


"""simple docstring"""



import mpmath  # for roots of unity
import numpy as np







class _lowerCAmelCase    :







   def __init__(     self						,     UpperCamelCase__=None						,     UpperCamelCase__=None						)     ->		Optional[Any]:

       '''simple docstring'''




       snake_case   :				Optional[int]				 =   list(poly_a or [0]						)[:]
       snake_case   :				Union[str, Any]				 =   list(poly_b or [0]						)[:]

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

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

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

       # The product
       snake_case   :				int				 =   self.__multiply()







   def 			lowerCamelCase		(     self						,     UpperCamelCase__						)     ->		int:

       '''simple docstring'''




       snake_case   :				int				 =   [[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]
       #
       snake_case   :				List[Any]				 =   self.c_max_length // 2
       while next_ncol > 0:
           snake_case   :				Union[str, Any]				 =   [[] for i in range(UpperCamelCase__						)]
           snake_case   :				Optional[int]				 =   self.root**next_ncol

           # First half of next step
           snake_case   :				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
           snake_case   :				Union[str, Any]				 =   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
           snake_case   :				Optional[int]				 =   new_dft
           snake_case   :				Union[str, Any]				 =   next_ncol // 2
       return dft[0]







   def 			lowerCamelCase		(     self						)     ->		Optional[Any]:

       '''simple docstring'''




       snake_case   :				Optional[Any]				 =   self.__dft("A"						)
       snake_case   :				Optional[Any]				 =   self.__dft("B"						)
       snake_case   :				List[str]				 =   [[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
       snake_case   :				Optional[int]				 =   2
       while next_ncol <= self.c_max_length:
           snake_case   :				List[Any]				 =   [[] for i in range(UpperCamelCase__						)]
           snake_case   :				Tuple				 =   self.root ** (next_ncol // 2)
           snake_case   :				Tuple				 =   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
           snake_case   :				Any				 =   new_inverse_c
           next_ncol *= 2
       # Unpack
       snake_case   :				Optional[Any]				 =   [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:

       '''simple docstring'''




       snake_case   :				List[Any]				 =   "A = " + " + ".join(
           F'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]						)						)
       snake_case   :				Optional[Any]				 =   "B = " + " + ".join(
           F'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]						)						)
       snake_case   :				List[Any]				 =   "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 doctest
import logging
import os
import unittest
from pathlib import Path
from typing import List, Union

import transformers
from transformers.testing_utils import require_tf, require_torch, slow


__snake_case             =   logging.getLogger()







@unittest.skip('''Temporarily disable the doc tests.'''     )
@require_torch
@require_tf
@slow
class _lowerCAmelCase    (				unittest.TestCase     ):







   def 			lowerCamelCase		(     self						,     UpperCamelCase__						,     UpperCamelCase__ = None						,     UpperCamelCase__ = None						,     UpperCamelCase__ = None						,     UpperCamelCase__ = True						,     )     ->		Tuple:

       '''simple docstring'''




       snake_case   :				List[Any]				 =   [file for file in os.listdir(UpperCamelCase__						) if os.path.isfile(os.path.join(UpperCamelCase__						,     UpperCamelCase__						)						)]

       if identifier is not None:
           snake_case   :				Optional[Any]				 =   [file for file in files if identifier in file]

       if n_identifier is not None:
           if isinstance(UpperCamelCase__						,     UpperCamelCase__						):
               for n_ in n_identifier:
                   snake_case   :				str				 =   [file for file in files if n_ not in file]
           else:
               snake_case   :				str				 =   [file for file in files if n_identifier not in file]

       snake_case   :				Tuple				 =   ignore_files or []
       ignore_files.append("__init__.py"						)
       snake_case   :				Optional[Any]				 =   [file for file in files if file not in ignore_files]

       for file in files:
           # Open all files
           print("Testing"						,     UpperCamelCase__						)

           if only_modules:
               snake_case   :				str				 =   file.split("."						)[0]
               try:
                   snake_case   :				Optional[int]				 =   getattr(UpperCamelCase__						,     UpperCamelCase__						)
                   snake_case   :				str				 =   doctest.DocTestSuite(UpperCamelCase__						)
                   snake_case   :				Optional[Any]				 =   unittest.TextTestRunner().run(UpperCamelCase__						)
                   self.assertIs(len(result.failures						)						,     0						)
               except AttributeError:
                   logger.info(F'{module_identifier} is not a module.'						)
           else:
               snake_case   :				Tuple				 =   doctest.testfile(str(".." / directory / file						)						,     optionflags=doctest.ELLIPSIS						)
               self.assertIs(result.failed						,     0						)







   def 			lowerCamelCase		(     self						)     ->		str:

       '''simple docstring'''




       snake_case   :				Tuple				 =   Path("src/transformers"						)
       snake_case   :				List[Any]				 =   "modeling"
       snake_case   :				Dict				 =   [
           "modeling_ctrl.py",
           "modeling_tf_ctrl.py",
       ]
       self.analyze_directory(UpperCamelCase__						,     identifier=UpperCamelCase__						,     ignore_files=UpperCamelCase__						)







   def 			lowerCamelCase		(     self						)     ->		Dict:

       '''simple docstring'''




       snake_case   :				Optional[Any]				 =   Path("src/transformers"						)
       snake_case   :				Optional[Any]				 =   "tokenization"
       self.analyze_directory(UpperCamelCase__						,     identifier=UpperCamelCase__						)







   def 			lowerCamelCase		(     self						)     ->		List[str]:

       '''simple docstring'''




       snake_case   :				Union[str, Any]				 =   Path("src/transformers"						)
       snake_case   :				Optional[Any]				 =   "configuration"
       self.analyze_directory(UpperCamelCase__						,     identifier=UpperCamelCase__						)







   def 			lowerCamelCase		(     self						)     ->		Optional[Any]:

       '''simple docstring'''




       snake_case   :				List[str]				 =   Path("src/transformers"						)
       snake_case   :				List[str]				 =   ["configuration", "modeling", "tokenization"]
       self.analyze_directory(UpperCamelCase__						,     n_identifier=UpperCamelCase__						)







   def 			lowerCamelCase		(     self						)     ->		List[Any]:

       '''simple docstring'''




       snake_case   :				Any				 =   Path("docs/source"						)
       snake_case   :				Tuple				 =   ["favicon.ico"]
       self.analyze_directory(UpperCamelCase__						,     ignore_files=UpperCamelCase__						,     only_modules=UpperCamelCase__						)





