world_size)    )

  lowercase							    =       sum(1 for _ in dataloader    )
  if local_size != expected_local_size:
    raise FailedTestError(f'local_size {local_size} != expected_local_size {expected_local_size}'    )


if __name__ == "__main__":
    main()


