


import mpmath  # for roots of unity
import numpy as np

class       __magic_name__	:


     def __init__(      self							:     int							,	lowerCamelCase__							:     int=None							,	lowerCamelCase__							:     Tuple=None			)  ->      List[str]:





      '''simple docstring'''






      UpperCamelCase__					:    int          =   list(poly_a or [0]			)[:]
      UpperCamelCase__					:    Optional[Any]          =   list(poly_b or [0]			)[:]

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

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

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

      # The product
      UpperCamelCase__					:    Optional[Any]          =   self.__multiply()


     def      UpperCAmelCase__	(      self							:     Tuple							,	lowerCamelCase__							:     int			)  ->      Any:





      '''simple docstring'''






      UpperCamelCase__					:    Optional[int]          =   [[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]
      #
      UpperCamelCase__					:    Optional[Any]          =   self.c_max_length // 2
      while next_ncol > 0:
       UpperCamelCase__					:    Any          =   [[] for i in range(UpperCamelCase__			)]
       UpperCamelCase__					:    Tuple          =   self.root**next_ncol

       # First half of next step
       UpperCamelCase__					:    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
       UpperCamelCase__					:    Any          =   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
       UpperCamelCase__					:    str          =   new_dft
       UpperCamelCase__					:    int          =   next_ncol // 2
      return dft[0]


     def      UpperCAmelCase__	(      self							:     Tuple			)  ->      int:





      '''simple docstring'''






      UpperCamelCase__					:    str          =   self.__dft('''A'''			)
      UpperCamelCase__					:    List[Any]          =   self.__dft('''B'''			)
      UpperCamelCase__					:    Dict          =   [[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__					:    List[Any]          =   2
      while next_ncol <= self.c_max_length:
       UpperCamelCase__					:    List[str]          =   [[] for i in range(UpperCamelCase__			)]
       UpperCamelCase__					:    Tuple          =   self.root ** (next_ncol // 2)
       UpperCamelCase__					:    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
       UpperCamelCase__					:    int          =   new_inverse_c
       next_ncol *= 2
      # Unpack
      UpperCamelCase__					:    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							:     Tuple			)  ->      Dict:





      '''simple docstring'''






      UpperCamelCase__					:    Any          =   'A = ' + ' + '.join(
          F"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]			)			)
      UpperCamelCase__					:    Union[str, Any]          =   'B = ' + ' + '.join(
          F"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]			)			)
      UpperCamelCase__					:    Union[str, 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 ...configuration_utils import PretrainedConfig
from ...utils import logging


__UpperCamelCase       :       Optional[int]						       =				logging.get_logger(__name__)

__UpperCamelCase       :       Optional[int]						       =				{
    "microsoft/markuplm-base": "https://huggingface.co/microsoft/markuplm-base/resolve/main/config.json",
    "microsoft/markuplm-large": "https://huggingface.co/microsoft/markuplm-large/resolve/main/config.json",
}

class       __magic_name__	(     __lowerCAmelCase):
     A:		Optional[Any]			=      "markuplm"


     def __init__(      self							:     List[Any]							,	lowerCamelCase__							:     Optional[int]=30522							,	lowerCamelCase__							:     Dict=768							,	lowerCamelCase__							:     List[str]=12							,	lowerCamelCase__							:     List[Any]=12							,	lowerCamelCase__							:     Optional[Any]=3072							,	lowerCamelCase__							:     int="gelu"							,	lowerCamelCase__							:     Union[str, Any]=0.1							,	lowerCamelCase__							:     Optional[int]=0.1							,	lowerCamelCase__							:     Tuple=512							,	lowerCamelCase__							:     List[str]=2							,	lowerCamelCase__							:     Union[str, Any]=0.02							,	lowerCamelCase__							:     Optional[Any]=1E-1_2							,	lowerCamelCase__							:     List[str]=0							,	lowerCamelCase__							:     Tuple=0							,	lowerCamelCase__							:     List[str]=2							,	lowerCamelCase__							:     List[Any]=256							,	lowerCamelCase__							:     List[str]=1024							,	lowerCamelCase__							:     Optional[int]=216							,	lowerCamelCase__							:     Any=1001							,	lowerCamelCase__							:     int=32							,	lowerCamelCase__							:     Tuple=50							,	lowerCamelCase__							:     str="absolute"							,	lowerCamelCase__							:     List[str]=True							,	lowerCamelCase__							:     List[Any]=None							,	**lowerCamelCase__							:     List[str]							,	)  ->      Union[str, Any]:





      '''simple docstring'''






      super().__init__(
          pad_token_id=lowerCamelCase__							,	bos_token_id=lowerCamelCase__							,	eos_token_id=lowerCamelCase__							,	**lowerCamelCase__							,	)
      UpperCamelCase__					:    Optional[int]          =   vocab_size
      UpperCamelCase__					:    List[Any]          =   hidden_size
      UpperCamelCase__					:    Any          =   num_hidden_layers
      UpperCamelCase__					:    Tuple          =   num_attention_heads
      UpperCamelCase__					:    Any          =   hidden_act
      UpperCamelCase__					:    Dict          =   intermediate_size
      UpperCamelCase__					:    Optional[Any]          =   hidden_dropout_prob
      UpperCamelCase__					:    Optional[int]          =   attention_probs_dropout_prob
      UpperCamelCase__					:    Tuple          =   max_position_embeddings
      UpperCamelCase__					:    List[str]          =   type_vocab_size
      UpperCamelCase__					:    Any          =   initializer_range
      UpperCamelCase__					:    Dict          =   layer_norm_eps
      UpperCamelCase__					:    Any          =   position_embedding_type
      UpperCamelCase__					:    Optional[Any]          =   use_cache
      UpperCamelCase__					:    int          =   classifier_dropout
      # additional properties
      UpperCamelCase__					:    int          =   max_depth
      UpperCamelCase__					:    Optional[Any]          =   max_xpath_tag_unit_embeddings
      UpperCamelCase__					:    List[Any]          =   max_xpath_subs_unit_embeddings
      UpperCamelCase__					:    List[Any]          =   tag_pad_id
      UpperCamelCase__					:    Optional[int]          =   subs_pad_id
      UpperCamelCase__					:    Optional[Any]          =   xpath_unit_hidden_size


