

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

def       a__					(		UpperCAmelCase							:      int      )  ->						Dict:

  # A local function to see if a dot lands in the circle.
  def is_in_circle(UpperCAmelCase							:      float    ,			UpperCAmelCase							:      float      ) -> bool:
    UpperCAmelCase	:							Dict					=			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
  UpperCAmelCase	:							List[str]					=			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.
  UpperCAmelCase	:							int					=			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__					(		UpperCAmelCase							:      int    ,			UpperCAmelCase							:      Callable[[float], float]    ,			UpperCAmelCase							:      float = 0.0    ,			UpperCAmelCase							:      float = 1.0    ,			)  ->						float:
  return mean(
      function_to_integrate(uniform(UpperCAmelCase    ,			UpperCAmelCase      )      ) for _ in range(UpperCAmelCase      )      ) * (max_value - min_value)

def       a__					(		UpperCAmelCase							:      int    ,			UpperCAmelCase							:      float = 0.0    ,			UpperCAmelCase							:      float = 1.0      )  ->						None:

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

  UpperCAmelCase	:							int					=			area_under_curve_estimator(
      UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase      )
  UpperCAmelCase	:							Tuple					=			(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__					(		UpperCAmelCase							:      int      )  ->						None:

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

  UpperCAmelCase	:							Optional[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()








from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_lowerCamelCase    :       str        =							{"configuration_xlnet": ["XLNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLNetConfig"]}

try:
     if not is_sentencepiece_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase    :       List[Any]        =							["XLNetTokenizer"]

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase    :       Optional[Any]        =							["XLNetTokenizerFast"]

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase    :       Dict        =							[
         "XLNET_PRETRAINED_MODEL_ARCHIVE_LIST",
         "XLNetForMultipleChoice",
         "XLNetForQuestionAnswering",
         "XLNetForQuestionAnsweringSimple",
         "XLNetForSequenceClassification",
         "XLNetForTokenClassification",
         "XLNetLMHeadModel",
         "XLNetModel",
         "XLNetPreTrainedModel",
         "load_tf_weights_in_xlnet",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase    :       Union[str, Any]        =							[
         "TF_XLNET_PRETRAINED_MODEL_ARCHIVE_LIST",
         "TFXLNetForMultipleChoice",
         "TFXLNetForQuestionAnsweringSimple",
         "TFXLNetForSequenceClassification",
         "TFXLNetForTokenClassification",
         "TFXLNetLMHeadModel",
         "TFXLNetMainLayer",
         "TFXLNetModel",
         "TFXLNetPreTrainedModel",
     ]


if TYPE_CHECKING:
     from .configuration_xlnet import XLNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLNetConfig

     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_xlnet import XLNetTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_xlnet_fast import XLNetTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_xlnet import (
              XLNET_PRETRAINED_MODEL_ARCHIVE_LIST,
              XLNetForMultipleChoice,
              XLNetForQuestionAnswering,
              XLNetForQuestionAnsweringSimple,
              XLNetForSequenceClassification,
              XLNetForTokenClassification,
              XLNetLMHeadModel,
              XLNetModel,
              XLNetPreTrainedModel,
              load_tf_weights_in_xlnet,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_xlnet import (
              TF_XLNET_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFXLNetForMultipleChoice,
              TFXLNetForQuestionAnsweringSimple,
              TFXLNetForSequenceClassification,
              TFXLNetForTokenClassification,
              TFXLNetLMHeadModel,
              TFXLNetMainLayer,
              TFXLNetModel,
              TFXLNetPreTrainedModel,
          )

else:
     import sys

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





