





import mpmath  # for roots of unity
import numpy as np



class     _UpperCAmelCase   :

   """simple docstring"""


   def __init__(    self			:		List[Any] ,  lowerCAmelCase_			:		Dict=None ,  lowerCAmelCase_			:		str=None					)							->						List[Any]:
      # Input as list
      __lowerCAmelCase							     =     list(poly_a or [0]					)[:]
      __lowerCAmelCase							     =     list(poly_b or [0]					)[:]

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

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

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

      # The product
      __lowerCAmelCase							     =     self.__multiply()






   def     lowercase		(    self			:		Optional[int] ,  lowerCAmelCase_			:		str					)							->						Optional[int]:
      __lowerCAmelCase							     =     [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
      # Corner case
      if len(lowerCAmelCase_					) <= 1:
         return dft[0]
      #
      __lowerCAmelCase							     =     self.c_max_length // 2
      while next_ncol > 0:
         __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
         __lowerCAmelCase							     =     self.root**next_ncol

         # First half of next step
         __lowerCAmelCase							     =     1
         for j in range(self.c_max_length // (next_ncol * 2)					):
            for i in range(lowerCAmelCase_					):
               new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]					)
            current_root *= root
         # Second half of next step
         __lowerCAmelCase							     =     1
         for j in range(self.c_max_length // (next_ncol * 2)					):
            for i in range(lowerCAmelCase_					):
               new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]					)
            current_root *= root
         # Update
         __lowerCAmelCase							     =     new_dft
         __lowerCAmelCase							     =     next_ncol // 2
      return dft[0]






   def     lowercase		(    self			:		Optional[int]					)							->						Any:
      __lowerCAmelCase							     =     self.__dft('A'					)
      __lowerCAmelCase							     =     self.__dft('B'					)
      __lowerCAmelCase							     =     [[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							     =     2
      while next_ncol <= self.c_max_length:
         __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
         __lowerCAmelCase							     =     self.root ** (next_ncol // 2)
         __lowerCAmelCase							     =     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							     =     new_inverse_c
         next_ncol *= 2
      # Unpack
      __lowerCAmelCase							     =     [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					)							->						int:
      __lowerCAmelCase							     =     'A = ' + ' + '.join(
          f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]					)					)
      __lowerCAmelCase							     =     'B = ' + ' + '.join(
          f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]					)					)
      __lowerCAmelCase							     =     '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()








import unittest

import numpy as np
import torch

from .utils_summarization import build_mask, compute_token_type_ids, process_story, truncate_or_pad



class     _UpperCAmelCase   (   unittest.TestCase   ):

  """simple docstring"""


  def     lowercase		(    self			:		Any					)							->						Optional[int]:
     __lowerCAmelCase							     =     1_0






  def     lowercase		(    self			:		int					)							->						Union[str, Any]:
     __lowerCAmelCase							     =     [1, 2, 3, 4]
     __lowerCAmelCase							     =     [1, 2, 3, 4, 0, 0, 0, 0, 0, 0]
     self.assertEqual(truncate_or_pad(lowerCAmelCase_ ,  self.block_size ,  0					) ,  lowerCAmelCase_					)






  def     lowercase		(    self			:		Optional[Any]					)							->						List[str]:
     __lowerCAmelCase							     =     [1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
     __lowerCAmelCase							     =     [1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
     self.assertEqual(truncate_or_pad(lowerCAmelCase_ ,  self.block_size ,  0					) ,  lowerCAmelCase_					)






  def     lowercase		(    self			:		Any					)							->						Optional[Any]:
     __lowerCAmelCase							     =     [1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0, 1_1, 1_2, 1_3]
     __lowerCAmelCase							     =     [1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
     self.assertEqual(truncate_or_pad(lowerCAmelCase_ ,  self.block_size ,  0					) ,  lowerCAmelCase_					)






  def     lowercase		(    self			:		List[str]					)							->						Any:
     __lowerCAmelCase							     =     'It was the year of Our Lord one thousand seven hundred and\n        seventy-five.\n\nSpiritual revelations were conceded to England at that\n        favoured period, as at this.'
     __lowerCAmelCase     ,     __lowerCAmelCase							     =     process_story(lowerCAmelCase_					)
     self.assertEqual(lowerCAmelCase_ ,  []					)






  def     lowercase		(    self			:		Any					)							->						str:
     __lowerCAmelCase							     =     ''
     __lowerCAmelCase     ,     __lowerCAmelCase							     =     process_story(lowerCAmelCase_					)
     self.assertEqual(lowerCAmelCase_ ,  []					)
     self.assertEqual(lowerCAmelCase_ ,  []					)






  def     lowercase		(    self			:		int					)							->						int:
     __lowerCAmelCase							     =     (
         'It was the year of Our Lord one thousand seven hundred and '
         'seventy-five\n\nSpiritual revelations were conceded to England '
         'at that favoured period, as at this.\n@highlight\n\nIt was the best of times'
     )
     __lowerCAmelCase     ,     __lowerCAmelCase							     =     process_story(lowerCAmelCase_					)

     __lowerCAmelCase							     =     [
         'It was the year of Our Lord one thousand seven hundred and seventy-five.',
         'Spiritual revelations were conceded to England at that favoured period, as at this.',
     ]
     self.assertEqual(lowerCAmelCase_ ,  lowerCAmelCase_					)

     __lowerCAmelCase							     =     ['It was the best of times.']
     self.assertEqual(lowerCAmelCase_ ,  lowerCAmelCase_					)






  def     lowercase		(    self			:		Dict					)							->						Any:
     __lowerCAmelCase							     =     torch.tensor([1, 2, 3, 4]					)
     __lowerCAmelCase							     =     torch.tensor([1, 1, 1, 1]					)
     np.testing.assert_array_equal(build_mask(lowerCAmelCase_ ,  0					).numpy() ,  expected.numpy()					)






  def     lowercase		(    self			:		List[Any]					)							->						Optional[int]:
     __lowerCAmelCase							     =     torch.tensor([1, 2, 3, 4, 2_3, 2_3, 2_3]					)
     __lowerCAmelCase							     =     torch.tensor([1, 1, 1, 1, 0, 0, 0]					)
     np.testing.assert_array_equal(build_mask(lowerCAmelCase_ ,  2_3					).numpy() ,  expected.numpy()					)






  def     lowercase		(    self			:		str					)							->						List[Any]:
     __lowerCAmelCase							     =     torch.tensor([8, 2, 3, 4, 1, 1, 1]					)
     __lowerCAmelCase							     =     torch.tensor([1, 1, 1, 1, 0, 0, 0]					)
     np.testing.assert_array_equal(build_mask(lowerCAmelCase_ ,  1					).numpy() ,  expected.numpy()					)






  def     lowercase		(    self			:		Optional[Any]					)							->						Optional[int]:
     __lowerCAmelCase							     =     1_0_1
     __lowerCAmelCase							     =     torch.tensor([[1, 2, 3, 4, 5, 6], [1, 2, 3, 1_0_1, 5, 6], [1, 1_0_1, 3, 4, 1_0_1, 6]]					)
     __lowerCAmelCase							     =     torch.tensor([[1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1]]					)

     __lowerCAmelCase							     =     compute_token_type_ids(lowerCAmelCase_ ,  lowerCAmelCase_					)
     np.testing.assert_array_equal(lowerCAmelCase_ ,  lowerCAmelCase_					)

