

"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np







class      __lowercase			:

		def __init__(  self		:			List[Any]					,A		:			Dict=None					,A		:			Optional[int]=None    ):






			'''simple docstring'''
			UpperCAmelCase__					:  Any					   =					list(poly_a or [0]    )[:]
			UpperCAmelCase__					:  Dict					   =					list(poly_b or [0]    )[:]

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

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

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

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

		def    __lowercase       (  self		:			Optional[Any]					,A		:			Union[str, Any]    ):






			'''simple docstring'''
			UpperCAmelCase__					:  Tuple					   =					[[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]
			#
			UpperCAmelCase__					:  List[Any]					   =					self.c_max_length // 2
			while next_ncol > 0:
				UpperCAmelCase__					:  str					   =					[[] for i in range(A    )]
				UpperCAmelCase__					:  List[str]					   =					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(A    ):
						new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]    )
					current_root *= root
				# Second half of next step
				UpperCAmelCase__					:  Any					   =					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
				UpperCAmelCase__					:  Tuple					   =					new_dft
				UpperCAmelCase__					:  List[Any]					   =					next_ncol // 2
			return dft[0]

		def    __lowercase       (  self		:			int    ):






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






			'''simple docstring'''
			UpperCAmelCase__					:  Optional[Any]					   =					'''A = ''' + ''' + '''.join(
			    f"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]    )    )
			UpperCAmelCase__					:  List[str]					   =					'''B = ''' + ''' + '''.join(
			    f"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]    )    )
			UpperCAmelCase__					:  Optional[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 typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__UpperCAmelCase =				{
    'configuration_roberta': ['ROBERTA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'RobertaConfig', 'RobertaOnnxConfig'],
    'tokenization_roberta': ['RobertaTokenizer'],
}

try:
      if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase =				['RobertaTokenizerFast']

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase =				[
          'ROBERTA_PRETRAINED_MODEL_ARCHIVE_LIST',
          'RobertaForCausalLM',
          'RobertaForMaskedLM',
          'RobertaForMultipleChoice',
          'RobertaForQuestionAnswering',
          'RobertaForSequenceClassification',
          'RobertaForTokenClassification',
          'RobertaModel',
          'RobertaPreTrainedModel',
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase =				[
          'TF_ROBERTA_PRETRAINED_MODEL_ARCHIVE_LIST',
          'TFRobertaForCausalLM',
          'TFRobertaForMaskedLM',
          'TFRobertaForMultipleChoice',
          'TFRobertaForQuestionAnswering',
          'TFRobertaForSequenceClassification',
          'TFRobertaForTokenClassification',
          'TFRobertaMainLayer',
          'TFRobertaModel',
          'TFRobertaPreTrainedModel',
      ]

try:
      if not is_flax_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase =				[
          'FlaxRobertaForCausalLM',
          'FlaxRobertaForMaskedLM',
          'FlaxRobertaForMultipleChoice',
          'FlaxRobertaForQuestionAnswering',
          'FlaxRobertaForSequenceClassification',
          'FlaxRobertaForTokenClassification',
          'FlaxRobertaModel',
          'FlaxRobertaPreTrainedModel',
      ]


if TYPE_CHECKING:
      from .configuration_roberta import ROBERTA_PRETRAINED_CONFIG_ARCHIVE_MAP, RobertaConfig, RobertaOnnxConfig
      from .tokenization_roberta import RobertaTokenizer

      try:
            if not is_tokenizers_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_roberta_fast import RobertaTokenizerFast

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_roberta import (
                ROBERTA_PRETRAINED_MODEL_ARCHIVE_LIST,
                RobertaForCausalLM,
                RobertaForMaskedLM,
                RobertaForMultipleChoice,
                RobertaForQuestionAnswering,
                RobertaForSequenceClassification,
                RobertaForTokenClassification,
                RobertaModel,
                RobertaPreTrainedModel,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_roberta import (
                TF_ROBERTA_PRETRAINED_MODEL_ARCHIVE_LIST,
                TFRobertaForCausalLM,
                TFRobertaForMaskedLM,
                TFRobertaForMultipleChoice,
                TFRobertaForQuestionAnswering,
                TFRobertaForSequenceClassification,
                TFRobertaForTokenClassification,
                TFRobertaMainLayer,
                TFRobertaModel,
                TFRobertaPreTrainedModel,
            )

      try:
            if not is_flax_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_flax_roberta import (
                FlaxRobertaForCausalLM,
                FlaxRobertaForMaskedLM,
                FlaxRobertaForMultipleChoice,
                FlaxRobertaForQuestionAnswering,
                FlaxRobertaForSequenceClassification,
                FlaxRobertaForTokenClassification,
                FlaxRobertaModel,
                FlaxRobertaPreTrainedModel,
            )

else:
      import sys

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





