


"""simple docstring"""







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




def      UpperCAmelCase__ (lowerCAmelCase_     ):




					'''simple docstring'''


					def is_in_circle(lowerCAmelCase_						,		lowerCAmelCase_     ) -> 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(lowerCAmelCase_     )     )
					# 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      UpperCAmelCase__ (lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_ = 0.0						,		lowerCAmelCase_ = 1.0						,		):




					'''simple docstring'''


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




def      UpperCAmelCase__ (lowerCAmelCase_						,		lowerCAmelCase_ = 0.0						,		lowerCAmelCase_ = 1.0     ):




					'''simple docstring'''


					def identity_function(lowerCAmelCase_     ) -> float:
										return x

					__SCREAMING_SNAKE_CASE		     =       area_under_curve_estimator(
					    lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_     )
					__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      UpperCAmelCase__ (lowerCAmelCase_     ):




					'''simple docstring'''


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

					__SCREAMING_SNAKE_CASE		     =       area_under_curve_estimator(
					    lowerCAmelCase_						,		lowerCAmelCase_						,		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 ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


a__       :							List[str]        =  {}


try:
		if not is_sentencepiece_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a__       :							int        =  ['''MLukeTokenizer''']

if TYPE_CHECKING:
		try:
				if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_mluke import MLukeTokenizer


else:
		import sys

		a__       :							Optional[Any]        =  _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
