




import mpmath  # for roots of unity
import numpy as np






class  _lowerCAmelCase     :

      def __init__(   self      ,				__UpperCAmelCase=None      ,				__UpperCAmelCase=None		):
        # Input as list
        lowerCAmelCase__				:  Tuple		       =     list(poly_a or [0]		)[:]
        lowerCAmelCase__				:  List[Any]		       =     list(poly_b or [0]		)[:]

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

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

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

        # The product
        lowerCAmelCase__				:  str		       =     self.__multiply()

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Union[str, Any]		       =     [[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]
        #
        lowerCAmelCase__				:  int		       =     self.c_max_length // 2
        while next_ncol > 0:
          lowerCAmelCase__				:  List[str]		       =     [[] for i in range(__UpperCAmelCase		)]
          lowerCAmelCase__				:  int		       =     self.root**next_ncol

          # First half of next step
          lowerCAmelCase__				:  Optional[Any]		       =     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
          lowerCAmelCase__				:  Dict		       =     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
          lowerCAmelCase__				:  Optional[int]		       =     new_dft
          lowerCAmelCase__				:  List[Any]		       =     next_ncol // 2
        return dft[0]

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

from diffusers import StableDiffusionInpaintPipeline as StableDiffusionInpaintPipeline  # noqa F401


warnings.warn(
    """The `inpainting.py` script is outdated. Please use directly `from diffusers import"""
    """ StableDiffusionInpaintPipeline` instead."""
)

