

import mpmath  # for roots of unity
import numpy as np






class        A_		:
							def __init__(		self		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			Union[str, Any]=None   ,SCREAMING_SNAKE_CASE__		:			str=None):
								# Input as list
								__lowerCamelCase				:				Optional[int]					       = list(poly_a or [0])[:]
								__lowerCamelCase				:				Dict					       = list(poly_b or [0])[:]

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

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

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

								# The product
								__lowerCamelCase				:				Optional[Any]					       = self.__multiply()
							def     lowerCAmelCase     (		self		:			Any   ,SCREAMING_SNAKE_CASE__		:			int):
								__lowerCamelCase				:				Optional[Any]					       = [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
								# Corner case
								if len(SCREAMING_SNAKE_CASE__) <= 1:
									return dft[0]
								#
								__lowerCamelCase				:				str					       = self.c_max_length // 2
								while next_ncol > 0:
									__lowerCamelCase				:				Optional[Any]					       = [[] for i in range(SCREAMING_SNAKE_CASE__)]
									__lowerCamelCase				:				Optional[int]					       = self.root**next_ncol

									# First half of next step
									__lowerCamelCase				:				Union[str, Any]					       = 1
									for j in range(self.c_max_length // (next_ncol * 2)):
										for i in range(SCREAMING_SNAKE_CASE__):
											new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j])
										current_root *= root
									# Second half of next step
									__lowerCamelCase				:				Optional[Any]					       = 1
									for j in range(self.c_max_length // (next_ncol * 2)):
										for i in range(SCREAMING_SNAKE_CASE__):
											new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j])
										current_root *= root
									# Update
									__lowerCamelCase				:				Union[str, Any]					       = new_dft
									__lowerCamelCase				:				Optional[Any]					       = next_ncol // 2
								return dft[0]
							def     lowerCAmelCase     (		self		:			List[str]):
								__lowerCamelCase				:				Optional[int]					       = self.__dft('A')
								__lowerCamelCase				:				Dict					       = self.__dft('B')
								__lowerCamelCase				:				Optional[Any]					       = [[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
								__lowerCamelCase				:				int					       = 2
								while next_ncol <= self.c_max_length:
									__lowerCamelCase				:				Dict					       = [[] for i in range(SCREAMING_SNAKE_CASE__)]
									__lowerCamelCase				:				Dict					       = self.root ** (next_ncol // 2)
									__lowerCamelCase				:				Union[str, Any]					       = 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
									__lowerCamelCase				:				List[Any]					       = new_inverse_c
									next_ncol *= 2
								# Unpack
								__lowerCamelCase				:				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):
								__lowerCamelCase				:				Union[str, Any]					       = 'A = ' + ' + '.join(
								    F"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]))
								__lowerCamelCase				:				Tuple					       = 'B = ' + ' + '.join(
								    F"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]))
								__lowerCamelCase				:				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()












import unittest

from transformers import load_tool
from transformers.utils import is_torch_available


if is_torch_available():
 import torch

from transformers.testing_utils import require_torch

from .test_tools_common import ToolTesterMixin





@require_torch
class 			__a  (    unittest.TestCase       ,   A__       ):







 def 					__lowercase					(		self					:   Any						):


      '''simple docstring'''






      UpperCamelCase__			:   Dict       				=  load_tool("text-to-speech"						)
      self.tool.setup()







 def 					__lowercase					(		self					:   Union[str, Any]						):


      '''simple docstring'''






      torch.manual_seed(0						)
      UpperCamelCase__			:   Union[str, Any]       				=  self.tool("hey"						)
      UpperCamelCase__			:   Any       				=  result.to_raw()
      self.assertTrue(
          torch.allclose(
              resulting_tensor[:3]							,   torch.tensor([-0.0_0_0_5_9_6_6_6_6_8_8_3_2_1_1_5_8_2_9, -0.0_0_0_3_6_5_7_6_4_0_1_9_0_7_9_5_0_6_4, -0.0_0_0_1_3_4_3_9_5_0_2_7_9_9_8_8_3_4_8_5]						)							,   )						)







 def 					__lowercase					(		self					:   List[Any]						):


      '''simple docstring'''






      torch.manual_seed(0						)
      UpperCamelCase__			:   List[Any]       				=  self.tool("hey"						)
      UpperCamelCase__			:   int       				=  result.to_raw()
      self.assertTrue(
          torch.allclose(
              resulting_tensor[:3]							,   torch.tensor([-0.0_0_0_5_9_6_6_6_6_8_8_3_2_1_1_5_8_2_9, -0.0_0_0_3_6_5_7_6_4_0_1_9_0_7_9_5_0_6_4, -0.0_0_0_1_3_4_3_9_5_0_2_7_9_9_8_8_3_4_8_5]						)							,   )						)