"""simple docstring"""
import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import TaBlock, TaConfig, TaLayerNorm

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



class   lowerCAmelCase_    (			lowerCAmelCase     ,    lowerCAmelCase     ,    lowerCAmelCase					):



				"""simple docstring"""

				@register_to_config
				def __init__(				self		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase		,    lowerCAmelCase = False		,    ):






										"""simple docstring"""

										super().__init__()

										snake_case								=			nn.Embedding(lowerCAmelCase		,    lowerCAmelCase    )

										snake_case								=			nn.Embedding(lowerCAmelCase		,    lowerCAmelCase    )
										snake_case								=			False

										snake_case								=			nn.Dropout(p=lowerCAmelCase    )

										snake_case								=			TaConfig(
										    vocab_size=lowerCAmelCase		,    d_model=lowerCAmelCase		,    num_heads=lowerCAmelCase		,    d_kv=lowerCAmelCase		,    d_ff=lowerCAmelCase		,    dropout_rate=lowerCAmelCase		,    feed_forward_proj=lowerCAmelCase		,    is_decoder=lowerCAmelCase		,    is_encoder_decoder=lowerCAmelCase		,    )

										snake_case								=			nn.ModuleList()
										for lyr_num in range(lowerCAmelCase    ):
																snake_case								=			TaBlock(lowerCAmelCase    )
																self.encoders.append(lowerCAmelCase    )

										snake_case								=			TaLayerNorm(lowerCAmelCase    )
										snake_case								=			nn.Dropout(p=lowerCAmelCase    )

				def 		snake_case (				self		,    lowerCAmelCase		,    lowerCAmelCase    ):






										"""simple docstring"""

										snake_case								=			self.token_embedder(lowerCAmelCase    )

										snake_case								=			encoder_input_tokens.shape[1]
										snake_case								=			torch.arange(lowerCAmelCase		,    device=encoder_input_tokens.device    )
										x += self.position_encoding(lowerCAmelCase    )

										snake_case								=			self.dropout_pre(lowerCAmelCase    )

										# inverted the attention mask
										snake_case								=			encoder_input_tokens.size()
										snake_case								=			self.get_extended_attention_mask(lowerCAmelCase		,    lowerCAmelCase    )

										for lyr in self.encoders:
																snake_case								=			lyr(lowerCAmelCase		,    lowerCAmelCase    )[0]
										snake_case								=			self.layer_norm(lowerCAmelCase    )

										return self.dropout_post(lowerCAmelCase    ), encoder_inputs_mask



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





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				Dict:





						"""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    lowerCAmelCase__    (			_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    lowerCAmelCase__    (			_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    lowerCAmelCase__    (			_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()


