


"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np




class 			__snake_case   :




							def __init__(     self:    List[str]     ,							A_:    Optional[Any]=None     ,							A_:    Optional[Any]=None   ):
										# 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   __a   (     self:    Optional[Any]     ,							A_:    List[Any]   ):
										__lowerCamelCase          =      [[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]
										#
										__lowerCamelCase          =      self.c_max_length // 2
										while next_ncol > 0:
													__lowerCamelCase          =      [[] for i in range(SCREAMING_SNAKE_CASE_   )]
													__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(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
													__lowerCamelCase          =      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
													__lowerCamelCase          =      new_dft
													__lowerCamelCase          =      next_ncol // 2
										return dft[0]




							def   __a   (     self:    Dict   ):
										__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(SCREAMING_SNAKE_CASE_   )]
													__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:    str   ):
										__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 os
from collections import namedtuple

import pytest

from datasets import ClassLabel, Features, Sequence, Value
from datasets.commands.test import TestCommand
from datasets.info import DatasetInfo, DatasetInfosDict


__a         =   namedtuple(
    '_TestCommandArgs',
    [
        'dataset',
        'name',
        'cache_dir',
        'data_dir',
        'all_configs',
        'save_infos',
        'ignore_verifications',
        'force_redownload',
        'clear_cache',
    ],
    defaults=[None, None, None, False, False, False, False, False],
)




def 							a		(				snake_case__:   Dict		,  snake_case__:   List[str]   ):


				'''simple docstring'''
				return (abs(source - target   ) / target) < 0.0_1




@pytest.mark.integration
def 							a		(				snake_case__:   int   ):


				'''simple docstring'''
				lowercase_	    =   _TestCommandArgs(dataset=snake_case__		,  all_configs=snake_case__		,  save_infos=snake_case__   )
				lowercase_	    =   TestCommand(*snake_case__   )
				test_command.run()
				lowercase_	    =   os.path.join(snake_case__		,  '''README.md'''   )
				assert os.path.exists(snake_case__   )
				lowercase_	    =   DatasetInfosDict.from_directory(snake_case__   )
				lowercase_	    =   DatasetInfosDict(
				    {
				        '''default''': DatasetInfo(
				            features=Features(
				                {
				                    '''tokens''': Sequence(Value('''string'''   )   ),
				                    '''ner_tags''': Sequence(
				                        ClassLabel(names=['''O''', '''B-PER''', '''I-PER''', '''B-ORG''', '''I-ORG''', '''B-LOC''', '''I-LOC''']   )   ),
				                    '''langs''': Sequence(Value('''string'''   )   ),
				                    '''spans''': Sequence(Value('''string'''   )   ),
				                }   )		,  splits=[
				                {
				                    '''name''': '''train''',
				                    '''num_bytes''': 2_351_563,
				                    '''num_examples''': 10_000,
				                },
				                {
				                    '''name''': '''validation''',
				                    '''num_bytes''': 238_418,
				                    '''num_examples''': 1_000,
				                },
				            ]		,  download_size=3_940_680		,  dataset_size=2_589_981		,  )
				    }   )
				assert dataset_infos.keys() == expected_dataset_infos.keys()
				for key in DatasetInfo._INCLUDED_INFO_IN_YAML:
								lowercase_    ,      lowercase_	    =   getattr(dataset_infos['''default''']		,  snake_case__   ), getattr(expected_dataset_infos['''default''']		,  snake_case__   )
								if key == "num_bytes":
												assert is_apercent_close(snake_case__		,  snake_case__   )
								elif key == "splits":
												assert list(snake_case__   ) == list(snake_case__   )
												for split in result:
																assert result[split].name == expected[split].name
																assert result[split].num_examples == expected[split].num_examples
																assert is_apercent_close(result[split].num_bytes		,  expected[split].num_bytes   )
								else:
												result == expected




