
"""simple docstring"""
import mpmath  # for roots of unity
import numpy as np

class __lowercase:




					'''simple docstring'''


					def __init__(    self						,	__a=None						,	__a=None     ):
								__lowerCamelCase					:	Optional[int]	       =				list(poly_a or [0]     )[:]
								__lowerCamelCase					:	Optional[Any]	       =				list(poly_b or [0]     )[:]

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

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

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

								# The product
								__lowerCamelCase					:	Tuple	       =				self.__multiply()
					def     snake_case_				(    self						,	__a     ):
								__lowerCamelCase					:	Union[str, Any]	       =				[[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]
								#
								__lowerCamelCase					:	Any	       =				self.c_max_length // 2
								while next_ncol > 0:
											__lowerCamelCase					:	Optional[int]	       =				[[] for i in range(UpperCAmelCase__     )]
											__lowerCamelCase					:	Tuple	       =				self.root**next_ncol

											# First half of next step
											__lowerCamelCase					:	str	       =				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
											__lowerCamelCase					:	int	       =				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
											__lowerCamelCase					:	Dict	       =				new_dft
											__lowerCamelCase					:	Tuple	       =				next_ncol // 2
								return dft[0]
					def     snake_case_				(    self     ):
								__lowerCamelCase					:	Any	       =				self.__dft('A'     )
								__lowerCamelCase					:	Any	       =				self.__dft('B'     )
								__lowerCamelCase					:	Optional[int]	       =				[[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					:	Optional[int]	       =				2
								while next_ncol <= self.c_max_length:
											__lowerCamelCase					:	Optional[int]	       =				[[] for i in range(UpperCAmelCase__     )]
											__lowerCamelCase					:	List[str]	       =				self.root ** (next_ncol // 2)
											__lowerCamelCase					:	Optional[int]	       =				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					:	List[Any]	       =				new_inverse_c
											next_ncol *= 2
								# Unpack
								__lowerCamelCase					:	Tuple	       =				[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     ):
								__lowerCamelCase					:	Any	       =				'''A = ''' + ''' + '''.join(
								    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]     )     )
								__lowerCamelCase					:	Tuple	       =				'''B = ''' + ''' + '''.join(
								    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]     )     )
								__lowerCamelCase					:	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()









"""simple docstring"""
import pytest

import datasets


# Import fixture modules as plugins
a_				:    Tuple										=     ['''tests.fixtures.files''', '''tests.fixtures.hub''', '''tests.fixtures.fsspec''']





def 						UpperCAmelCase				(			A__:    List[Any]							,				A__:    Optional[Any]     )  ->     List[str]:
			# Mark tests as "unit" by default if not marked as "integration" (or already marked as "unit")
			for item in items:
						if any(marker in item.keywords for marker in ['integration', 'unit']     ):
									continue
						item.add_marker(pytest.mark.unit     )





def 						UpperCAmelCase				(			A__:    int     )  ->     Optional[int]:
			config.addinivalue_line('markers'							,				'torchaudio_latest: mark test to run with torchaudio>=0.12'     )





@pytest.fixture(autouse=A__     )
def 						UpperCAmelCase				(			A__:    Optional[Any]							,				A__:    List[Any]     )  ->     Any:
			# test_hf_cache_home = tmp_path_factory.mktemp("cache")  # TODO: why a cache dir per test function does not work?
			__lowerCamelCase					:	str	       =				tmp_path_factory.getbasetemp() / 'cache'
			__lowerCamelCase					:	Dict	       =				test_hf_cache_home / 'datasets'
			__lowerCamelCase					:	int	       =				test_hf_cache_home / 'metrics'
			__lowerCamelCase					:	List[str]	       =				test_hf_cache_home / 'modules'
			monkeypatch.setattr('datasets.config.HF_DATASETS_CACHE'							,				str(A__     )     )
			monkeypatch.setattr('datasets.config.HF_METRICS_CACHE'							,				str(A__     )     )
			monkeypatch.setattr('datasets.config.HF_MODULES_CACHE'							,				str(A__     )     )
			__lowerCamelCase					:	List[Any]	       =				test_hf_datasets_cache / 'downloads'
			monkeypatch.setattr('datasets.config.DOWNLOADED_DATASETS_PATH'							,				str(A__     )     )
			__lowerCamelCase					:	Optional[int]	       =				test_hf_datasets_cache / 'downloads' / 'extracted'
			monkeypatch.setattr('datasets.config.EXTRACTED_DATASETS_PATH'							,				str(A__     )     )





@pytest.fixture(autouse=A__							,				scope='session'     )
def 						UpperCAmelCase				(			)  ->     Any:
			datasets.disable_progress_bar()





@pytest.fixture(autouse=A__     )
def 						UpperCAmelCase				(			A__:    Optional[Any]     )  ->     Dict:
			# don't take tests into account when counting downloads
			monkeypatch.setattr('datasets.config.HF_UPDATE_DOWNLOAD_COUNTS'							,				A__     )






@pytest.fixture
def 						UpperCAmelCase				(			A__:    Union[str, Any]     )  ->     Optional[Any]:
			# Required to suppress RemovedIn20Warning when feature(s) are not compatible with SQLAlchemy 2.0
			# To be removed once SQLAlchemy 2.0 supported
			monkeypatch.setattr('sqlalchemy.util.deprecations.SILENCE_UBER_WARNING'							,				A__     )



