




import mpmath  # for roots of unity
import numpy as np


class     UpperCamelCase_   :

    '''simple docstring'''






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





           '''simple docstring'''

           A__							=   list(poly_a or [0])[:]
           A__							=   list(poly_b or [0])[:]

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

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

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

           # The product
           A__							=   self.__multiply()


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str] ,			UpperCAmelCase__				:     List[str])						->Dict:





           '''simple docstring'''

           A__							=   [[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]
           #
           A__							=   self.c_max_length // 2
           while next_ncol > 0:
                  A__							=   [[] for i in range(UpperCAmelCase__)]
                  A__							=   self.root**next_ncol

                  # First half of next step
                  A__							=   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
                  A__							=   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
                  A__							=   new_dft
                  A__							=   next_ncol // 2
           return dft[0]


    def 	SCREAMING_SNAKE_CASE							(      self				:     int)						->Any:





           '''simple docstring'''

           A__							=   self.__dft('''A''')
           A__							=   self.__dft('''B''')
           A__							=   [[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
           A__							=   2
           while next_ncol <= self.c_max_length:
                  A__							=   [[] for i in range(UpperCAmelCase__)]
                  A__							=   self.root ** (next_ncol // 2)
                  A__							=   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
                  A__							=   new_inverse_c
                  next_ncol *= 2
           # Unpack
           A__							=   [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				:     List[str])						->List[str]:





           '''simple docstring'''

           A__							=   '''A = ''' + ''' + '''.join(
               f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]))
           A__							=   '''B = ''' + ''' + '''.join(
               f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]))
           A__							=   '''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_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


_lowerCamelCase     :		Optional[Any]								=       {
    """configuration_trocr""": ["""TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP""", """TrOCRConfig"""],
    """processing_trocr""": ["""TrOCRProcessor"""],
}


try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCamelCase     :		Any								=       [
      """TROCR_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """TrOCRForCausalLM""",
      """TrOCRPreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
  from .processing_trocr import TrOCRProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
  import sys

  _lowerCamelCase     :		List[str]								=       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)


