
import mpmath  # for roots of unity
import numpy as np




class        UpperCAmelCase_			:


  '''simple docstring'''







  def __init__( self			: int			,							UpperCamelCase__			: str=None			,							UpperCamelCase__			: int=None    )			->	List[str]:







    """simple docstring"""






    __magic_name__				     =       list(poly_a or [0]    )[:]
    __magic_name__				     =       list(poly_b or [0]    )[:]

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

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

    # Add 0 to make lengths equal a power of 2
    __magic_name__				     =       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
    __magic_name__				     =       complex(mpmath.root(x=1			,							n=self.c_max_length			,							k=1    )    )

    # The product
    __magic_name__				     =       self.__multiply()
  def 							_lowercase							( self			: int			,							UpperCamelCase__			: Any    )			->	Optional[int]:







    """simple docstring"""






    __magic_name__				     =       [[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
    # Corner case
    if len(UpperCamelCase__    ) <= 1:
      return dft[0]
    #
    __magic_name__				     =       self.c_max_length // 2
    while next_ncol > 0:
      __magic_name__				     =       [[] for i in range(UpperCamelCase__    )]
      __magic_name__				     =       self.root**next_ncol

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







    """simple docstring"""






    __magic_name__				     =       self.__dft("""A"""    )
    __magic_name__				     =       self.__dft("""B"""    )
    __magic_name__				     =       [[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
    __magic_name__				     =       2
    while next_ncol <= self.c_max_length:
      __magic_name__				     =       [[] for i in range(UpperCamelCase__    )]
      __magic_name__				     =       self.root ** (next_ncol // 2)
      __magic_name__				     =       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
      __magic_name__				     =       new_inverse_c
      next_ncol *= 2
    # Unpack
    __magic_name__				     =       [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[Any]    )			->	Dict:







    """simple docstring"""






    __magic_name__				     =       """A = """ + """ + """.join(
        F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
    __magic_name__				     =       """B = """ + """ + """.join(
        F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
    __magic_name__				     =       """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'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


lowerCamelCase							:   str  						=	{
    'configuration_rag': ['RagConfig'],
    'retrieval_rag': ['RagRetriever'],
    'tokenization_rag': ['RagTokenizer'],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase							:   Dict  						=	[
     'RagModel',
     'RagPreTrainedModel',
     'RagSequenceForGeneration',
     'RagTokenForGeneration',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase							:   Optional[int]  						=	[
     'TFRagModel',
     'TFRagPreTrainedModel',
     'TFRagSequenceForGeneration',
     'TFRagTokenForGeneration',
 ]


if TYPE_CHECKING:
 from .configuration_rag import RagConfig
 from .retrieval_rag import RagRetriever
 from .tokenization_rag import RagTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_rag import RagModel, RagPreTrainedModel, RagSequenceForGeneration, RagTokenForGeneration

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_rag import (
      TFRagModel,
      TFRagPreTrainedModel,
      TFRagSequenceForGeneration,
      TFRagTokenForGeneration,
  )

else:
 import sys

 lowerCamelCase							:   Tuple  						=	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




