




'''simple docstring'''

import math







def 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			float:
	return math.pow(_lowerCAmelCase,				2					) - a







def 						__UpperCamelCase				(							_lowercase					) ->			float:
	return 2 * x







def 						__UpperCamelCase				(							_lowercase					) ->			float:
	_lowercase					:       Dict       =		2.0

	while start <= a:
		_lowercase					:       Dict       =		math.pow(_lowerCAmelCase,				2					)

	return start







def 						__UpperCamelCase				(							_lowercase,				_lowercase = 9999,				_lowercase = 0.0_0_0_0_0_0_0_0_0_0_0_0_0_1					) ->			float:

	if a < 0:
		raise ValueError('math domain error'					)

	_lowercase					:       str       =		get_initial_point(_lowerCAmelCase					)

	for _ in range(_lowerCAmelCase					):
		_lowercase					:       List[str]       =		value
		_lowercase					:       Optional[int]       =		value - fx(_lowerCAmelCase,				_lowerCAmelCase					) / fx_derivative(_lowerCAmelCase					)
		if abs(prev_value - value					) < tolerance:
			return value

	return value


if __name__ == "__main__":
		from doctest import testmod

		testmod()





'''simple docstring'''

import torch
from torch import nn
from torch.nn import CrossEntropyLoss, MSELoss

from transformers.file_utils import add_start_docstrings, add_start_docstrings_to_model_forward
from transformers.models.bert.modeling_bert import (
    BERT_INPUTS_DOCSTRING,
    BERT_START_DOCSTRING,
    BertEmbeddings,
    BertLayer,
    BertPooler,
    BertPreTrainedModel,
)







def 						__UpperCamelCase				(							_lowercase					) ->			Tuple:
	_lowercase					:       int       =		torch.exp(_lowercase					)
	_lowercase					:       List[str]       =		torch.sum(_lowercase,				dim=1					)  # sum of exp(x_i)
	_lowercase					:       str       =		torch.sum(x * exp_x,				dim=1					)  # sum of x_i * exp(x_i)
	return torch.log(_lowercase					) - B / A



class 		lowerCamelCase__      (						nn.Module     ):




					'''simple docstring'''



					def __init__(  self				:	Optional[Any]     ,  UpperCamelCase_				:	List[str]					)  ->       Optional[Any]:



						'''simple docstring'''





						super().__init__()
						_lowercase					:       int       =		config.output_attentions
						_lowercase					:       int       =		config.output_hidden_states
						_lowercase					:       Union[str, Any]       =		nn.ModuleList([BertLayer(UpperCamelCase_					) for _ in range(config.num_hidden_layers					)]					)
						_lowercase					:       List[Any]       =		nn.ModuleList([BertHighway(UpperCamelCase_					) for _ in range(config.num_hidden_layers					)]					)

						_lowercase					:       Tuple       =		[-1 for _ in range(config.num_hidden_layers					)]




					def 						__UpperCAmelCase     (  self				:	Tuple     ,  UpperCamelCase_				:	str					)  ->       int:



						'''simple docstring'''





						if (type(UpperCamelCase_					) is float) or (type(UpperCamelCase_					) is int):
							for i in range(len(self.early_exit_entropy					)					):
								_lowercase					:       Optional[Any]       =		x
						else:
							_lowercase					:       Optional[int]       =		x




					def 						__UpperCAmelCase     (  self				:	List[Any]     ,  UpperCamelCase_				:	List[Any]					)  ->       Dict:



						'''simple docstring'''





						_lowercase					:       Optional[int]       =		pooler.state_dict()
						for highway in self.highway:
							for name, param in highway.pooler.state_dict().items():
								param.copy_(loaded_model[name]					)




					def 						__UpperCAmelCase     (  self				:	int     ,  UpperCamelCase_				:	Tuple     ,  UpperCamelCase_				:	List[Any]=None     ,  UpperCamelCase_				:	Optional[int]=None     ,  UpperCamelCase_				:	Union[str, Any]=None     ,  UpperCamelCase_				:	Optional[Any]=None     ,  )  ->       Optional[int]:



						'''simple docstring'''





						_lowercase					:       int       =		()
						_lowercase					:       List[Any]       =		()
						_lowercase					:       Tuple       =		()
						for i, layer_module in enumerate(self.layer					):
							if self.output_hidden_states:
								_lowercase					:       Optional[int]       =		all_hidden_states + (hidden_states,)

							_lowercase					:       str       =		layer_module(
							    UpperCamelCase_     ,  UpperCamelCase_     ,  head_mask[i]     ,  UpperCamelCase_     ,  UpperCamelCase_					)
							_lowercase					:       List[str]       =		layer_outputs[0]

							if self.output_attentions:
								_lowercase					:       Tuple       =		all_attentions + (layer_outputs[1],)

							_lowercase					:       Optional[int]       =		(hidden_states,)
							if self.output_hidden_states:
								_lowercase					:       str       =		current_outputs + (all_hidden_states,)
							if self.output_attentions:
								_lowercase					:       Optional[int]       =		current_outputs + (all_attentions,)

							_lowercase					:       List[Any]       =		self.highway[i](UpperCamelCase_					)
							# logits, pooled_output

							if not self.training:
								_lowercase					:       Dict       =		highway_exit[0]
								_lowercase					:       Tuple       =		entropy(UpperCamelCase_					)
								_lowercase					:       Dict       =		highway_exit + (highway_entropy,)  # logits, hidden_states(?), entropy
								_lowercase					:       str       =		all_highway_exits + (highway_exit,)

								if highway_entropy < self.early_exit_entropy[i]:
									_lowercase					:       Tuple       =		(highway_logits,) + current_outputs[1:] + (all_highway_exits,)
									raise HighwayException(UpperCamelCase_     ,  i + 1					)
							else:
								_lowercase					:       Optional[int]       =		all_highway_exits + (highway_exit,)

        # Add last layer
						if self.output_hidden_states:
							_lowercase					:       str       =		all_hidden_states + (hidden_states,)

						_lowercase					:       Optional[Any]       =		(hidden_states,)
						if self.output_hidden_states:
							_lowercase					:       Dict       =		outputs + (all_hidden_states,)
						if self.output_attentions:
							_lowercase					:       Optional[Any]       =		outputs + (all_attentions,)

						_lowercase					:       Optional[int]       =		outputs + (all_highway_exits,)
						return outputs  # last-layer hidden state, (all hidden states), (all attentions), all highway exits






@add_start_docstrings(
    """The Bert Model transformer with early exiting (DeeBERT). """	,   A	,   )
class 		lowerCamelCase__      (						A     ):




					'''simple docstring'''



					def __init__(  self				:	int     ,  UpperCamelCase_				:	Optional[int]					)  ->       Optional[Any]:



						'''simple docstring'''





						super().__init__(UpperCamelCase_					)
						_lowercase					:       int       =		config

						_lowercase					:       int       =		BertEmbeddings(UpperCamelCase_					)
						_lowercase					:       List[Any]       =		DeeBertEncoder(UpperCamelCase_					)
						_lowercase					:       Any       =		BertPooler(UpperCamelCase_					)

						self.init_weights()




					def 						__UpperCAmelCase     (  self				:	int					)  ->       Union[str, Any]:



						'''simple docstring'''





						self.encoder.init_highway_pooler(self.pooler					)




					def 						__UpperCAmelCase     (  self				:	Optional[int]					)  ->       List[str]:



						'''simple docstring'''





						return self.embeddings.word_embeddings




					def 						__UpperCAmelCase     (  self				:	Dict     ,  UpperCamelCase_				:	Dict					)  ->       Any:



						'''simple docstring'''





						_lowercase					:       Optional[Any]       =		value




					def 						__UpperCAmelCase     (  self				:	Optional[int]     ,  UpperCamelCase_				:	int					)  ->       Union[str, Any]:



						'''simple docstring'''





						for layer, heads in heads_to_prune.items():
							self.encoder.layer[layer].attention.prune_heads(UpperCamelCase_					)




					@add_start_docstrings_to_model_forward(UpperCamelCase_					)
					def 						__UpperCAmelCase     (  self				:	Tuple     ,  UpperCamelCase_				:	Optional[Any]=None     ,  UpperCamelCase_				:	str=None     ,  UpperCamelCase_				:	Optional[Any]=None     ,  UpperCamelCase_				:	Tuple=None     ,  UpperCamelCase_				:	Any=None     ,  UpperCamelCase_				:	Optional[int]=None     ,  UpperCamelCase_				:	int=None     ,  UpperCamelCase_				:	Tuple=None     ,  )  ->       Union[str, Any]:



						'''simple docstring'''





						if input_ids is not None and inputs_embeds is not None:
							raise ValueError('You cannot specify both input_ids and inputs_embeds at the same time'					)
						elif input_ids is not None:
							_lowercase					:       Any       =		input_ids.size()
						elif inputs_embeds is not None:
							_lowercase					:       Any       =		inputs_embeds.size()[:-1]
						else:
							raise ValueError('You have to specify either input_ids or inputs_embeds'					)

						_lowercase					:       str       =		input_ids.device if input_ids is not None else inputs_embeds.device

						if attention_mask is None:
							_lowercase					:       Tuple       =		torch.ones(UpperCamelCase_     ,  device=UpperCamelCase_					)
						if encoder_attention_mask is None:
							_lowercase					:       Dict       =		torch.ones(UpperCamelCase_     ,  device=UpperCamelCase_					)
						if token_type_ids is None:
							_lowercase					:       int       =		torch.zeros(UpperCamelCase_     ,  dtype=torch.long     ,  device=UpperCamelCase_					)

						# We can provide a self-attention mask of dimensions [batch_size, from_seq_length, to_seq_length]
						# ourselves in which case we just need to make it broadcastable to all heads.
						_lowercase					:       torch.Tensor       =		self.get_extended_attention_mask(UpperCamelCase_     ,  UpperCamelCase_     ,  UpperCamelCase_					)

						# If a 2D ou 3D attention mask is provided for the cross-attention
						# we need to make broadcastable to [batch_size, num_heads, seq_length, seq_length]
						if encoder_attention_mask.dim() == 3:
							_lowercase					:       int       =		encoder_attention_mask[:, None, :, :]
						if encoder_attention_mask.dim() == 2:
							_lowercase					:       int       =		encoder_attention_mask[:, None, None, :]

						_lowercase					:       str       =		encoder_extended_attention_mask.to(
						    dtype=next(self.parameters()					).dtype					)  # fp16 compatibility
						_lowercase					:       Optional[int]       =		(1.0 - encoder_extended_attention_mask) * -1_00_00.0

						# Prepare head mask if needed
						# 1.0 in head_mask indicate we keep the head
						# attention_probs has shape bsz x n_heads x N x N
						# input head_mask has shape [num_heads] or [num_hidden_layers x num_heads]
						# and head_mask is converted to shape [num_hidden_layers x batch x num_heads x seq_length x seq_length]
						_lowercase					:       Optional[int]       =		self.get_head_mask(UpperCamelCase_     ,  self.config.num_hidden_layers					)

						_lowercase					:       Dict       =		self.embeddings(
						    input_ids=UpperCamelCase_     ,  position_ids=UpperCamelCase_     ,  token_type_ids=UpperCamelCase_     ,  inputs_embeds=UpperCamelCase_					)
						_lowercase					:       List[Any]       =		self.encoder(
						    UpperCamelCase_     ,  attention_mask=UpperCamelCase_     ,  head_mask=UpperCamelCase_     ,  encoder_hidden_states=UpperCamelCase_     ,  encoder_attention_mask=UpperCamelCase_     ,  )
						_lowercase					:       int       =		encoder_outputs[0]
						_lowercase					:       str       =		self.pooler(UpperCamelCase_					)

						_lowercase					:       List[Any]       =		(
						    sequence_output,
						    pooled_output,
						) + encoder_outputs[
						    1:
						]  # add hidden_states and attentions if they are here
						return outputs  # sequence_output, pooled_output, (hidden_states), (attentions), highway exits






class 		lowerCamelCase__      (						A     ):




					'''simple docstring'''



					def __init__(  self				:	Dict     ,  UpperCamelCase_				:	List[str]     ,  UpperCamelCase_				:	Dict					)  ->       Optional[Any]:



						'''simple docstring'''





						_lowercase					:       Any       =		message
						_lowercase					:       Dict       =		exit_layer  # start from 1!






class 		lowerCamelCase__      (						nn.Module     ):




					'''simple docstring'''



					def __init__(  self				:	int     ,  UpperCamelCase_				:	List[str]					)  ->       Dict:



						'''simple docstring'''





						super().__init__()
						_lowercase					:       Optional[Any]       =		BertPooler(UpperCamelCase_					)
						_lowercase					:       List[Any]       =		nn.Dropout(config.hidden_dropout_prob					)
						_lowercase					:       int       =		nn.Linear(config.hidden_size     ,  config.num_labels					)




					def 						__UpperCAmelCase     (  self				:	Optional[Any]     ,  UpperCamelCase_				:	Optional[int]					)  ->       List[Any]:



						'''simple docstring'''





						_lowercase					:       str       =		encoder_outputs[0]
						_lowercase					:       int       =		self.pooler(UpperCamelCase_					)
						# "return" pooler_output

						# BertModel
						_lowercase					:       Optional[int]       =		(pooler_input, pooler_output) + encoder_outputs[1:]
						# "return" bmodel_output

						# Dropout and classification
						_lowercase					:       Dict       =		bmodel_output[1]

						_lowercase					:       Union[str, Any]       =		self.dropout(UpperCamelCase_					)
						_lowercase					:       str       =		self.classifier(UpperCamelCase_					)

						return logits, pooled_output






@add_start_docstrings(
    """Bert Model (with early exiting - DeeBERT) with a classifier on top,
    also takes care of multi-layer training. """	,   A	,   )
class 		lowerCamelCase__      (						A     ):




					'''simple docstring'''



					def __init__(  self				:	int     ,  UpperCamelCase_				:	List[Any]					)  ->       List[str]:



						'''simple docstring'''





						super().__init__(UpperCamelCase_					)
						_lowercase					:       Dict       =		config.num_labels
						_lowercase					:       Any       =		config.num_hidden_layers

						_lowercase					:       Optional[int]       =		DeeBertModel(UpperCamelCase_					)
						_lowercase					:       Any       =		nn.Dropout(config.hidden_dropout_prob					)
						_lowercase					:       Optional[Any]       =		nn.Linear(config.hidden_size     ,  self.config.num_labels					)

						self.init_weights()




					@add_start_docstrings_to_model_forward(UpperCamelCase_					)
					def 						__UpperCAmelCase     (  self				:	Dict     ,  UpperCamelCase_				:	Dict=None     ,  UpperCamelCase_				:	Union[str, Any]=None     ,  UpperCamelCase_				:	List[Any]=None     ,  UpperCamelCase_				:	Tuple=None     ,  UpperCamelCase_				:	Any=None     ,  UpperCamelCase_				:	Optional[int]=None     ,  UpperCamelCase_				:	Optional[int]=None     ,  UpperCamelCase_				:	str=-1     ,  UpperCamelCase_				:	Union[str, Any]=False     ,  )  ->       Tuple:



						'''simple docstring'''





						_lowercase					:       Union[str, Any]       =		self.num_layers
						try:
							_lowercase					:       Tuple       =		self.bert(
							    UpperCamelCase_     ,  attention_mask=UpperCamelCase_     ,  token_type_ids=UpperCamelCase_     ,  position_ids=UpperCamelCase_     ,  head_mask=UpperCamelCase_     ,  inputs_embeds=UpperCamelCase_     ,  )
							# sequence_output, pooled_output, (hidden_states), (attentions), highway exits

							_lowercase					:       List[Any]       =		outputs[1]

							_lowercase					:       int       =		self.dropout(UpperCamelCase_					)
							_lowercase					:       Optional[int]       =		self.classifier(UpperCamelCase_					)
							_lowercase					:       Union[str, Any]       =		(logits,) + outputs[2:]  # add hidden states and attention if they are here
						except HighwayException as e:
							_lowercase					:       Union[str, Any]       =		e.message
							_lowercase					:       Any       =		e.exit_layer
							_lowercase					:       Optional[int]       =		outputs[0]

						if not self.training:
							_lowercase					:       Union[str, Any]       =		entropy(UpperCamelCase_					)
							_lowercase					:       Tuple       =		[]
							_lowercase					:       Tuple       =		[]
						if labels is not None:
							if self.num_labels == 1:
								#  We are doing regression
								_lowercase					:       Tuple       =		MSELoss()
								_lowercase					:       Tuple       =		loss_fct(logits.view(-1					)     ,  labels.view(-1					)					)
							else:
								_lowercase					:       Union[str, Any]       =		CrossEntropyLoss()
								_lowercase					:       Tuple       =		loss_fct(logits.view(-1     ,  self.num_labels					)     ,  labels.view(-1					)					)

							# work with highway exits
							_lowercase					:       Optional[Any]       =		[]
							for highway_exit in outputs[-1]:
								_lowercase					:       Optional[Any]       =		highway_exit[0]
								if not self.training:
									highway_logits_all.append(UpperCamelCase_					)
									highway_entropy.append(highway_exit[2]					)
								if self.num_labels == 1:
									#  We are doing regression
									_lowercase					:       Union[str, Any]       =		MSELoss()
									_lowercase					:       Any       =		loss_fct(highway_logits.view(-1					)     ,  labels.view(-1					)					)
								else:
									_lowercase					:       Dict       =		CrossEntropyLoss()
									_lowercase					:       Optional[int]       =		loss_fct(highway_logits.view(-1     ,  self.num_labels					)     ,  labels.view(-1					)					)
								highway_losses.append(UpperCamelCase_					)

							if train_highway:
								_lowercase					:       List[str]       =		(sum(highway_losses[:-1]					),) + outputs
								# exclude the final highway, of course
							else:
								_lowercase					:       Optional[Any]       =		(loss,) + outputs
						if not self.training:
							_lowercase					:       List[Any]       =		outputs + ((original_entropy, highway_entropy), exit_layer)
							if output_layer >= 0:
								_lowercase					:       Dict       =		(
								    (outputs[0],) + (highway_logits_all[output_layer],) + outputs[2:]
								)  # use the highway of the last layer

						return outputs  # (loss), logits, (hidden_states), (attentions), (highway_exits)
