


import mpmath  # for roots of unity
import numpy as np


class 	A_ :




      '''simple docstring'''


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

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

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

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

       # The product
       __lowerCamelCase		:							Optional[int]		 =						self.__multiply()




      def 					_snake_case     (    self:	Tuple						,				a:	Optional[Any]    ):
       __lowerCamelCase		:							List[str]		 =						[[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]
       #
       __lowerCamelCase		:							Any		 =						self.c_max_length // 2
       while next_ncol > 0:
        __lowerCamelCase		:							int		 =						[[] for i in range(a    )]
        __lowerCamelCase		:							Any		 =						self.root**next_ncol

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




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


class 	A_ (	__UpperCamelCase   ):




      '''simple docstring'''


      warnings.warn(
          """Importing `TFGenerationMixin` from `src/transformers/generation_tf_utils.py` is deprecated and will """
          """be removed in Transformers v5. Import as `from transformers import TFGenerationMixin` instead.""" ,				__UpperCamelCase ,				)

