

'''simple docstring'''







import mpmath  # for roots of unity
import numpy as np


class        A__   :



    def __init__(       self		,					UpperCamelCase__=None		,					UpperCamelCase__=None							)    ->   Dict:





           '''simple docstring'''
           A_						       =   list(poly_a or [0]							)[:]
           A_						       =   list(poly_b or [0]							)[:]

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

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

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

           # The product
           A_						       =   self.__multiply()



    def        snake_case_      (       self		,					UpperCamelCase__							)    ->   Dict:





           '''simple docstring'''
           A_						       =   [[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]
           #
           A_						       =   self.c_max_length // 2
           while next_ncol > 0:
                  A_						       =   [[] for i in range(UpperCamelCase_							)]
                  A_						       =   self.root**next_ncol

                  # First half of next step
                  A_						       =   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
                  A_						       =   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
                  A_						       =   new_dft
                  A_						       =   next_ncol // 2
           return dft[0]



    def        snake_case_      (       self							)    ->   Optional[int]:





           '''simple docstring'''
           A_						       =   self.__dft("""A"""							)
           A_						       =   self.__dft("""B"""							)
           A_						       =   [[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
           A_						       =   2
           while next_ncol <= self.c_max_length:
                  A_						       =   [[] for i in range(UpperCamelCase_							)]
                  A_						       =   self.root ** (next_ncol // 2)
                  A_						       =   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
                  A_						       =   new_inverse_c
                  next_ncol *= 2
           # Unpack
           A_						       =   [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							)    ->   Dict:





           '''simple docstring'''
           A_						       =   '''A = ''' + ''' + '''.join(
               f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
           A_						       =   '''B = ''' + ''' + '''.join(
               f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
           A_						       =   '''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 importlib
import os
import sys


# This is required to make the module import works (when the python process is running from the root of the repo)
sys.path.append('''.''')


def      a (     __a  )    ->      List[str]:



					'''simple docstring'''






					UpperCamelCase__  :int				   =					test_file.split(os.path.sep  )
					if components[0:2] != ["tests", "models"]:
										raise ValueError(
										    '''`test_file` should start with `tests/models/` (with `/` being the OS specific path separator). Got '''
										    f'''{test_file} instead.'''  )
					UpperCamelCase__  :List[Any]				   =					components[-1]
					if not test_fn.endswith('''py'''  ):
										raise ValueError(f'''`test_file` should be a python file. Got {test_fn} instead.'''  )
					if not test_fn.startswith('''test_modeling_'''  ):
										raise ValueError(
										    f'''`test_file` should point to a file name of the form `test_modeling_*.py`. Got {test_fn} instead.'''  )

					UpperCamelCase__  :Optional[Any]				   =					components[:-1] + [test_fn.replace('''.py'''					,   ''''''  )]
					UpperCamelCase__  :str				   =					'''.'''.join(__a  )

					return test_module_path


def      a (     __a  )    ->      Tuple:



					'''simple docstring'''






					UpperCamelCase__  :Dict				   =					get_module_path(__a  )
					UpperCamelCase__  :List[str]				   =					importlib.import_module(__a  )

					return test_module


def      a (     __a  )    ->      int:



					'''simple docstring'''






					UpperCamelCase__  :Dict				   =					[]
					UpperCamelCase__  :Optional[Any]				   =					get_test_module(__a  )
					for attr in dir(__a  ):
										if attr.endswith('''ModelTester'''  ):
															tester_classes.append(getattr(__a					,   __a  )  )

    # sort with class names
					return sorted(__a					,   key=lambda __a  : x.__name__  )


def      a (     __a  )    ->      List[Any]:



					'''simple docstring'''






					UpperCamelCase__  :List[Any]				   =					[]
					UpperCamelCase__  :Dict				   =					get_test_module(__a  )
					for attr in dir(__a  ):
										UpperCamelCase__  :Dict				   =					getattr(__a					,   __a  )
										# (TF/Flax)ModelTesterMixin is also an attribute in specific model test module. Let's exclude them by checking
										# `all_model_classes` is not empty (which also excludes other special classes).
										UpperCamelCase__  :Optional[int]				   =					getattr(__a					,   '''all_model_classes'''					,   []  )
										if len(__a  ) > 0:
															test_classes.append(__a  )

    # sort with class names
					return sorted(__a					,   key=lambda __a  : x.__name__  )


def      a (     __a  )    ->      Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__  :int				   =					get_test_classes(__a  )
					UpperCamelCase__  :Any				   =					set()
					for test_class in test_classes:
										model_classes.update(test_class.all_model_classes  )

					# sort with class names
					return sorted(__a					,   key=lambda __a  : x.__name__  )


def      a (     __a  )    ->      Dict:



					'''simple docstring'''






					UpperCamelCase__  :Optional[Any]				   =					test_class()
					if hasattr(__a					,   '''setUp'''  ):
										test.setUp()

					UpperCamelCase__  :Union[str, Any]				   =					None
					if hasattr(__a					,   '''model_tester'''  ):
										# `(TF/Flax)ModelTesterMixin` has this attribute default to `None`. Let's skip this case.
										if test.model_tester is not None:
															UpperCamelCase__  :List[str]				   =					test.model_tester.__class__

					return model_tester


def      a (     __a					,   __a  )    ->      Any:



					'''simple docstring'''






					UpperCamelCase__  :str				   =					get_test_classes(__a  )

					UpperCamelCase__  :List[str]				   =					[]
					for test_class in test_classes:
										if model_class in test_class.all_model_classes:
															target_test_classes.append(__a  )

    # sort with class names
					return sorted(__a					,   key=lambda __a  : x.__name__  )


def      a (     __a					,   __a  )    ->      Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__  :Optional[int]				   =					get_test_classes_for_model(__a					,   __a  )

					UpperCamelCase__  :List[str]				   =					[]
					for test_class in test_classes:
										UpperCamelCase__  :int				   =					get_model_tester_from_test_class(__a  )
										if tester_class is not None:
															tester_classes.append(__a  )

    # sort with class names
					return sorted(__a					,   key=lambda __a  : x.__name__  )


def      a (     __a  )    ->      int:



					'''simple docstring'''






					UpperCamelCase__  :Any				   =					get_test_classes(__a  )
					UpperCamelCase__  :Dict				   =					{test_class: get_model_tester_from_test_class(__a  ) for test_class in test_classes}
					return test_tester_mapping


def      a (     __a  )    ->      List[str]:



					'''simple docstring'''






					UpperCamelCase__  :Any				   =					get_model_classes(__a  )
					UpperCamelCase__  :Tuple				   =					{
					    model_class: get_test_classes_for_model(__a					,   __a  ) for model_class in model_classes
					}
					return model_test_mapping


def      a (     __a  )    ->      Tuple:



					'''simple docstring'''






					UpperCamelCase__  :List[str]				   =					get_model_classes(__a  )
					UpperCamelCase__  :Union[str, Any]				   =					{
					    model_class: get_tester_classes_for_model(__a					,   __a  ) for model_class in model_classes
					}
					return model_to_tester_mapping







def      a (     __a  )    ->      List[Any]:



					'''simple docstring'''






					if isinstance(__a					,   __a  ):
										return o
					elif isinstance(__a					,   __a  ):
										return o.__name__
					elif isinstance(__a					,   (list, tuple)  ):
										return [to_json(__a  ) for x in o]
					elif isinstance(__a					,   __a  ):
										return {to_json(__a  ): to_json(__a  ) for k, v in o.items()}
					else:
										return o