
import mpmath  # for roots of unity
import numpy as np
class 					lowercase__:



	"""simple docstring"""




	def __init__(			self    :     List[str]			,				SCREAMING_SNAKE_CASE_    :     Optional[Any]=None			,				SCREAMING_SNAKE_CASE_    :     Optional[Any]=None			)			->	Union[str, Any]:
					# Input as list
					lowercase_	    =   list(poly_a or [0]			)[:]
					lowercase_	    =   list(poly_b or [0]			)[:]

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

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

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

					# The product
					lowercase_	    =   self.__multiply()
	def 		_lowercase    (			self    :     Optional[Any]			,				SCREAMING_SNAKE_CASE_    :     List[Any]			)			->	Any:
					lowercase_	    =   [[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]
					#
					lowercase_	    =   self.c_max_length // 2
					while next_ncol > 0:
									lowercase_	    =   [[] for i in range(SCREAMING_SNAKE_CASE_			)]
									lowercase_	    =   self.root**next_ncol

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

import datasets.config
from datasets.utils.info_utils import is_small_dataset




@pytest.mark.parametrize('''dataset_size'''		,  [None, 400 * 2**20, 600 * 2**20]   )
@pytest.mark.parametrize('''input_in_memory_max_size'''		,  ['''default''', 0, 100 * 2**20, 900 * 2**20]   )
def 							a		(				snake_case__:   int		,  snake_case__:   Dict		,  snake_case__:   Dict   ):


				'''simple docstring'''
				if input_in_memory_max_size != "default":
								monkeypatch.setattr(datasets.config		,  '''IN_MEMORY_MAX_SIZE'''		,  snake_case__   )
				lowercase_	    =   datasets.config.IN_MEMORY_MAX_SIZE
				if input_in_memory_max_size == "default":
								assert in_memory_max_size == 0
				else:
								assert in_memory_max_size == input_in_memory_max_size
				if dataset_size and in_memory_max_size:
								lowercase_	    =   dataset_size < in_memory_max_size
				else:
								lowercase_	    =   False
				lowercase_	    =   is_small_dataset(snake_case__   )
				assert result == expected




