"""simple docstring"""


import mpmath  # for roots of unity
import numpy as np


class 				a :


    def __init__(    self		:     Tuple      , __lowerCAmelCase		:     Any=None      , __lowerCAmelCase		:     Any=None    ):
      # Input as list
      _UpperCAmelCase         =					list(poly_a or [0]    )[:]
      _UpperCAmelCase         =					list(poly_b or [0]    )[:]

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

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

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

      # The product
      _UpperCAmelCase         =					self.__multiply()


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

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


    def    lowerCAmelCase_     (    self		:     str    ):
      _UpperCAmelCase         =					self.__dft("""A"""    )
      _UpperCAmelCase         =					self.__dft("""B"""    )
      _UpperCAmelCase         =					[[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         =					2
      while next_ncol <= self.c_max_length:
        _UpperCAmelCase         =					[[] for i in range(_lowerCamelCase    )]
        _UpperCAmelCase         =					self.root ** (next_ncol // 2)
        _UpperCAmelCase         =					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         =					new_inverse_c
        next_ncol *= 2
      # Unpack
      _UpperCAmelCase         =					[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    ):
      _UpperCAmelCase         =					'''A = ''' + ''' + '''.join(
          f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
      _UpperCAmelCase         =					'''B = ''' + ''' + '''.join(
          f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
      _UpperCAmelCase         =					'''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()




from pathlib import PurePosixPath
from typing import Optional

import fsspec
from fsspec import AbstractFileSystem
from huggingface_hub.hf_api import DatasetInfo

from ..utils.file_utils import get_authentication_headers_for_url
from ..utils.hub import hf_hub_url







class 		_snake_case  (      _snake_case							):
 SCREAMING_SNAKE_CASE__      =       ''
 SCREAMING_SNAKE_CASE__      =       'hf-legacy'  # "hf://"" is reserved for hffs




 def __init__(		self					,  _lowerCamelCase = None					,  _lowerCamelCase = None					,  **_lowerCamelCase					,  ):
       super().__init__(self					,  **_lowerCamelCase    )
       a						:Union[str, Any] 							=       repo_info
       a						:int 							=       token
       a						:int 							=       None




 def        SCREAMING_SNAKE_CASE__				(		self    ):
       if self.dir_cache is None:
             a						:Dict 							=       {}
             for hf_file in self.repo_info.siblings:
                   # TODO(QL): add sizes
                   a						:List[Any] 							=       {
                       '''name''': hf_file.rfilename,
                       '''size''': None,
                       '''type''': '''file''',
                   }
                   self.dir_cache.update(
                       {
                           str(_lowerCamelCase    ): {'''name''': str(_lowerCamelCase    ), '''size''': None, '''type''': '''directory'''}
                           for d in list(PurePosixPath(hf_file.rfilename    ).parents    )[:-1]
                       }    )




 def        SCREAMING_SNAKE_CASE__				(		self					,  _lowerCamelCase					,  _lowerCamelCase = "rb"					,  **_lowerCamelCase					,  ):
       if not isinstance(self.repo_info					,  _lowerCamelCase    ):
             raise NotImplementedError(F'''Open is only implemented for dataset repositories, but got {self.repo_info}'''    )
       a						:Optional[int] 							=       hf_hub_url(self.repo_info.id					,  _lowerCamelCase					,  revision=self.repo_info.sha    )
       return fsspec.open(
           _lowerCamelCase					,  mode=_lowerCamelCase					,  headers=get_authentication_headers_for_url(_lowerCamelCase					,  use_auth_token=self.token    )					,  client_kwargs={'''trust_env''': True}					,  ).open()




 def        SCREAMING_SNAKE_CASE__				(		self					,  _lowerCamelCase					,  **_lowerCamelCase    ):
       self._get_dirs()
       a						:Union[str, Any] 							=       self._strip_protocol(_lowerCamelCase    )
       if path in self.dir_cache:
             return self.dir_cache[path]
       else:
             raise FileNotFoundError(_lowerCamelCase    )




 def        SCREAMING_SNAKE_CASE__				(		self					,  _lowerCamelCase					,  _lowerCamelCase=False					,  **_lowerCamelCase    ):
       self._get_dirs()
       a						:str 							=       PurePosixPath(path.strip('''/'''    )    )
       a						:Tuple 							=       {}
       for p, f in self.dir_cache.items():
             a						:Optional[int] 							=       PurePosixPath(p.strip('''/'''    )    )
             a						:str 							=       p.parent
             if root == path:
                   a						:List[str] 							=       f
       a						:Any 							=       list(paths.values()    )
       if detail:
             return out
       else:
             return sorted(f['''name'''] for f in out    )





