




"""simple docstring"""



import mpmath  # for roots of unity
import numpy as np




class      UpperCAmelCase_  :




    def __init__(   self						:	List[Any]     ,			snake_case_						:	int=None     ,			snake_case_						:	Dict=None				)				->							Optional[Any]:




     '''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 							__magic_name__							(   self						:	str     ,			snake_case_						:	Tuple				)				->							List[str]:




     '''simple docstring'''

     A__	=    [[x] for x in self.polyA] if which == "A" else [[x] for x in self.polyB]
     # Corner case
     if len(snake_case_				) <= 1:
      return dft[0]
     #
     A__	=    self.c_max_length // 2
     while next_ncol > 0:
      A__	=    [[] for i in range(snake_case_				)]
      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(snake_case_				):
        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(snake_case_				):
        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 							__magic_name__							(   self						:	int				)				->							Dict:




     '''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(snake_case_				)]
      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						:	List[Any]				)				->							List[Any]:




     '''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 unittest

from transformers.testing_utils import CaptureStdout
from transformers.tools.python_interpreter import evaluate







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		int:
 return x + 2






class      UpperCAmelCase_  (						unittest.TestCase							):




    def 							__magic_name__							(   self						:	Any				)				->							Any:




     '''simple docstring'''

     A__	=    "x = 3"
     A__	=    {}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     assert result == 3
     self.assertDictEqual(snake_case_     ,			{"x": 3}				)

     A__	=    "x = y"
     A__	=    {"y": 5}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     # evaluate returns the value of the last assignment.
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 5, "y": 5}				)




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




     '''simple docstring'''

     A__	=    "y = add_two(x)"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{"add_two": add_two}     ,			state=snake_case_				)
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 3, "y": 5}				)

     # Won't work without the tool
     with CaptureStdout() as out:
      A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     assert result is None
     assert "tried to execute add_two" in out.out




    def 							__magic_name__							(   self						:	Dict				)				->							List[str]:




     '''simple docstring'''

     A__	=    "x = 3"
     A__	=    {}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     assert result == 3
     self.assertDictEqual(snake_case_     ,			{"x": 3}				)




    def 							__magic_name__							(   self						:	Dict				)				->							Optional[Any]:




     '''simple docstring'''

     A__	=    "test_dict = {'x': x, 'y': add_two(x)}"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{"add_two": add_two}     ,			state=snake_case_				)
     self.assertDictEqual(snake_case_     ,			{"x": 3, "y": 5}				)
     self.assertDictEqual(snake_case_     ,			{"x": 3, "test_dict": {"x": 3, "y": 5}}				)




    def 							__magic_name__							(   self						:	int				)				->							str:




     '''simple docstring'''

     A__	=    "x = 3\ny = 5"
     A__	=    {}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     # evaluate returns the value of the last assignment.
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 3, "y": 5}				)




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




     '''simple docstring'''

     A__	=    "text = f'This is x: {x}.'"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     # evaluate returns the value of the last assignment.
     assert result == "This is x: 3."
     self.assertDictEqual(snake_case_     ,			{"x": 3, "text": "This is x: 3."}				)




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




     '''simple docstring'''

     A__	=    "if x <= 3:\n    y = 2\nelse:\n    y = 5"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     # evaluate returns the value of the last assignment.
     assert result == 2
     self.assertDictEqual(snake_case_     ,			{"x": 3, "y": 2}				)

     A__	=    {"x": 8}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     # evaluate returns the value of the last assignment.
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 8, "y": 5}				)




    def 							__magic_name__							(   self						:	List[str]				)				->							Tuple:




     '''simple docstring'''

     A__	=    "test_list = [x, add_two(x)]"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{"add_two": add_two}     ,			state=snake_case_				)
     self.assertListEqual(snake_case_     ,			[3, 5]				)
     self.assertDictEqual(snake_case_     ,			{"x": 3, "test_list": [3, 5]}				)




    def 							__magic_name__							(   self						:	Tuple				)				->							int:




     '''simple docstring'''

     A__	=    "y = x"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{}     ,			state=snake_case_				)
     assert result == 3
     self.assertDictEqual(snake_case_     ,			{"x": 3, "y": 3}				)




    def 							__magic_name__							(   self						:	str				)				->							Dict:




     '''simple docstring'''

     A__	=    "test_list = [x, add_two(x)]\ntest_list[1]"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{"add_two": add_two}     ,			state=snake_case_				)
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 3, "test_list": [3, 5]}				)

     A__	=    "test_dict = {'x': x, 'y': add_two(x)}\ntest_dict['y']"
     A__	=    {"x": 3}
     A__	=    evaluate(snake_case_     ,			{"add_two": add_two}     ,			state=snake_case_				)
     assert result == 5
     self.assertDictEqual(snake_case_     ,			{"x": 3, "test_dict": {"x": 3, "y": 5}}				)




    def 							__magic_name__							(   self						:	Optional[int]				)				->							Tuple:




     '''simple docstring'''

     A__	=    "x = 0\nfor i in range(3):\n    x = i"
     A__	=    {}
     A__	=    evaluate(snake_case_     ,			{"range": range}     ,			state=snake_case_				)
     assert result == 2
     self.assertDictEqual(snake_case_     ,			{"x": 2, "i": 2}				)





