import mpmath  # for roots of unity
import numpy as np


class       UpperCAmelCase__     :



  """simple docstring"""






  def __init__(					self:      str					,					__lowerCAmelCase:      Optional[int]=None					,					__lowerCAmelCase:      Any=None )			->			Any:




    '''simple docstring'''




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

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

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

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

    # The product
    __UpperCAmelCase         =							self.__multiply()






  def 						_UpperCAmelCase					(					self:      int					,					__lowerCAmelCase:      Union[str, Any] )			->			Optional[Any]:




    '''simple docstring'''




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

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






  def 						_UpperCAmelCase					(					self:      Optional[Any] )			->			List[str]:




    '''simple docstring'''




    __UpperCAmelCase         =							self.__dft("A" )
    __UpperCAmelCase         =							self.__dft("B" )
    __UpperCAmelCase         =							[[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
    __UpperCAmelCase         =							2
    while next_ncol <= self.c_max_length:
      __UpperCAmelCase         =							[[] for i in range(A__ )]
      __UpperCAmelCase         =							self.root ** (next_ncol // 2)
      __UpperCAmelCase         =							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
      __UpperCAmelCase         =							new_inverse_c
      next_ncol *= 2
    # Unpack
    __UpperCAmelCase         =							[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:      Union[str, Any] )			->			Optional[Any]:




    '''simple docstring'''




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











import warnings


warnings.warn(
    'memory_utils has been reorganized to utils.memory. Import `find_executable_batchsize` from the main `__init__`: '
    '`from accelerate import find_executable_batch_size` to avoid this warning.',
    FutureWarning,
)



