import mpmath  # for roots of unity
import numpy as np



class  SCREAMING_SNAKE_CASE_ :
  '''simple docstring'''


  def __init__(				self    :					Dict      ,	SCREAMING_SNAKE_CASE__    :					Tuple=None      ,	SCREAMING_SNAKE_CASE__    :					Optional[Any]=None     )    ->				Tuple:
         # Input as list
         A						:     Optional[Any]         =list(poly_a or [0]     )[:]
         A						:     int         =list(poly_b or [0]     )[:]

         # Remove leading zero coefficients
         while self.polyA[-1] == 0:
                self.polyA.pop()
         A						:     List[str]         =len(self.polyA     )

         while self.polyB[-1] == 0:
                self.polyB.pop()
         A						:     Optional[int]         =len(self.polyB     )

         # Add 0 to make lengths equal a power of 2
         A						:     List[Any]         =int(
             2 ** np.ceil(np.loga(len(self.polyA     ) + len(self.polyB     ) - 1     )     )     )

         while len(self.polyA     ) < self.c_max_length:
                self.polyA.append(0     )
         while len(self.polyB     ) < self.c_max_length:
                self.polyB.append(0     )
         # A complex root used for the fourier transform
         A						:     Optional[Any]         =complex(mpmath.root(x=1      ,	n=self.c_max_length      ,	k=1     )     )

         # The product
         A						:     List[Any]         =self.__multiply()







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Optional[int]      ,	SCREAMING_SNAKE_CASE__    :					Optional[Any]     )    ->				Tuple:
         A						:     str         =[[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
         # Corner case
         if len(SCREAMING_SNAKE_CASE__     ) <= 1:
                return dft[0]
         #
         A						:     List[str]         =self.c_max_length // 2
         while next_ncol > 0:
                A						:     Any         =[[] for i in range(SCREAMING_SNAKE_CASE__     )]
                A						:     Optional[Any]         =self.root**next_ncol

                # First half of next step
                A						:     Tuple         =1
                for j in range(self.c_max_length // (next_ncol * 2)     ):
                       for i in range(SCREAMING_SNAKE_CASE__     ):
                              new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]     )
                       current_root *= root
                # Second half of next step
                A						:     Optional[Any]         =1
                for j in range(self.c_max_length // (next_ncol * 2)     ):
                       for i in range(SCREAMING_SNAKE_CASE__     ):
                              new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]     )
                       current_root *= root
                # Update
                A						:     Dict         =new_dft
                A						:     Optional[int]         =next_ncol // 2
         return dft[0]







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Any     )    ->				Tuple:
         A						:     List[Any]         =self.__dft('A'     )
         A						:     Dict         =self.__dft('B'     )
         A						:     Optional[Any]         =[[dft_a[i] * dft_b[i] for i in range(self.c_max_length     )]]
         del dft_a
         del dft_b

         # Corner Case
         if len(inverce_c[0]     ) <= 1:
                return inverce_c[0]
         # Inverse DFT
         A						:     Union[str, Any]         =2
         while next_ncol <= self.c_max_length:
                A						:     Optional[int]         =[[] for i in range(SCREAMING_SNAKE_CASE__     )]
                A						:     Any         =self.root ** (next_ncol // 2)
                A						:     Union[str, Any]         =1
                # First half of next step
                for j in range(self.c_max_length // next_ncol     ):
                       for i in range(next_ncol // 2     ):
                              # Even positions
                              new_inverse_c[i].append(
                                  (
                                      inverce_c[i][j]
                                      + inverce_c[i][j + self.c_max_length // next_ncol]
                                  )
                                  / 2     )
                              # Odd positions
                              new_inverse_c[i + next_ncol // 2].append(
                                  (
                                      inverce_c[i][j]
                                      - inverce_c[i][j + self.c_max_length // next_ncol]
                                  )
                                  / (2 * current_root)     )
                       current_root *= root
                # Update
                A						:     Any         =new_inverse_c
                next_ncol *= 2
         # Unpack
         A						:     List[Any]         =[round(x[0].real      ,	8     ) + round(x[0].imag      ,	8     ) * 1j for x in inverce_c]

         # Remove leading 0's
         while inverce_c[-1] == 0:
                inverce_c.pop()
         return inverce_c







  def __str__(				self    :					str     )    ->				int:
         A						:     List[Any]         ='A = ' + ' + '.join(
             f'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]     )     )
         A						:     List[str]         ='B = ' + ' + '.join(
             f'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]     )     )
         A						:     List[Any]         ='A*B = ' + ' + '.join(
             f'{coef}*x^{i}' for coef, i in enumerate(self.product     )     )

         return f'{a}\n{b}\n{c}'


# Unit tests
if __name__ == "__main__":
    import doctest

    doctest.testmod()







from typing import Optional

import numpy as np
import torch
from torch import nn
from transformers import GPTaConfig, GPTaLMHeadModel
from transformers.modeling_utils import ModuleUtilsMixin

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



class  SCREAMING_SNAKE_CASE_ (					lowerCAmelCase_   ,						lowerCAmelCase_   ,						lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Tuple            =				[r"h\.\d+\.attn\.bias", r"h\.\d+\.attn\.masked_bias"]







  @register_to_config
  def __init__(				self    :					Any      ,	SCREAMING_SNAKE_CASE__    :					int      ,	SCREAMING_SNAKE_CASE__    :					int      ,	SCREAMING_SNAKE_CASE__    :					Optional[int] = None      ,	SCREAMING_SNAKE_CASE__    :					int = 5_02_57      ,	SCREAMING_SNAKE_CASE__    :					int = 10_24      ,	SCREAMING_SNAKE_CASE__    :					int = 7_68      ,	SCREAMING_SNAKE_CASE__    :					int = 12      ,	SCREAMING_SNAKE_CASE__    :					int = 12      ,	SCREAMING_SNAKE_CASE__    :					Optional[int] = None      ,	SCREAMING_SNAKE_CASE__    :					str = "gelu_new"      ,	SCREAMING_SNAKE_CASE__    :					float = 0.1      ,	SCREAMING_SNAKE_CASE__    :					float = 0.1      ,	SCREAMING_SNAKE_CASE__    :					float = 0.1      ,	SCREAMING_SNAKE_CASE__    :					float = 1e-5      ,	SCREAMING_SNAKE_CASE__    :					float = 0.0_2      ,	SCREAMING_SNAKE_CASE__    :					bool = True      ,	SCREAMING_SNAKE_CASE__    :					bool = True      ,	SCREAMING_SNAKE_CASE__    :					bool = False      ,	SCREAMING_SNAKE_CASE__    :					bool = False      ,	)    ->				List[str]:
         super().__init__()

         A						:     str         =prefix_length

         if prefix_inner_dim != n_embd and prefix_hidden_dim is None:
                raise ValueError(
                    f'`prefix_hidden_dim` cannot be `None` when `prefix_inner_dim`: {prefix_hidden_dim} and'
                    f' `n_embd`: {n_embd} are not equal.'     )

         A						:     List[Any]         =prefix_inner_dim
         A						:     Dict         =prefix_hidden_dim

         A						:     List[str]         =(
             nn.Linear(self.prefix_inner_dim      ,	self.prefix_hidden_dim     )
             if self.prefix_hidden_dim is not None
             else nn.Identity()
         )
         A						:     Optional[int]         =(
             nn.Linear(self.prefix_hidden_dim      ,	SCREAMING_SNAKE_CASE__     ) if self.prefix_hidden_dim is not None else nn.Identity()
         )

         A						:     Dict         =GPTaConfig(
             vocab_size=SCREAMING_SNAKE_CASE__      ,	n_positions=SCREAMING_SNAKE_CASE__      ,	n_embd=SCREAMING_SNAKE_CASE__      ,	n_layer=SCREAMING_SNAKE_CASE__      ,	n_head=SCREAMING_SNAKE_CASE__      ,	n_inner=SCREAMING_SNAKE_CASE__      ,	activation_function=SCREAMING_SNAKE_CASE__      ,	resid_pdrop=SCREAMING_SNAKE_CASE__      ,	embd_pdrop=SCREAMING_SNAKE_CASE__      ,	attn_pdrop=SCREAMING_SNAKE_CASE__      ,	layer_norm_epsilon=SCREAMING_SNAKE_CASE__      ,	initializer_range=SCREAMING_SNAKE_CASE__      ,	scale_attn_weights=SCREAMING_SNAKE_CASE__      ,	use_cache=SCREAMING_SNAKE_CASE__      ,	scale_attn_by_inverse_layer_idx=SCREAMING_SNAKE_CASE__      ,	reorder_and_upcast_attn=SCREAMING_SNAKE_CASE__      ,	)
         A						:     Dict         =GPTaLMHeadModel(SCREAMING_SNAKE_CASE__     )







  def 		SCREAMING_SNAKE_CASE_		(				self    :					List[Any]      ,	SCREAMING_SNAKE_CASE__    :					torch.Tensor      ,	SCREAMING_SNAKE_CASE__    :					torch.Tensor      ,	SCREAMING_SNAKE_CASE__    :					Optional[torch.Tensor] = None      ,	SCREAMING_SNAKE_CASE__    :					Optional[torch.Tensor] = None      ,	)    ->				Optional[Any]:
         A						:     str         =self.transformer.transformer.wte(SCREAMING_SNAKE_CASE__     )
         A						:     Any         =self.encode_prefix(SCREAMING_SNAKE_CASE__     )
         A						:     Optional[Any]         =self.decode_prefix(SCREAMING_SNAKE_CASE__     )
         A						:     Optional[int]         =torch.cat((prefix_embeds, embedding_text)      ,	dim=1     )

         if labels is not None:
                A						:     int         =self.get_dummy_token(input_ids.shape[0]      ,	input_ids.device     )
                A						:     Optional[int]         =torch.cat((dummy_token, input_ids)      ,	dim=1     )
         A						:     Dict         =self.transformer(inputs_embeds=SCREAMING_SNAKE_CASE__      ,	labels=SCREAMING_SNAKE_CASE__      ,	attention_mask=SCREAMING_SNAKE_CASE__     )
         if self.prefix_hidden_dim is not None:
                return out, hidden
         else:
                return out







  def 		SCREAMING_SNAKE_CASE_		(				self    :					List[str]      ,	SCREAMING_SNAKE_CASE__    :					int      ,	SCREAMING_SNAKE_CASE__    :					torch.device     )    ->				torch.Tensor:
         return torch.zeros(SCREAMING_SNAKE_CASE__      ,	self.prefix_length      ,	dtype=torch.intaa      ,	device=SCREAMING_SNAKE_CASE__     )







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Union[str, Any]      ,	SCREAMING_SNAKE_CASE__    :					Optional[int]     )    ->				List[str]:
         return self.encode_prefix(SCREAMING_SNAKE_CASE__     )







  @torch.no_grad()
  def 		SCREAMING_SNAKE_CASE_		(				self    :					List[Any]      ,	SCREAMING_SNAKE_CASE__    :					List[str]      ,	SCREAMING_SNAKE_CASE__    :					Union[str, Any]      ,	SCREAMING_SNAKE_CASE__    :					Any     )    ->				Dict:
         A						:     Dict         =torch.split(SCREAMING_SNAKE_CASE__      ,	1      ,	dim=0     )
         A						:     int         =[]
         A						:     Optional[int]         =[]
         for feature in features:
                A						:     int         =self.decode_prefix(feature.to(SCREAMING_SNAKE_CASE__     )     )  # back to the clip feature
                # Only support beam search for now
                A  ,  A						:     Dict         =self.generate_beam(
                    input_embeds=SCREAMING_SNAKE_CASE__      ,	device=SCREAMING_SNAKE_CASE__      ,	eos_token_id=SCREAMING_SNAKE_CASE__     )
                generated_tokens.append(output_tokens[0]     )
                generated_seq_lengths.append(seq_lengths[0]     )
         A						:     str         =torch.stack(SCREAMING_SNAKE_CASE__     )
         A						:     int         =torch.stack(SCREAMING_SNAKE_CASE__     )
         return generated_tokens, generated_seq_lengths







  @torch.no_grad()
  def 		SCREAMING_SNAKE_CASE_		(				self    :					Optional[int]      ,	SCREAMING_SNAKE_CASE__    :					Union[str, Any]=None      ,	SCREAMING_SNAKE_CASE__    :					List[Any]=None      ,	SCREAMING_SNAKE_CASE__    :					Tuple=None      ,	SCREAMING_SNAKE_CASE__    :					int = 5      ,	SCREAMING_SNAKE_CASE__    :					int = 67      ,	SCREAMING_SNAKE_CASE__    :					float = 1.0      ,	SCREAMING_SNAKE_CASE__    :					Optional[int] = None      ,	)    ->				Dict:
         A						:     Dict         =eos_token_id
         A						:     str         =None
         A						:     List[Any]         =None
         A						:     List[Any]         =torch.ones(SCREAMING_SNAKE_CASE__      ,	device=SCREAMING_SNAKE_CASE__      ,	dtype=torch.int     )
         A						:     str         =torch.zeros(SCREAMING_SNAKE_CASE__      ,	device=SCREAMING_SNAKE_CASE__      ,	dtype=torch.bool     )

         if input_embeds is not None:
                A						:     Any         =input_embeds
         else:
                A						:     List[Any]         =self.transformer.transformer.wte(SCREAMING_SNAKE_CASE__     )

         for i in range(SCREAMING_SNAKE_CASE__     ):
                A						:     Any         =self.transformer(inputs_embeds=SCREAMING_SNAKE_CASE__     )
                A						:     str         =outputs.logits
                A						:     Union[str, Any]         =logits[:, -1, :] / (temperature if temperature > 0 else 1.0)
                A						:     List[str]         =logits.softmax(-1     ).log()

                if scores is None:
                       A  ,  A						:     Any         =logits.topk(SCREAMING_SNAKE_CASE__      ,	-1     )
                       A						:     Any         =generated.expand(SCREAMING_SNAKE_CASE__      ,	*generated.shape[1:]     )
                       A  ,  A						:     Tuple         =next_tokens.permute(1      ,	0     ), scores.squeeze(0     )
                       if tokens is None:
                              A						:     Union[str, Any]         =next_tokens
                       else:
                              A						:     str         =tokens.expand(SCREAMING_SNAKE_CASE__      ,	*tokens.shape[1:]     )
                              A						:     Optional[int]         =torch.cat((tokens, next_tokens)      ,	dim=1     )
                else:
                       A						:     Optional[Any]         =-float(np.inf     )
                       A						:     Tuple         =0
                       A						:     Optional[Any]         =scores[:, None] + logits
                       seq_lengths[~is_stopped] += 1
                       A						:     int         =scores_sum / seq_lengths[:, None]
                       A  ,  A						:     Optional[int]         =scores_sum_average.view(-1     ).topk(SCREAMING_SNAKE_CASE__      ,	-1     )
                       A						:     Dict         =next_tokens // scores_sum.shape[1]
                       A						:     Optional[Any]         =seq_lengths[next_tokens_source]
                       A						:     Tuple         =next_tokens % scores_sum.shape[1]
                       A						:     Optional[Any]         =next_tokens.unsqueeze(1     )
                       A						:     Optional[Any]         =tokens[next_tokens_source]
                       A						:     Any         =torch.cat((tokens, next_tokens)      ,	dim=1     )
                       A						:     List[str]         =generated[next_tokens_source]
                       A						:     List[Any]         =scores_sum_average * seq_lengths
                       A						:     Optional[Any]         =is_stopped[next_tokens_source]

                A						:     Optional[int]         =self.transformer.transformer.wte(next_tokens.squeeze()     ).view(generated.shape[0]      ,	1      ,	-1     )
                A						:     Any         =torch.cat((generated, next_token_embed)      ,	dim=1     )
                A						:     Optional[int]         =is_stopped + next_tokens.eq(SCREAMING_SNAKE_CASE__     ).squeeze()
                if is_stopped.all():
                       break

         A						:     Optional[Any]         =scores / seq_lengths
         A						:     str         =scores.argsort(descending=SCREAMING_SNAKE_CASE__     )
         # tokens tensors are already padded to max_seq_length
         A						:     Optional[Any]         =[tokens[i] for i in order]
         A						:     Any         =torch.stack(SCREAMING_SNAKE_CASE__      ,	dim=0     )
         A						:     str         =torch.tensor([seq_lengths[i] for i in order]      ,	dtype=seq_lengths.dtype     )
         return output_texts, seq_lengths






