






import mpmath  # for roots of unity
import numpy as np

class 		lowerCAmelCase     :

					'''simple docstring'''

					def __init__(  self				:	Union[str, Any]		,     __a				:	List[Any]=None		,     __a				:	Optional[Any]=None							)			->  Tuple:


												"""simple docstring"""

												__lowercase      :							Optional[int]				=     list(poly_a or [0]							)[:]
												__lowercase      :							Optional[Any]				=     list(poly_b or [0]							)[:]

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

												while self.polyB[-1] == 0:
																			self.polyB.pop()
												__lowercase      :							Dict				=     len(self.polyB							)

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

												# The product
												__lowercase      :							Tuple				=     self.__multiply()



					def       lowerCAmelCase				(  self				:	Union[str, Any]		,     __a				:	Tuple							)			->  Dict:


												"""simple docstring"""

												__lowercase      :							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]
												#
												__lowercase      :							Any				=     self.c_max_length // 2
												while next_ncol > 0:
																			__lowercase      :							Optional[int]				=     [[] for i in range(UpperCAmelCase__							)]
																			__lowercase      :							Tuple				=     self.root**next_ncol

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



					def       lowerCAmelCase				(  self				:	List[Any]							)			->  List[str]:


												"""simple docstring"""

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


												"""simple docstring"""

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

from . import BaseTransformersCLICommand
def       snake_case_		(     lowerCAmelCase_       :						Dict      ):
							return DownloadCommand(args.model       ,       args.cache_dir       ,       args.force       ,       args.trust_remote_code      )



class 		lowerCAmelCase     ( __a			):

					'''simple docstring'''

					@staticmethod
					def       lowerCAmelCase				(  __a				:	ArgumentParser							)			->  Optional[Any]:


												"""simple docstring"""

												__lowercase      :							Union[str, Any]				=     parser.add_parser("""download"""							)
												download_parser.add_argument(
												    """--cache-dir"""		,     type=__a		,     default=__a		,     help="""Path to location to store the models"""							)
												download_parser.add_argument(
												    """--force"""		,     action="""store_true"""		,     help="""Force the model to be download even if already in cache-dir"""							)
												download_parser.add_argument(
												    """--trust-remote-code"""		,     action="""store_true"""		,     help="""Whether or not to allow for custom models defined on the Hub in their own modeling files. Use only if you've reviewed the code as it will execute on your local machine"""		,     )
												download_parser.add_argument("""model"""		,     type=__a		,     help="""Name of the model to download"""							)
												download_parser.set_defaults(func=__a							)



					def __init__(  self				:	Dict		,     __a				:	str		,     __a				:	str		,     __a				:	bool		,     __a				:	bool							)			->  Union[str, Any]:


												"""simple docstring"""

												__lowercase      :							Dict				=     model
												__lowercase      :							List[Any]				=     cache
												__lowercase      :							Any				=     force
												__lowercase      :							Optional[int]				=     trust_remote_code



					def       lowerCAmelCase				(  self				:	str							)			->  List[str]:


												"""simple docstring"""

												from ..models.auto import AutoModel, AutoTokenizer

												AutoModel.from_pretrained(
												    self._model		,     cache_dir=self._cache		,     force_download=self._force		,     trust_remote_code=self._trust_remote_code							)
												AutoTokenizer.from_pretrained(
												    self._model		,     cache_dir=self._cache		,     force_download=self._force		,     trust_remote_code=self._trust_remote_code							)