import mpmath  # for roots of unity
import numpy as np


class 	lowerCamelCase_     :






    '''simple docstring'''






    def __init__(	self , __lowercase=None , __lowercase=None)       ->	List[Any]:
        # Input as list
        __UpperCamelCase     :Optional[int]			  =		list(poly_a or [0])[:]
        __UpperCamelCase     :Dict			  =		list(poly_b or [0])[:]

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

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

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

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







    def 			UpperCamelCase__   (	self , __lowercase)       ->	List[Any]:
        __UpperCamelCase     :List[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]
        #
        __UpperCamelCase     :Union[str, Any]			  =		self.c_max_length // 2
        while next_ncol > 0:
            __UpperCamelCase     :List[Any]			  =		[[] for i in range(SCREAMING_SNAKE_CASE_)]
            __UpperCamelCase     :str			  =		self.root**next_ncol

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







    def 			UpperCamelCase__   (	self)       ->	Dict:
        __UpperCamelCase     :Optional[Any]			  =		self.__dft('''A''')
        __UpperCamelCase     :int			  =		self.__dft('''B''')
        __UpperCamelCase     :str			  =		[[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     :Optional[Any]			  =		2
        while next_ncol <= self.c_max_length:
            __UpperCamelCase     :Dict			  =		[[] for i in range(SCREAMING_SNAKE_CASE_)]
            __UpperCamelCase     :List[Any]			  =		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     :Dict			  =		new_inverse_c
            next_ncol *= 2
        # Unpack
        __UpperCamelCase     :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)       ->	Optional[int]:
        __UpperCamelCase     :Optional[int]			  =		'''A = ''' + ''' + '''.join(
            f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]))
        __UpperCamelCase     :Dict			  =		'''B = ''' + ''' + '''.join(
            f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]))
        __UpperCamelCase     :List[str]			  =		'''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  lowercase__(				unittest.TestCase							):



	"""simple docstring"""




	def 						_lowercase  (       self  :			List[str]       )       ->     List[Any]:
					lowercase_       =					1_0
	def 						_lowercase  (       self  :			int       )       ->     List[str]:
					lowercase_       =					[1, 2, 3, 4]
					lowercase_       =					[1, 2, 3, 4, 0, 0, 0, 0, 0, 0]
					self.assertEqual(truncate_or_pad(SCREAMING_SNAKE_CASE_       ,							self.block_size       ,							0       )       ,							SCREAMING_SNAKE_CASE_       )
	def 						_lowercase  (       self  :			int       )       ->     Optional[Any]:
					lowercase_       =					[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
					lowercase_       =					[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
					self.assertEqual(truncate_or_pad(SCREAMING_SNAKE_CASE_       ,							self.block_size       ,							0       )       ,							SCREAMING_SNAKE_CASE_       )
	def 						_lowercase  (       self  :			Union[str, Any]       )       ->     Optional[int]:
					lowercase_       =					[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0, 1_1, 1_2, 1_3]
					lowercase_       =					[1, 2, 3, 4, 5, 6, 7, 8, 9, 1_0]
					self.assertEqual(truncate_or_pad(SCREAMING_SNAKE_CASE_       ,							self.block_size       ,							0       )       ,							SCREAMING_SNAKE_CASE_       )
	def 						_lowercase  (       self  :			Any       )       ->     List[Any]:
					lowercase_       =					'''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.'''
					lowercase_  ,	lowercase_       =					process_story(SCREAMING_SNAKE_CASE_       )
					self.assertEqual(SCREAMING_SNAKE_CASE_       ,							[]       )
	def 						_lowercase  (       self  :			List[str]       )       ->     List[str]:
					lowercase_       =					''''''
					lowercase_  ,	lowercase_       =					process_story(SCREAMING_SNAKE_CASE_       )
					self.assertEqual(SCREAMING_SNAKE_CASE_       ,							[]       )
					self.assertEqual(SCREAMING_SNAKE_CASE_       ,							[]       )
	def 						_lowercase  (       self  :			Union[str, Any]       )       ->     Union[str, Any]:
					lowercase_       =					(
					    '''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'''
					)
					lowercase_  ,	lowercase_       =					process_story(SCREAMING_SNAKE_CASE_       )

					lowercase_       =					[
					    '''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(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )

					lowercase_       =					['''It was the best of times.''']
					self.assertEqual(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )
	def 						_lowercase  (       self  :			Union[str, Any]       )       ->     Optional[Any]:
					lowercase_       =					torch.tensor([1, 2, 3, 4]       )
					lowercase_       =					torch.tensor([1, 1, 1, 1]       )
					np.testing.assert_array_equal(build_mask(SCREAMING_SNAKE_CASE_       ,							0       ).numpy()       ,							expected.numpy()       )
	def 						_lowercase  (       self  :			List[Any]       )       ->     Tuple:
					lowercase_       =					torch.tensor([1, 2, 3, 4, 2_3, 2_3, 2_3]       )
					lowercase_       =					torch.tensor([1, 1, 1, 1, 0, 0, 0]       )
					np.testing.assert_array_equal(build_mask(SCREAMING_SNAKE_CASE_       ,							2_3       ).numpy()       ,							expected.numpy()       )
	def 						_lowercase  (       self  :			int       )       ->     Dict:
					lowercase_       =					torch.tensor([8, 2, 3, 4, 1, 1, 1]       )
					lowercase_       =					torch.tensor([1, 1, 1, 1, 0, 0, 0]       )
					np.testing.assert_array_equal(build_mask(SCREAMING_SNAKE_CASE_       ,							1       ).numpy()       ,							expected.numpy()       )




	def 						_lowercase  (       self  :			List[str]       )       ->     Tuple:
					lowercase_       =					1_0_1
					lowercase_       =					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]]       )
					lowercase_       =					torch.tensor([[1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1]]       )

					lowercase_       =					compute_token_type_ids(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )
					np.testing.assert_array_equal(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )




