





"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np




class 			_a						:






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




										'''simple docstring'''



										_UpperCamelCase      : Tuple         =   list(poly_a or [0]							)[:]
										_UpperCamelCase      : int         =   list(poly_b or [0]							)[:]

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

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

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

										# The product
										_UpperCamelCase      : Dict         =   self.__multiply()






				def     snake_case     (			self		:   Dict,			lowerCAmelCase__		:   Optional[int]							)     ->				List[str]:




										'''simple docstring'''



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

																# First half of next step
																_UpperCamelCase      : Union[str, Any]         =   1
																for j in range(self.c_max_length // (next_ncol * 2)							):
																						for i in range(lowerCAmelCase__							):
																												new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]							)
																						current_root *= root
																# Second half of next step
																_UpperCamelCase      : Dict         =   1
																for j in range(self.c_max_length // (next_ncol * 2)							):
																						for i in range(lowerCAmelCase__							):
																												new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]							)
																						current_root *= root
																# Update
																_UpperCamelCase      : int         =   new_dft
																_UpperCamelCase      : Optional[Any]         =   next_ncol // 2
										return dft[0]






				def     snake_case     (			self		:   Any							)     ->				List[Any]:




										'''simple docstring'''



										_UpperCamelCase      : Optional[int]         =   self.__dft('''A'''							)
										_UpperCamelCase      : Union[str, Any]         =   self.__dft('''B'''							)
										_UpperCamelCase      : 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
										_UpperCamelCase      : Optional[Any]         =   2
										while next_ncol <= self.c_max_length:
																_UpperCamelCase      : Tuple         =   [[] for i in range(lowerCAmelCase__							)]
																_UpperCamelCase      : Optional[int]         =   self.root ** (next_ncol // 2)
																_UpperCamelCase      : Union[str, 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
																_UpperCamelCase      : str         =   new_inverse_c
																next_ncol *= 2
										# Unpack
										_UpperCamelCase      : List[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		:   Optional[Any]							)     ->				Union[str, Any]:




										'''simple docstring'''



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










"""simple docstring"""




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."""
)



