


'''simple docstring'''







import mpmath  # for roots of unity
import numpy as np
class 					lowercase_     :


    def __init__(     self  ,					a=None  ,					a=None    ):
          # Input as list
          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    __a							(     self  ,					a    ):
          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    __a							(     self    ):
          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    ):
          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()






from ..utils import DummyObject, requires_backends




class    _UpperCamelCase      (						metaclass=_UpperCAmelCase ):


			"""simple docstring"""






			__a  : Dict			 =						['''keras_nlp''']





			def __init__(   self      ,   *lowerCAmelCase__      ,   **lowerCAmelCase__						)     ->					Tuple:

							'''simple docstring'''


							requires_backends(self      ,   ['''keras_nlp''']						)