




'''simple docstring'''





import mpmath  # for roots of unity
import numpy as np




class 			UpperCAmelCase_      :




							'''simple docstring'''



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

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

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

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

										# The product
										SCREAMING_SNAKE_CASE           =					self.__multiply()





							def    _UpperCAmelCase     (					self       :	int       ,     a       :	Union[str, Any]			)			->					str:
										SCREAMING_SNAKE_CASE           =					[[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
										# Corner case
										if len(a			) <= 1:
													return dft[0]
										#
										SCREAMING_SNAKE_CASE           =					self.c_max_length // 2
										while next_ncol > 0:
													SCREAMING_SNAKE_CASE           =					[[] for i in range(a			)]
													SCREAMING_SNAKE_CASE           =					self.root**next_ncol

													# First half of next step
													SCREAMING_SNAKE_CASE           =					1
													for j in range(self.c_max_length // (next_ncol * 2)			):
																for i in range(a			):
																			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           =					1
													for j in range(self.c_max_length // (next_ncol * 2)			):
																for i in range(a			):
																			new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]			)
																current_root *= root
													# Update
													SCREAMING_SNAKE_CASE           =					new_dft
													SCREAMING_SNAKE_CASE           =					next_ncol // 2
										return dft[0]





							def    _UpperCAmelCase     (					self       :	Any			)			->					str:
										SCREAMING_SNAKE_CASE           =					self.__dft("""A"""			)
										SCREAMING_SNAKE_CASE           =					self.__dft("""B"""			)
										SCREAMING_SNAKE_CASE           =					[[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           =					2
										while next_ncol <= self.c_max_length:
													SCREAMING_SNAKE_CASE           =					[[] for i in range(a			)]
													SCREAMING_SNAKE_CASE           =					self.root ** (next_ncol // 2)
													SCREAMING_SNAKE_CASE           =					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           =					new_inverse_c
													next_ncol *= 2
										# Unpack
										SCREAMING_SNAKE_CASE           =					[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       :	int			)			->					Union[str, Any]:
										SCREAMING_SNAKE_CASE           =					"""A = """ + """ + """.join(
										    f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]			)			)
										SCREAMING_SNAKE_CASE           =					"""B = """ + """ + """.join(
										    f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]			)			)
										SCREAMING_SNAKE_CASE           =					"""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 importlib
import shutil
import threading
import warnings
from typing import List

import fsspec
import fsspec.asyn

from . import compression
from .hffilesystem import HfFileSystem


__A						:							Tuple							=  importlib.util.find_spec("""s3fs""") is not None

if _has_safs:
		from .safilesystem import SaFileSystem  # noqa: F401

__A						:							List[compression.BaseCompressedFileFileSystem]							=  [
    compression.BzaFileSystem,
    compression.GzipFileSystem,
    compression.LzaFileSystem,
    compression.XzFileSystem,
    compression.ZstdFileSystem,
]

# Register custom filesystems
for fs_class in COMPRESSION_FILESYSTEMS + [HfFileSystem]:
		if fs_class.protocol in fsspec.registry and fsspec.registry[fs_class.protocol] is not fs_class:
				warnings.warn(f'''A filesystem protocol was already set for {fs_class.protocol} and will be overwritten.''')
		fsspec.register_implementation(fs_class.protocol, fs_class, clobber=True)
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			if "://" in dataset_path:
						SCREAMING_SNAKE_CASE           =					dataset_path.split("""://"""   )[1]
			return dataset_path
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			if fs is not None and fs.protocol != "file":
						return True
			else:
						return False
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			SCREAMING_SNAKE_CASE           =					not is_remote_filesystem(SCREAMING_SNAKE_CASE   )
			if is_local:
						# LocalFileSystem.mv does copy + rm, it is more efficient to simply move a local directory
						shutil.move(fs._strip_protocol(SCREAMING_SNAKE_CASE   )					,	fs._strip_protocol(SCREAMING_SNAKE_CASE   )   )
			else:
						fs.mv(SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE					,	recursive=SCREAMING_SNAKE_CASE   )




def 					lowerCamelCase_    (    ):
			'''simple docstring'''
			if hasattr(fsspec.asyn					,	"""reset_lock"""   ):
						# for future fsspec>2022.05.0
						fsspec.asyn.reset_lock()
			else:
						SCREAMING_SNAKE_CASE           =					None
						SCREAMING_SNAKE_CASE           =					None
						SCREAMING_SNAKE_CASE           =					threading.Lock()






