
import mpmath  # for roots of unity
import numpy as np

class __snake_case		:
    def __init__(  self		,snake_case=None		,snake_case=None      ):



           '''simple docstring'''







           lowercase							:     List[str]       	=      list(poly_a or [0]      )[:]
           lowercase							:     List[str]       	=      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							:     List[str]       	=      len(self.polyB      )

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

           # The product
           lowercase							:     Any       	=      self.__multiply()
    def       _SCREAMING_SNAKE_CASE       (  self		,snake_case      ):



           '''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(snake_case      ) <= 1:
                  return dft[0]
           #
           lowercase							:     Optional[Any]       	=      self.c_max_length // 2
           while next_ncol > 0:
                  lowercase							:     Tuple       	=      [[] for i in range(snake_case      )]
                  lowercase							:     int       	=      self.root**next_ncol

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



           '''simple docstring'''







           lowercase							:     Optional[Any]       	=      self.__dft("""A"""      )
           lowercase							:     List[str]       	=      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							:     Dict       	=      2
           while next_ncol <= self.c_max_length:
                  lowercase							:     Any       	=      [[] for i in range(snake_case      )]
                  lowercase							:     Optional[Any]       	=      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							:     str       	=      new_inverse_c
                  next_ncol *= 2
           # Unpack
           lowercase							:     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      ):



           '''simple docstring'''







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


from typing import TYPE_CHECKING

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


lowercase  :					str						    =							{
    """configuration_funnel""": ["""FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP""", """FunnelConfig"""],
    """convert_funnel_original_tf_checkpoint_to_pytorch""": [],
    """tokenization_funnel""": ["""FunnelTokenizer"""],
}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase  :					Tuple						    =							["""FunnelTokenizerFast"""]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase  :					List[str]						    =							[
      """FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """FunnelBaseModel""",
      """FunnelForMaskedLM""",
      """FunnelForMultipleChoice""",
      """FunnelForPreTraining""",
      """FunnelForQuestionAnswering""",
      """FunnelForSequenceClassification""",
      """FunnelForTokenClassification""",
      """FunnelModel""",
      """FunnelPreTrainedModel""",
      """load_tf_weights_in_funnel""",
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase  :					Optional[Any]						    =							[
      """TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """TFFunnelBaseModel""",
      """TFFunnelForMaskedLM""",
      """TFFunnelForMultipleChoice""",
      """TFFunnelForPreTraining""",
      """TFFunnelForQuestionAnswering""",
      """TFFunnelForSequenceClassification""",
      """TFFunnelForTokenClassification""",
      """TFFunnelModel""",
      """TFFunnelPreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_funnel import FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP, FunnelConfig
  from .tokenization_funnel import FunnelTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_funnel_fast import FunnelTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_funnel import (
        FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
        FunnelBaseModel,
        FunnelForMaskedLM,
        FunnelForMultipleChoice,
        FunnelForPreTraining,
        FunnelForQuestionAnswering,
        FunnelForSequenceClassification,
        FunnelForTokenClassification,
        FunnelModel,
        FunnelPreTrainedModel,
        load_tf_weights_in_funnel,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_funnel import (
        TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFFunnelBaseModel,
        TFFunnelForMaskedLM,
        TFFunnelForMultipleChoice,
        TFFunnelForPreTraining,
        TFFunnelForQuestionAnswering,
        TFFunnelForSequenceClassification,
        TFFunnelForTokenClassification,
        TFFunnelModel,
        TFFunnelPreTrainedModel,
    )

else:
  import sys

  lowercase  :					Any						    =							_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
