

import mpmath  # for roots of unity
import numpy as np



class     _a						:


					'''simple docstring'''






					def __init__( self    ,       A__=None    ,       A__=None			):
						# Input as list
						A__							:    List[Any]        =		list(poly_a or [0]			)[:]
						A__							:    Dict        =		list(poly_b or [0]			)[:]

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

						while self.polyB[-1] == 0:
							self.polyB.pop()
						A__							:    List[str]        =		len(self.polyB			)

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

						# The product
						A__							:    Tuple        =		self.__multiply()






					def   __A			( self    ,       A__			):
						A__							:    Any        =		[[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
						# Corner case
						if len(A__			) <= 1:
							return dft[0]
						#
						A__							:    Union[str, Any]        =		self.c_max_length // 2
						while next_ncol > 0:
							A__							:    List[str]        =		[[] for i in range(A__			)]
							A__							:    Any        =		self.root**next_ncol

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






					def   __A			( self			):
						A__							:    List[str]        =		self.__dft("""A"""			)
						A__							:    List[Any]        =		self.__dft("""B"""			)
						A__							:    Dict        =		[[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__							:    Union[str, Any]        =		2
						while next_ncol <= self.c_max_length:
							A__							:    int        =		[[] for i in range(A__			)]
							A__							:    Dict        =		self.root ** (next_ncol // 2)
							A__							:    Optional[int]        =		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__							:    int        =		[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			):
						A__							:    Tuple        =		"""A = """ + """ + """.join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]			)			)
						A__							:    Tuple        =		"""B = """ + """ + """.join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]			)			)
						A__							:    Optional[int]        =		"""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 ...configuration_utils import PretrainedConfig
from ...utils import logging


A_       : int         =			logging.get_logger(__name__)

A_       : Optional[Any]         =			{
    'alibaba-damo/mgp-str-base': 'https://huggingface.co/alibaba-damo/mgp-str-base/resolve/main/config.json',
}



class     _a						(__magic_name__				):


					'''simple docstring'''






					UpperCAmelCase__:   List[Any]  							=       '''mgp-str'''






					def __init__( self    ,       A__=[32, 128]    ,       A__=4    ,       A__=3    ,       A__=27    ,       A__=38    ,       A__=5_0257    ,       A__=3_0522    ,       A__=768    ,       A__=12    ,       A__=12    ,       A__=4.0    ,       A__=True    ,       A__=False    ,       A__=1e-5    ,       A__=0.0    ,       A__=0.0    ,       A__=0.0    ,       A__=False    ,       A__=0.0_2    ,       **A__    ,       ):
						super().__init__(**A__			)

						A__							:    Dict        =		image_size
						A__							:    int        =		patch_size
						A__							:    Dict        =		num_channels
						A__							:    List[Any]        =		max_token_length
						A__							:    str        =		num_character_labels
						A__							:    Tuple        =		num_bpe_labels
						A__							:    Optional[Any]        =		num_wordpiece_labels
						A__							:    Optional[int]        =		hidden_size
						A__							:    Tuple        =		num_hidden_layers
						A__							:    Any        =		num_attention_heads
						A__							:    List[Any]        =		mlp_ratio
						A__							:    Tuple        =		distilled
						A__							:    Union[str, Any]        =		layer_norm_eps
						A__							:    Tuple        =		drop_rate
						A__							:    List[str]        =		qkv_bias
						A__							:    Optional[Any]        =		attn_drop_rate
						A__							:    Union[str, Any]        =		drop_path_rate
						A__							:    Optional[Any]        =		output_aa_attentions
						A__							:    Optional[int]        =		initializer_range



