




'''simple docstring'''





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





def       __a      (  _UpperCamelCase:       int       )		->					Optional[int]:

     """simple docstring"""




     def is_in_circle(_UpperCamelCase:       float   ,		_UpperCamelCase:       float       ) -> bool:
          _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
     _snake_case				= 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.
     _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      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       Callable[[float], float]   ,		_UpperCamelCase:       float = 0.0   ,		_UpperCamelCase:       float = 1.0   ,		)		->					float:

     """simple docstring"""




     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:

     """simple docstring"""




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

     _snake_case				= area_under_curve_estimator(
         _UpperCamelCase   ,		_UpperCamelCase   ,		_UpperCamelCase   ,		_UpperCamelCase       )
     _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      (  _UpperCamelCase:       int       )		->					None:

     """simple docstring"""




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

     _snake_case				= 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 ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase_		:     Dict          =		{
    '''configuration_roformer''': ['''ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''RoFormerConfig''', '''RoFormerOnnxConfig'''],
    '''tokenization_roformer''': ['''RoFormerTokenizer'''],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_		:     Union[str, Any]          =		['''RoFormerTokenizerFast''']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_		:     Tuple          =		[
       '''ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''RoFormerForCausalLM''',
       '''RoFormerForMaskedLM''',
       '''RoFormerForMultipleChoice''',
       '''RoFormerForQuestionAnswering''',
       '''RoFormerForSequenceClassification''',
       '''RoFormerForTokenClassification''',
       '''RoFormerLayer''',
       '''RoFormerModel''',
       '''RoFormerPreTrainedModel''',
       '''load_tf_weights_in_roformer''',
   ]


try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_		:     str          =		[
       '''TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''TFRoFormerForCausalLM''',
       '''TFRoFormerForMaskedLM''',
       '''TFRoFormerForMultipleChoice''',
       '''TFRoFormerForQuestionAnswering''',
       '''TFRoFormerForSequenceClassification''',
       '''TFRoFormerForTokenClassification''',
       '''TFRoFormerLayer''',
       '''TFRoFormerModel''',
       '''TFRoFormerPreTrainedModel''',
   ]


try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_		:     Tuple          =		[
       '''FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''FlaxRoFormerForMaskedLM''',
       '''FlaxRoFormerForMultipleChoice''',
       '''FlaxRoFormerForQuestionAnswering''',
       '''FlaxRoFormerForSequenceClassification''',
       '''FlaxRoFormerForTokenClassification''',
       '''FlaxRoFormerModel''',
       '''FlaxRoFormerPreTrainedModel''',
   ]


if TYPE_CHECKING:
   from .configuration_roformer import ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, RoFormerConfig, RoFormerOnnxConfig
   from .tokenization_roformer import RoFormerTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_roformer_fast import RoFormerTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_roformer import (
          ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          RoFormerForCausalLM,
          RoFormerForMaskedLM,
          RoFormerForMultipleChoice,
          RoFormerForQuestionAnswering,
          RoFormerForSequenceClassification,
          RoFormerForTokenClassification,
          RoFormerLayer,
          RoFormerModel,
          RoFormerPreTrainedModel,
          load_tf_weights_in_roformer,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_roformer import (
          TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFRoFormerForCausalLM,
          TFRoFormerForMaskedLM,
          TFRoFormerForMultipleChoice,
          TFRoFormerForQuestionAnswering,
          TFRoFormerForSequenceClassification,
          TFRoFormerForTokenClassification,
          TFRoFormerLayer,
          TFRoFormerModel,
          TFRoFormerPreTrainedModel,
      )

   try:
      if not is_flax_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_flax_roformer import (
          FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          FlaxRoFormerForMaskedLM,
          FlaxRoFormerForMultipleChoice,
          FlaxRoFormerForQuestionAnswering,
          FlaxRoFormerForSequenceClassification,
          FlaxRoFormerForTokenClassification,
          FlaxRoFormerModel,
          FlaxRoFormerPreTrainedModel,
      )


else:
   import sys

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


