import mpmath  # for roots of unity
import numpy as np





class UpperCAmelCase						:


				'''simple docstring'''






				def __init__(						self		,     lowercase=None		,     lowercase=None ):



						"""simple docstring"""





						A_		:    List[str]         =				list(poly_a or [0] )[:]
						A_		:    Any         =				list(poly_b or [0] )[:]

						# Remove leading zero coefficients
						while self.polyA[-1] == 0:
								self.polyA.pop()
						A_		:    Union[str, Any]         =				len(self.polyA )

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

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

						# The product
						A_		:    List[Any]         =				self.__multiply()
				def   lowerCAmelCase_       (						self		,     lowercase ):



						"""simple docstring"""





						A_		:    List[str]         =				[[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
						# Corner case
						if len(lowercase ) <= 1:
								return dft[0]
						#
						A_		:    Tuple         =				self.c_max_length // 2
						while next_ncol > 0:
								A_		:    Any         =				[[] for i in range(lowercase )]
								A_		:    List[str]         =				self.root**next_ncol

								# First half of next step
								A_		:    List[str]         =				1
								for j in range(self.c_max_length // (next_ncol * 2) ):
										for i in range(lowercase ):
												new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j] )
										current_root *= root
								# Second half of next step
								A_		:    Optional[Any]         =				1
								for j in range(self.c_max_length // (next_ncol * 2) ):
										for i in range(lowercase ):
												new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j] )
										current_root *= root
								# Update
								A_		:    List[Any]         =				new_dft
								A_		:    str         =				next_ncol // 2
						return dft[0]
				def   lowerCAmelCase_       (						self ):



						"""simple docstring"""





						A_		:    Tuple         =				self.__dft('A' )
						A_		:    List[str]         =				self.__dft('B' )
						A_		:    Union[str, 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
						A_		:    List[Any]         =				2
						while next_ncol <= self.c_max_length:
								A_		:    int         =				[[] for i in range(lowercase )]
								A_		:    str         =				self.root ** (next_ncol // 2)
								A_		:    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
								A_		:    Dict         =				new_inverse_c
								next_ncol *= 2
						# Unpack
						A_		:    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 ):



						"""simple docstring"""





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







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


_UpperCAmelCase            =		{
    """configuration_bridgetower""": [
        """BRIDGETOWER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """BridgeTowerConfig""",
        """BridgeTowerTextConfig""",
        """BridgeTowerVisionConfig""",
    ],
    """processing_bridgetower""": ["""BridgeTowerProcessor"""],
}

try:
	if not is_vision_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_UpperCAmelCase            =		["""BridgeTowerImageProcessor"""]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_UpperCAmelCase            =		[
	    """BRIDGETOWER_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """BridgeTowerForContrastiveLearning""",
	    """BridgeTowerForImageAndTextRetrieval""",
	    """BridgeTowerForMaskedLM""",
	    """BridgeTowerModel""",
	    """BridgeTowerPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_bridgetower import (
	    BRIDGETOWER_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    BridgeTowerConfig,
	    BridgeTowerTextConfig,
	    BridgeTowerVisionConfig,
	)
	from .processing_bridgetower import BridgeTowerProcessor

	try:
		if not is_vision_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .image_processing_bridgetower import BridgeTowerImageProcessor

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_bridgetower import (
		    BRIDGETOWER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    BridgeTowerForContrastiveLearning,
		    BridgeTowerForImageAndTextRetrieval,
		    BridgeTowerForMaskedLM,
		    BridgeTowerModel,
		    BridgeTowerPreTrainedModel,
		)


else:
	import sys

	_UpperCAmelCase            =		_LazyModule(__name__, globals()["""__file__"""], _import_structure)






