



import mpmath  # for roots of unity
import numpy as np


class       a							:



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

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

						while self.polyB[-1] == 0:
										self.polyB.pop()
						snake_case__	:      int     		=	len(self.polyB  )

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

						# The product
						snake_case__	:      str     		=	self.__multiply()



		def 	__lowerCamelCase			(     self     :Dict   ,__lowercase     :List[str]  ):
						snake_case__	:      List[Any]     		=	[[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
						# Corner case
						if len(__lowercase  ) <= 1:
										return dft[0]
						#
						snake_case__	:      str     		=	self.c_max_length // 2
						while next_ncol > 0:
										snake_case__	:      Tuple     		=	[[] for i in range(__lowercase  )]
										snake_case__	:      Dict     		=	self.root**next_ncol

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



		def 	__lowerCamelCase			(     self     :str  ):
						snake_case__	:      Optional[int]     		=	self.__dft('''A'''  )
						snake_case__	:      List[Any]     		=	self.__dft('''B'''  )
						snake_case__	:      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
						snake_case__	:      List[Any]     		=	2
						while next_ncol <= self.c_max_length:
										snake_case__	:      List[Any]     		=	[[] for i in range(__lowercase  )]
										snake_case__	:      int     		=	self.root ** (next_ncol // 2)
										snake_case__	:      List[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
										snake_case__	:      Optional[Any]     		=	new_inverse_c
										next_ncol *= 2
						# Unpack
						snake_case__	:      List[str]     		=	[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[int]  ):
						snake_case__	:      str     		=	'''A = ''' + ''' + '''.join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]  )  )
						snake_case__	:      Optional[Any]     		=	'''B = ''' + ''' + '''.join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]  )  )
						snake_case__	:      int     		=	'''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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


A__								=						{
    '''configuration_ctrl''': ['''CTRL_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''CTRLConfig'''],
    '''tokenization_ctrl''': ['''CTRLTokenizer'''],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				A__								=						[
				    '''CTRL_PRETRAINED_MODEL_ARCHIVE_LIST''',
				    '''CTRLForSequenceClassification''',
				    '''CTRLLMHeadModel''',
				    '''CTRLModel''',
				    '''CTRLPreTrainedModel''',
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				A__								=						[
				    '''TF_CTRL_PRETRAINED_MODEL_ARCHIVE_LIST''',
				    '''TFCTRLForSequenceClassification''',
				    '''TFCTRLLMHeadModel''',
				    '''TFCTRLModel''',
				    '''TFCTRLPreTrainedModel''',
				]


if TYPE_CHECKING:
				from .configuration_ctrl import CTRL_PRETRAINED_CONFIG_ARCHIVE_MAP, CTRLConfig
				from .tokenization_ctrl import CTRLTokenizer

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_ctrl import (
								    CTRL_PRETRAINED_MODEL_ARCHIVE_LIST,
								    CTRLForSequenceClassification,
								    CTRLLMHeadModel,
								    CTRLModel,
								    CTRLPreTrainedModel,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_ctrl import (
								    TF_CTRL_PRETRAINED_MODEL_ARCHIVE_LIST,
								    TFCTRLForSequenceClassification,
								    TFCTRLLMHeadModel,
								    TFCTRLModel,
								    TFCTRLPreTrainedModel,
								)

else:
				import sys

				A__								=						_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

