



import mpmath  # for roots of unity
import numpy as np

class 							a__:







    def __init__(				self			:  Optional[Any]						,      __snake_case			:  List[Any]=None						,      __snake_case			:  str=None     ):
      # Input as list
      a						: Union[str, Any]					       =					list(poly_a or [0]     )[:]
      a						: Tuple					       =					list(poly_b or [0]     )[:]

      # Remove leading zero coefficients
      while self.polyA[-1] == 0:
        self.polyA.pop()
      a						: Union[str, Any]					       =					len(self.polyA     )

      while self.polyB[-1] == 0:
        self.polyB.pop()
      a						: Tuple					       =					len(self.polyB     )

      # Add 0 to make lengths equal a power of 2
      a						: Optional[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						: List[Any]					       =					complex(mpmath.root(x=1						,      n=self.c_max_length						,      k=1     )     )

      # The product
      a						: Tuple					       =					self.__multiply()







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

        # First half of next step
        a						: List[Any]					       =					1
        for j in range(self.c_max_length // (next_ncol * 2)     ):
          for i in range(__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						: Tuple					       =					1
        for j in range(self.c_max_length // (next_ncol * 2)     ):
          for i in range(__snake_case     ):
            new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]     )
          current_root *= root
        # Update
        a						: Any					       =					new_dft
        a						: List[str]					       =					next_ncol // 2
      return dft[0]







    def       lowercase_	(				self			:  str     ):
      a						: Dict					       =					self.__dft('A'     )
      a						: Dict					       =					self.__dft('B'     )
      a						: Union[str, 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						: Optional[int]					       =					2
      while next_ncol <= self.c_max_length:
        a						: Tuple					       =					[[] for i in range(__snake_case     )]
        a						: Any					       =					self.root ** (next_ncol // 2)
        a						: str					       =					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						: List[Any]					       =					new_inverse_c
        next_ncol *= 2
      # Unpack
      a						: Union[str, 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			:  Optional[int]     ):
      a						: Any					       =					'A = ' + ' + '.join(
          F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]     )     )
      a						: Tuple					       =					'B = ' + ' + '.join(
          F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]     )     )
      a						: 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()




'''simple docstring'''






import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase: Any							=						logging.get_logger(__name__)

class 							a__( lowerCamelCase__     ):
    lowercase__			=   """encoder-decoder"""
    lowercase__			=   True







    def __init__(				self			:  Dict						,      **__snake_case			:  Union[str, Any]     ):
      super().__init__(**__snake_case     )
      assert (
          "encoder" in kwargs and "decoder" in kwargs
      ), "Config has to be initialized with encoder and decoder config"
      a						: List[str]					       =					kwargs.pop('encoder'     )
      a						: Optional[Any]					       =					encoder_config.pop('model_type'     )
      a						: Tuple					       =					kwargs.pop('decoder'     )
      a						: Optional[int]					       =					decoder_config.pop('model_type'     )

      from ..auto.configuration_auto import AutoConfig

      a						: Any					       =					AutoConfig.for_model(__snake_case						,      **__snake_case     )
      a						: Optional[int]					       =					AutoConfig.for_model(__snake_case						,      **__snake_case     )
      a						: Tuple					       =					True







    @classmethod
    def       lowercase_	(				cls			:  int						,      __snake_case			:  PretrainedConfig						,      __snake_case			:  PretrainedConfig						,      **__snake_case			:  Union[str, Any]     ):
      logger.info('Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config'     )
      a						: List[Any]					       =					True
      a						: Tuple					       =					True

      return cls(encoder=encoder_config.to_dict()						,      decoder=decoder_config.to_dict()						,      **__snake_case     )







    def       lowercase_	(				self			:  List[Any]     ):
      a						: int					       =					copy.deepcopy(self.__dict__     )
      a						: List[str]					       =					self.encoder.to_dict()
      a						: Optional[int]					       =					self.decoder.to_dict()
      a						: Optional[Any]					       =					self.__class__.model_type
      return output