
"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np

class 						a__		:
   def __init__(     self      ,       _a=None      ,       _a=None							):
          # Input as list
          lowercase       :							Tuple									=				list(poly_a or [0]							)[:]
          lowercase       :							int									=				list(poly_b or [0]							)[:]

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

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

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

          # The product
          lowercase       :							List[str]									=				self.__multiply()
   def      __magic_name__     (     self      ,       _a							):
          lowercase       :							Union[str, 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]
          #
          lowercase       :							Optional[Any]									=				self.c_max_length // 2
          while next_ncol > 0:
                 lowercase       :							Tuple									=				[[] for i in range(_a							)]
                 lowercase       :							List[str]									=				self.root**next_ncol

                 # First half of next step
                 lowercase       :							Union[str, Any]									=				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
                 lowercase       :							Union[str, Any]									=				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
                 lowercase       :							int									=				new_dft
                 lowercase       :							List[str]									=				next_ncol // 2
          return dft[0]
   def      __magic_name__     (     self							):
          lowercase       :							int									=				self.__dft("A"							)
          lowercase       :							Union[str, Any]									=				self.__dft("B"							)
          lowercase       :							List[str]									=				[[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       :							Any									=				2
          while next_ncol <= self.c_max_length:
                 lowercase       :							List[Any]									=				[[] for i in range(_a							)]
                 lowercase       :							Optional[Any]									=				self.root ** (next_ncol // 2)
                 lowercase       :							Optional[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
                 lowercase       :							Union[str, Any]									=				new_inverse_c
                 next_ncol *= 2
          # Unpack
          lowercase       :							List[str]									=				[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							):
          lowercase       :							Union[str, Any]									=				"A = " + " + ".join(
              f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]							)							)
          lowercase       :							Union[str, Any]									=				"B = " + " + ".join(
              f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]							)							)
          lowercase       :							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()




"""simple docstring"""




from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


_A     :			str  						=			logging.get_logger(__name__)

_A     :			Tuple  						=			{
    """google/bigbird-roberta-base""": """https://huggingface.co/google/bigbird-roberta-base/resolve/main/config.json""",
    """google/bigbird-roberta-large""": """https://huggingface.co/google/bigbird-roberta-large/resolve/main/config.json""",
    """google/bigbird-base-trivia-itc""": """https://huggingface.co/google/bigbird-base-trivia-itc/resolve/main/config.json""",
    # See all BigBird models at https://huggingface.co/models?filter=big_bird
}

class 						a__		( a_		):
   __lowerCAmelCase				=							"""big_bird"""
   def __init__(     self      ,       _a=50_358      ,       _a=768      ,       _a=12      ,       _a=12      ,       _a=3_072      ,       _a="gelu_new"      ,       _a=0.1      ,       _a=0.1      ,       _a=4_096      ,       _a=2      ,       _a=0.0_2      ,       _a=1E-12      ,       _a=True      ,       _a=0      ,       _a=1      ,       _a=2      ,       _a=66      ,       _a="block_sparse"      ,       _a=True      ,       _a=False      ,       _a=64      ,       _a=3      ,       _a=None      ,       **_a      ,       ):
          super().__init__(
              pad_token_id=_a      ,       bos_token_id=_a      ,       eos_token_id=_a      ,       sep_token_id=_a      ,       **_a      ,       )

          lowercase       :							List[Any]									=				vocab_size
          lowercase       :							Optional[Any]									=				max_position_embeddings
          lowercase       :							str									=				hidden_size
          lowercase       :							int									=				num_hidden_layers
          lowercase       :							Optional[Any]									=				num_attention_heads
          lowercase       :							List[Any]									=				intermediate_size
          lowercase       :							int									=				hidden_act
          lowercase       :							str									=				hidden_dropout_prob
          lowercase       :							List[Any]									=				attention_probs_dropout_prob
          lowercase       :							Tuple									=				initializer_range
          lowercase       :							Optional[int]									=				type_vocab_size
          lowercase       :							str									=				layer_norm_eps
          lowercase       :							Tuple									=				use_cache

          lowercase       :							Any									=				rescale_embeddings
          lowercase       :							List[str]									=				attention_type
          lowercase       :							int									=				use_bias
          lowercase       :							Dict									=				block_size
          lowercase       :							List[str]									=				num_random_blocks
          lowercase       :							int									=				classifier_dropout


class 						a__		( a_		):
   @property
   def      __magic_name__     (     self							):
          if self.task == "multiple-choice":
                 lowercase       :							Union[str, Any]									=				{0: "batch", 1: "choice", 2: "sequence"}
          else:
                 lowercase       :							Dict									=				{0: "batch", 1: "sequence"}
          return OrderedDict(
              [
                  ("input_ids", dynamic_axis),
                  ("attention_mask", dynamic_axis),
              ]							)


