


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



					'''simple docstring'''







					def __init__(				self ,       snake_case_=None ,       snake_case_=None						)   ->			List[str]:







								'''simple docstring'''

								__lowercase 					=   list(poly_a or [0]						)[:]
								__lowercase 					=   list(poly_b or [0]						)[:]

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

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

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

								# The product
								__lowercase 					=   self.__multiply()






					def A      (				self ,       snake_case_						)   ->			int:







								'''simple docstring'''

								__lowercase 					=   [[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]
								#
								__lowercase 					=   self.c_max_length // 2
								while next_ncol > 0:
											__lowercase 					=   [[] for i in range(snake_case_						)]
											__lowercase 					=   self.root**next_ncol

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






					def A      (				self						)   ->			Union[str, Any]:







								'''simple docstring'''

								__lowercase 					=   self.__dft('''A'''						)
								__lowercase 					=   self.__dft('''B'''						)
								__lowercase 					=   [[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
								__lowercase 					=   2
								while next_ncol <= self.c_max_length:
											__lowercase 					=   [[] for i in range(snake_case_						)]
											__lowercase 					=   self.root ** (next_ncol // 2)
											__lowercase 					=   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
											__lowercase 					=   new_inverse_c
											next_ncol *= 2
								# Unpack
								__lowercase 					=   [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'''

								__lowercase 					=   '''A = ''' + ''' + '''.join(
								    F'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]						)						)
								__lowercase 					=   '''B = ''' + ''' + '''.join(
								    F'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]						)						)
								__lowercase 					=   '''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()






# limitations under the License.

# NOTE: This file is deprecated and will be removed in a future version.
# It only exists so that temporarely `from diffusers.pipelines import DiffusionPipeline` works

from .pipelines import DiffusionPipeline, ImagePipelineOutput  # noqa: F401
from .utils import deprecate


deprecate(
    '''pipelines_utils''',
    '''0.22.0''',
    '''Importing `DiffusionPipeline` or `ImagePipelineOutput` from diffusers.pipeline_utils is deprecated. Please import from diffusers.pipelines.pipeline_utils instead.''',
    standard_warn=False,
    stacklevel=3,
)


