
"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np



class 	lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__=None   ,       SCREAMING_SNAKE_CASE__=None    )					->		Dict:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   list(poly_a or [0]    )[:]
											SCREAMING_SNAKE_CASE__						:       Tuple           =   list(poly_b or [0]    )[:]

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

											while self.polyB[-1] == 0:
																		self.polyB.pop()
											SCREAMING_SNAKE_CASE__						:       List[str]           =   len(self.polyB    )

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

											# The product
											SCREAMING_SNAKE_CASE__						:       Tuple           =   self.__multiply()



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Union[str, Any]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       str           =   [[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
											# Corner case
											if len(SCREAMING_SNAKE_CASE__    ) <= 1:
																		return dft[0]
											#
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   self.c_max_length // 2
											while next_ncol > 0:
																		SCREAMING_SNAKE_CASE__						:       Any           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root**next_ncol

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



				def 	__magic_name__    (self    )					->		int:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self.__dft("""A"""    )
											SCREAMING_SNAKE_CASE__						:       Dict           =   self.__dft("""B"""    )
											SCREAMING_SNAKE_CASE__						:       List[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
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   2
											while next_ncol <= self.c_max_length:
																		SCREAMING_SNAKE_CASE__						:       List[str]           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root ** (next_ncol // 2)
																		SCREAMING_SNAKE_CASE__						:       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
																		SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   new_inverse_c
																		next_ncol *= 2
											# Unpack
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   [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]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[str]           =   """A = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   """B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
											SCREAMING_SNAKE_CASE__						:       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()











"""simple docstring"""





import unittest

import numpy as np
import torch

from .utils_summarization import build_mask, compute_token_type_ids, process_story, truncate_or_pad






class 					_lowerCAmelCase   (     unittest.TestCase       ):
       """simple docstring"""




       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Dict											=							1_0






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Optional[int]											=							[1, 2, 3, 4]
         lowerCAmelCase__			:Tuple											=							[1, 2, 3, 4, 0, 0, 0, 0, 0, 0]
         self.assertEqual(truncate_or_pad(__UpperCAmelCase    , self.block_size    , 0      )    , __UpperCAmelCase      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Optional[Any]											=							[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
         lowerCAmelCase__			:List[Any]											=							[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
         self.assertEqual(truncate_or_pad(__UpperCAmelCase    , self.block_size    , 0      )    , __UpperCAmelCase      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Dict											=							[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0, 1_1, 1_2, 1_3]
         lowerCAmelCase__			:List[Any]											=							[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
         self.assertEqual(truncate_or_pad(__UpperCAmelCase    , self.block_size    , 0      )    , __UpperCAmelCase      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Tuple											=							'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__			:List[Any]											=							process_story(__UpperCAmelCase      )
         self.assertEqual(__UpperCAmelCase    , []      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Any											=							''
         lowerCAmelCase__							,				lowerCAmelCase__			:Any											=							process_story(__UpperCAmelCase      )
         self.assertEqual(__UpperCAmelCase    , []      )
         self.assertEqual(__UpperCAmelCase    , []      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:List[str]											=							(
             '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__			:str											=							process_story(__UpperCAmelCase      )

         lowerCAmelCase__			:List[str]											=							[
             '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(__UpperCAmelCase    , __UpperCAmelCase      )

         lowerCAmelCase__			:List[str]											=							['It was the best of times.']
         self.assertEqual(__UpperCAmelCase    , __UpperCAmelCase      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Tuple											=							torch.tensor([1, 2, 3, 4]      )
         lowerCAmelCase__			:List[str]											=							torch.tensor([1, 1, 1, 1]      )
         np.testing.assert_array_equal(build_mask(__UpperCAmelCase    , 0      ).numpy()    , expected.numpy()      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:List[Any]											=							torch.tensor([1, 2, 3, 4, 2_3, 2_3, 2_3]      )
         lowerCAmelCase__			:Optional[int]											=							torch.tensor([1, 1, 1, 1, 0, 0, 0]      )
         np.testing.assert_array_equal(build_mask(__UpperCAmelCase    , 2_3      ).numpy()    , expected.numpy()      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:List[Any]											=							torch.tensor([8, 2, 3, 4, 1, 1, 1]      )
         lowerCAmelCase__			:Optional[Any]											=							torch.tensor([1, 1, 1, 1, 0, 0, 0]      )
         np.testing.assert_array_equal(build_mask(__UpperCAmelCase    , 1      ).numpy()    , expected.numpy()      )






       def      snake_case						(    self      ):



         '''simple docstring'''

         lowerCAmelCase__			:Optional[Any]											=							1_0_1
         lowerCAmelCase__			:str											=							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__			:Any											=							torch.tensor([[1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1]]      )

         lowerCAmelCase__			:List[Any]											=							compute_token_type_ids(__UpperCAmelCase    , __UpperCAmelCase      )
         np.testing.assert_array_equal(__UpperCAmelCase    , __UpperCAmelCase      )
