import mpmath  # for roots of unity
import numpy as np

class 					_lowercase    :






    '''simple docstring'''




    def __init__(    self       ,						lowerCamelCase__=None       ,						lowerCamelCase__=None ):
       # Input as list
       lowerCAmelCase_:							str       =	list(poly_a or [0] )[:]
       lowerCAmelCase_:							List[str]       =	list(poly_b or [0] )[:]

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

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

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

       # The product
       lowerCAmelCase_:							List[str]       =	self.__multiply()




    def      _a    (    self       ,						lowerCamelCase__ ):
       lowerCAmelCase_:							Optional[int]       =	[[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]
       #
       lowerCAmelCase_:							Tuple       =	self.c_max_length // 2
       while next_ncol > 0:
          lowerCAmelCase_:							List[Any]       =	[[] for i in range(lowerCamelCase__ )]
          lowerCAmelCase_:							Optional[int]       =	self.root**next_ncol

          # First half of next step
          lowerCAmelCase_:							Dict       =	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
          lowerCAmelCase_:							List[str]       =	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
          lowerCAmelCase_:							str       =	new_dft
          lowerCAmelCase_:							Optional[int]       =	next_ncol // 2
       return dft[0]




    def      _a    (    self ):
       lowerCAmelCase_:							Tuple       =	self.__dft("A" )
       lowerCAmelCase_:							str       =	self.__dft("B" )
       lowerCAmelCase_:							Optional[int]       =	[[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
       lowerCAmelCase_:							str       =	2
       while next_ncol <= self.c_max_length:
          lowerCAmelCase_:							Any       =	[[] for i in range(lowerCamelCase__ )]
          lowerCAmelCase_:							List[str]       =	self.root ** (next_ncol // 2)
          lowerCAmelCase_:							str       =	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
          lowerCAmelCase_:							Tuple       =	new_inverse_c
          next_ncol *= 2
       # Unpack
       lowerCAmelCase_:							Dict       =	[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 ):
       lowerCAmelCase_:							List[Any]       =	"A = " + " + ".join(
           F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A] ) )
       lowerCAmelCase_:							Optional[Any]       =	"B = " + " + ".join(
           F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B] ) )
       lowerCAmelCase_:							str       =	"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  :      List[Any]            =    logging.get_logger(__name__)

a  :      Any            =    {"""openai-gpt""": """https://huggingface.co/openai-gpt/resolve/main/config.json"""}

class 					_lowercase    (     UpperCAmelCase__			):






    '''simple docstring'''
    SCREAMING_SNAKE_CASE:				int          =    'openai-gpt'
    SCREAMING_SNAKE_CASE:				List[str]          =    {
        'max_position_embeddings': 'n_positions',
        'hidden_size': 'n_embd',
        'num_attention_heads': 'n_head',
        'num_hidden_layers': 'n_layer',
    }




    def __init__(    self       ,						lowerCamelCase__=40_478       ,						lowerCamelCase__=512       ,						lowerCamelCase__=768       ,						lowerCamelCase__=12       ,						lowerCamelCase__=12       ,						lowerCamelCase__="gelu"       ,						lowerCamelCase__=0.1       ,						lowerCamelCase__=0.1       ,						lowerCamelCase__=0.1       ,						lowerCamelCase__=1E-5       ,						lowerCamelCase__=0.0_2       ,						lowerCamelCase__="cls_index"       ,						lowerCamelCase__=True       ,						lowerCamelCase__=None       ,						lowerCamelCase__=True       ,						lowerCamelCase__=0.1       ,						**lowerCamelCase__       ,						):
       lowerCAmelCase_:							Union[str, Any]       =	vocab_size
       lowerCAmelCase_:							List[Any]       =	n_positions
       lowerCAmelCase_:							Tuple       =	n_embd
       lowerCAmelCase_:							Optional[int]       =	n_layer
       lowerCAmelCase_:							Optional[int]       =	n_head
       lowerCAmelCase_:							int       =	afn
       lowerCAmelCase_:							str       =	resid_pdrop
       lowerCAmelCase_:							Optional[int]       =	embd_pdrop
       lowerCAmelCase_:							Optional[int]       =	attn_pdrop
       lowerCAmelCase_:							Dict       =	layer_norm_epsilon
       lowerCAmelCase_:							List[Any]       =	initializer_range
       lowerCAmelCase_:							Union[str, Any]       =	summary_type
       lowerCAmelCase_:							Any       =	summary_use_proj
       lowerCAmelCase_:							Dict       =	summary_activation
       lowerCAmelCase_:							Dict       =	summary_first_dropout
       lowerCAmelCase_:							List[Any]       =	summary_proj_to_labels
       super().__init__(**lowerCamelCase__ )