



'''simple docstring'''




import mpmath  # for roots of unity
import numpy as np






class 						_UpperCamelCase  :


			'''simple docstring'''

			def __init__(							self     : List[str]							,     lowerCAmelCase__     : int=None							,     lowerCAmelCase__     : List[Any]=None						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Dict           =		list(poly_a or [0]						)[:]
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		list(poly_b or [0]						)[:]

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

					while self.polyB[-1] == 0:
							self.polyB.pop()
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		len(self.polyB						)

					# Add 0 to make lengths equal a power of 2
					__SCREAMING_SNAKE_CASE       :		Dict           =		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
					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		complex(mpmath.root(x=1							,     n=self.c_max_length							,     k=1						)						)

					# The product
					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		self.__multiply()

			def UpperCamelCase__					(							self     : Dict							,     lowerCAmelCase__     : str						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Any           =		[[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]
					#
					__SCREAMING_SNAKE_CASE       :		Any           =		self.c_max_length // 2
					while next_ncol > 0:
							__SCREAMING_SNAKE_CASE       :		str           =		[[] for i in range(lowerCAmelCase__						)]
							__SCREAMING_SNAKE_CASE       :		Tuple           =		self.root**next_ncol

							# First half of next step
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		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
							__SCREAMING_SNAKE_CASE       :		int           =		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
							__SCREAMING_SNAKE_CASE       :		Tuple           =		new_dft
							__SCREAMING_SNAKE_CASE       :		Tuple           =		next_ncol // 2
					return dft[0]

			def UpperCamelCase__					(							self     : int						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Dict           =		self.__dft("""A"""						)
					__SCREAMING_SNAKE_CASE       :		List[str]           =		self.__dft("""B"""						)
					__SCREAMING_SNAKE_CASE       :		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
					__SCREAMING_SNAKE_CASE       :		Any           =		2
					while next_ncol <= self.c_max_length:
							__SCREAMING_SNAKE_CASE       :		Any           =		[[] for i in range(lowerCAmelCase__						)]
							__SCREAMING_SNAKE_CASE       :		int           =		self.root ** (next_ncol // 2)
							__SCREAMING_SNAKE_CASE       :		Dict           =		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
							__SCREAMING_SNAKE_CASE       :		List[Any]           =		new_inverse_c
							next_ncol *= 2
					# Unpack
					__SCREAMING_SNAKE_CASE       :		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     : List[str]						):





					"""simple docstring"""






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




'''simple docstring'''




from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

UpperCamelCase__       :	Dict    = [
    '''python''',
    '''tqdm''',
    '''regex''',
    '''requests''',
    '''packaging''',
    '''filelock''',
    '''numpy''',
    '''tokenizers''',
    '''huggingface-hub''',
    '''safetensors''',
    '''accelerate''',
    '''pyyaml''',
]

for pkg in pkgs_to_check_at_runtime:
						if pkg in deps:
												if pkg == "tokenizers":
																		# must be loaded here, or else tqdm check may fail
																		from .utils import is_tokenizers_available

																		if not is_tokenizers_available():
																								continue  # not required, check version only if installed
												elif pkg == "accelerate":
																		# must be loaded here, or else tqdm check may fail
																		from .utils import is_accelerate_available

																		# Maybe switch to is_torch_available in the future here so that Accelerate is hard dep of
																		# Transformers with PyTorch
																		if not is_accelerate_available():
																								continue  # not required, check version only if installed

												require_version_core(deps[pkg])
						else:
												raise ValueError(f"can't find {pkg} in {deps.keys()}, check dependency_versions_table.py")


def 				lowerCAmelCase_   (	_lowerCamelCase:   List[Any]       ,      _lowerCamelCase:   Optional[int]=None					):
		require_version(deps[pkg]       ,      _lowerCamelCase					)