'''simple docstring'''





from typing import TYPE_CHECKING

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


SCREAMING_SNAKE_CASE_:     int  ={
    'configuration_ernie': ['ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ErnieConfig', 'ErnieOnnxConfig'],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    SCREAMING_SNAKE_CASE_:     List[str]  =[
        'ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST',
        'ErnieForCausalLM',
        'ErnieForMaskedLM',
        'ErnieForMultipleChoice',
        'ErnieForNextSentencePrediction',
        'ErnieForPreTraining',
        'ErnieForQuestionAnswering',
        'ErnieForSequenceClassification',
        'ErnieForTokenClassification',
        'ErnieModel',
        'ErniePreTrainedModel',
    ]

if TYPE_CHECKING:
    from .configuration_ernie import ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP, ErnieConfig, ErnieOnnxConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_ernie import (
            ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST,
            ErnieForCausalLM,
            ErnieForMaskedLM,
            ErnieForMultipleChoice,
            ErnieForNextSentencePrediction,
            ErnieForPreTraining,
            ErnieForQuestionAnswering,
            ErnieForSequenceClassification,
            ErnieForTokenClassification,
            ErnieModel,
            ErniePreTrainedModel,
        )

else:
    import sys

    SCREAMING_SNAKE_CASE_:     Union[str, Any]  =_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)








"""simple docstring"""





import mpmath  # for roots of unity
import numpy as np



class 						snake_case_:






     def __init__(		self     :    str    , UpperCamelCase_     :    int=None    , UpperCamelCase_     :    List[str]=None ):
           # Input as list
           lowerCAmelCase    :		str				=      list(poly_a or [0] )[:]
           lowerCAmelCase    :		Any				=      list(poly_b or [0] )[:]

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

           while self.polyB[-1] == 0:
                 self.polyB.pop()
           lowerCAmelCase    :		Union[str, Any]				=      len(self.polyB )

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

           # The product
           lowerCAmelCase    :		int				=      self.__multiply()






     def    lowerCamelCase__   (		self     :    List[str]    , UpperCamelCase_     :    str ):
           lowerCAmelCase    :		Optional[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]
           #
           lowerCAmelCase    :		Tuple				=      self.c_max_length // 2
           while next_ncol > 0:
                 lowerCAmelCase    :		Dict				=      [[] for i in range(UpperCamelCase_ )]
                 lowerCAmelCase    :		List[Any]				=      self.root**next_ncol

                 # First half of next step
                 lowerCAmelCase    :		Dict				=      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
                 lowerCAmelCase    :		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
                 lowerCAmelCase    :		Optional[Any]				=      new_dft
                 lowerCAmelCase    :		Union[str, Any]				=      next_ncol // 2
           return dft[0]






     def    lowerCamelCase__   (		self     :    List[Any] ):
           lowerCAmelCase    :		Optional[Any]				=      self.__dft('''A''' )
           lowerCAmelCase    :		Optional[int]				=      self.__dft('''B''' )
           lowerCAmelCase    :		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
           lowerCAmelCase    :		str				=      2
           while next_ncol <= self.c_max_length:
                 lowerCAmelCase    :		Union[str, Any]				=      [[] for i in range(UpperCamelCase_ )]
                 lowerCAmelCase    :		Optional[Any]				=      self.root ** (next_ncol // 2)
                 lowerCAmelCase    :		Tuple				=      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
                 lowerCAmelCase    :		Any				=      new_inverse_c
                 next_ncol *= 2
           # Unpack
           lowerCAmelCase    :		Optional[int]				=      [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     :    int ):
           lowerCAmelCase    :		int				=      '''A = ''' + ''' + '''.join(
               F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A] ) )
           lowerCAmelCase    :		str				=      '''B = ''' + ''' + '''.join(
               F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B] ) )
           lowerCAmelCase    :		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()


