





'''simple docstring'''

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






       """simple docstring"""





       def __init__(				self  :						str			,					lowerCAmelCase__  :						Dict=None			,					lowerCAmelCase__  :						List[str]=None	)       ->	int:

            '''simple docstring'''




            _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 snake_case__		(				self  :						List[Any]			,					lowerCAmelCase__  :						Optional[Any]	)       ->	Optional[int]:

            '''simple docstring'''




            _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 snake_case__		(				self  :						Tuple	)       ->	Any:

            '''simple docstring'''




            _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  :						Tuple	)       ->	Dict:

            '''simple docstring'''




            _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()










'''simple docstring'''

import unittest

from accelerate import debug_launcher
from accelerate.test_utils import require_cpu, test_ops, test_script
@require_cpu
class 							__lowerCAmelCase	(       unittest.TestCase					):






       """simple docstring"""





       def snake_case__		(				self  :						str	)       ->	Optional[int]:

            '''simple docstring'''




            debug_launcher(test_script.main	)







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

            '''simple docstring'''




            debug_launcher(test_ops.main	)



