


'''simple docstring'''
import mpmath  # for roots of unity
import numpy as np
class        lowercase     :

		"""simple docstring"""

		def __init__(		self   ,       UpperCamelCase_=None   ,       UpperCamelCase_=None							):

							'''simple docstring'''


							UpperCamelCase__       :List[Any]							 =			list(poly_a or [0]							)[:]
							UpperCamelCase__       :str							 =			list(poly_b or [0]							)[:]

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

							while self.polyB[-1] == 0:
												self.polyB.pop()
							UpperCamelCase__       :Union[str, Any]							 =			len(self.polyB							)

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

							# The product
							UpperCamelCase__       :int							 =			self.__multiply()




		def    lowerCAmelCase__    (		self   ,       UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__       :List[str]							 =			[[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]
							#
							UpperCamelCase__       :List[str]							 =			self.c_max_length // 2
							while next_ncol > 0:
												UpperCamelCase__       :List[Any]							 =			[[] for i in range(UpperCamelCase_							)]
												UpperCamelCase__       :Dict							 =			self.root**next_ncol

												# First half of next step
												UpperCamelCase__       :Tuple							 =			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
												UpperCamelCase__       :Tuple							 =			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
												UpperCamelCase__       :Tuple							 =			new_dft
												UpperCamelCase__       :List[Any]							 =			next_ncol // 2
							return dft[0]




		def    lowerCAmelCase__    (		self							):

							'''simple docstring'''


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

							'''simple docstring'''


							UpperCamelCase__       :str							 =			'''A = ''' + ''' + '''.join(
							    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
							UpperCamelCase__       :Dict							 =			'''B = ''' + ''' + '''.join(
							    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
							UpperCamelCase__       :List[Any]							 =			'''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'''
from argparse import ArgumentParser

from .env import EnvironmentCommand


def       a				(      )  ->     Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__       :Union[str, Any]							 =			ArgumentParser('''Diffusers CLI tool'''			, usage='''diffusers-cli <command> [<args>]'''       )
					UpperCamelCase__       :Union[str, Any]							 =			parser.add_subparsers(help='''diffusers-cli command helpers'''       )

					# Register commands
					EnvironmentCommand.register_subcommand(__a       )

					# Let's go
					UpperCamelCase__       :Optional[int]							 =			parser.parse_args()

					if not hasattr(__a			, '''func'''       ):
										parser.print_help()
										exit(1       )

					# Run
					UpperCamelCase__       :Optional[int]							 =			args.func(__a       )
					service.run()


if __name__ == "__main__":
		main()