

'''simple docstring'''



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







def   a__			(    a__		):




     """simple docstring"""


     def is_in_circle(a__ ,       a__		) -> 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(a__		)		)
     # 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__			(    a__ ,       a__ ,       a__ = 0.0 ,       a__ = 1.0 ,       ):




     """simple docstring"""


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







def   a__			(    a__ ,       a__ = 0.0 ,       a__ = 1.0		):




     """simple docstring"""


     def identity_function(a__		) -> float:
          return x

     __SCREAMING_SNAKE_CASE      = area_under_curve_estimator(
         a__ ,       a__ ,       a__ ,       a__		)
     __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__			(    a__		):




     """simple docstring"""


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

     __SCREAMING_SNAKE_CASE      = area_under_curve_estimator(
         a__ ,       a__ ,       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 Optional, Union

import torch
from torch import nn

from ...configuration_utils import ConfigMixin, register_to_config
from ...models.modeling_utils import ModelMixin







class 		lowerCAmelCase__  ( a					,   a   ):



 """simple docstring"""



 @register_to_config
 def __init__(						self   :			int   ,				__SCREAMING_SNAKE_CASE   :			int = 768   ,				)    ->					int:


      """simple docstring"""




      super().__init__()

      __SCREAMING_SNAKE_CASE      = nn.Parameter(torch.zeros(1   ,				__SCREAMING_SNAKE_CASE     )     )
      __SCREAMING_SNAKE_CASE      = nn.Parameter(torch.ones(1   ,				__SCREAMING_SNAKE_CASE     )     )
 def  UpperCAmelCase__						(						self   :			Any   ,				__SCREAMING_SNAKE_CASE   :			Optional[Union[str, torch.device]] = None   ,				__SCREAMING_SNAKE_CASE   :			Optional[torch.dtype] = None   ,				)    ->					List[str]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = nn.Parameter(self.mean.to(__SCREAMING_SNAKE_CASE     ).to(__SCREAMING_SNAKE_CASE     )     )
      __SCREAMING_SNAKE_CASE      = nn.Parameter(self.std.to(__SCREAMING_SNAKE_CASE     ).to(__SCREAMING_SNAKE_CASE     )     )
      return self
 def  UpperCAmelCase__						(						self   :			Optional[Any]   ,				__SCREAMING_SNAKE_CASE   :			Optional[int]     )    ->					Optional[int]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = (embeds - self.mean) * 1.0 / self.std
      return embeds


 def  UpperCAmelCase__						(						self   :			Tuple   ,				__SCREAMING_SNAKE_CASE   :			Any     )    ->					Optional[int]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = (embeds * self.std) + self.mean
      return embeds






