




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






def 					snake_case(				__magic_name__    ) ->							Tuple:





     '''simple docstring'''


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





     '''simple docstring'''


     return mean(
         function_to_integrate(uniform(_UpperCAmelCase ,		_UpperCAmelCase    )    ) for _ in range(_UpperCAmelCase    )    ) * (max_value - min_value)






def 					snake_case(				__magic_name__ ,		__magic_name__ = 0.0 ,		__magic_name__ = 1.0    ) ->							None:





     '''simple docstring'''


     def identity_function(__magic_name__    ) -> float:
          return x

     lowercase					:   str								= area_under_curve_estimator(
         _UpperCAmelCase ,		_UpperCAmelCase ,		_UpperCAmelCase ,		_UpperCAmelCase    )
     lowercase					:   Optional[Any]								= (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 					snake_case(				__magic_name__    ) ->							None:





     '''simple docstring'''


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

     lowercase					:   int								= area_under_curve_estimator(
         _UpperCAmelCase ,		_UpperCAmelCase ,		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'''




from typing import TYPE_CHECKING

from ...file_utils import _LazyModule, is_tokenizers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


__SCREAMING_SNAKE_CASE       :     Optional[int]     =  {"""configuration_gpt_neox""": ["""GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoXConfig"""]}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __SCREAMING_SNAKE_CASE       :     Tuple     =  ["""GPTNeoXTokenizerFast"""]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __SCREAMING_SNAKE_CASE       :     Dict     =  [
      """GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """GPTNeoXForCausalLM""",
      """GPTNeoXForQuestionAnswering""",
      """GPTNeoXForSequenceClassification""",
      """GPTNeoXForTokenClassification""",
      """GPTNeoXLayer""",
      """GPTNeoXModel""",
      """GPTNeoXPreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_gpt_neox import GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoXConfig

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_gpt_neox_fast import GPTNeoXTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_gpt_neox import (
        GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST,
        GPTNeoXForCausalLM,
        GPTNeoXForQuestionAnswering,
        GPTNeoXForSequenceClassification,
        GPTNeoXForTokenClassification,
        GPTNeoXLayer,
        GPTNeoXModel,
        GPTNeoXPreTrainedModel,
    )


else:
  import sys

  __SCREAMING_SNAKE_CASE       :     Any     =  _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

