'''simple docstring'''





import mpmath  # for roots of unity
import numpy as np






class 				UpperCAmelCase :




    '''simple docstring'''







    def __init__(       self    ,							lowercase__=None    ,							lowercase__=None )							-> Optional[Any]:
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       list(poly_a or [0] )[:]
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       list(poly_b or [0] )[:]

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

         while self.polyB[-1] == 0:
              self.polyB.pop()
         SCREAMING_SNAKE_CASE					:			Tuple    	=       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					:			Dict    	=       complex(mpmath.root(x=1    ,							n=self.c_max_length    ,							k=1 ) )

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






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> List[str]:
         SCREAMING_SNAKE_CASE					:			Tuple    	=       [[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]
         #
         SCREAMING_SNAKE_CASE					:			Any    	=       self.c_max_length // 2
         while next_ncol > 0:
              SCREAMING_SNAKE_CASE					:			List[Any]    	=       [[] for i in range(lowercase__ )]
              SCREAMING_SNAKE_CASE					:			List[str]    	=       self.root**next_ncol

              # First half of next step
              SCREAMING_SNAKE_CASE					:			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
              # Second half of next step
              SCREAMING_SNAKE_CASE					:			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
              # Update
              SCREAMING_SNAKE_CASE					:			List[str]    	=       new_dft
              SCREAMING_SNAKE_CASE					:			str    	=       next_ncol // 2
         return dft[0]






    def       _UpperCamelCase    (       self )							-> str:
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self.__dft('A' )
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self.__dft('B' )
         SCREAMING_SNAKE_CASE					:			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
         SCREAMING_SNAKE_CASE					:			Tuple    	=       2
         while next_ncol <= self.c_max_length:
              SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       [[] for i in range(lowercase__ )]
              SCREAMING_SNAKE_CASE					:			List[str]    	=       self.root ** (next_ncol // 2)
              SCREAMING_SNAKE_CASE					:			List[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
              SCREAMING_SNAKE_CASE					:			List[str]    	=       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 )							-> Tuple:
         SCREAMING_SNAKE_CASE					:			str    	=       'A = ' + ' + '.join(
             F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A] ) )
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       'B = ' + ' + '.join(
             F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B] ) )
         SCREAMING_SNAKE_CASE					:			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 Any, Mapping, Optional

from ... import PreTrainedTokenizer
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig, OnnxConfigWithPast, OnnxSeqaSeqConfigWithPast
from ...onnx.utils import compute_effective_axis_dimension
from ...utils import TensorType, is_torch_available, logging


_lowerCAmelCase  :Union[str, Any]  				=    logging.get_logger(__name__)

_lowerCAmelCase  :int  				=    {
    """Helsinki-NLP/opus-mt-en-de""": """https://huggingface.co/Helsinki-NLP/opus-mt-en-de/resolve/main/config.json""",
    # See all Marian models at https://huggingface.co/models?filter=marian
}






class 				UpperCAmelCase (       _SCREAMING_SNAKE_CASE ):




    '''simple docstring'''







    snake_case__							:   List[str]							=						"marian"
    snake_case__							:   Union[str, Any]							=						["past_key_values"]
    snake_case__							:   str							=						{"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}






    def __init__(       self    ,							lowercase__=58_101    ,							lowercase__=None    ,							lowercase__=1_024    ,							lowercase__=12    ,							lowercase__=4_096    ,							lowercase__=16    ,							lowercase__=12    ,							lowercase__=4_096    ,							lowercase__=16    ,							lowercase__=0.0    ,							lowercase__=0.0    ,							lowercase__=True    ,							lowercase__=True    ,							lowercase__="gelu"    ,							lowercase__=1_024    ,							lowercase__=0.1    ,							lowercase__=0.0    ,							lowercase__=0.0    ,							lowercase__=0.0_2    ,							lowercase__=58_100    ,							lowercase__=False    ,							lowercase__=58_100    ,							lowercase__=0    ,							lowercase__=0    ,							lowercase__=True    ,							**lowercase__    ,							)							-> int:
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       vocab_size
         SCREAMING_SNAKE_CASE					:			Dict    	=       decoder_vocab_size or vocab_size
         SCREAMING_SNAKE_CASE					:			int    	=       max_position_embeddings
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       d_model
         SCREAMING_SNAKE_CASE					:			Dict    	=       encoder_ffn_dim
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       encoder_layers
         SCREAMING_SNAKE_CASE					:			Dict    	=       encoder_attention_heads
         SCREAMING_SNAKE_CASE					:			int    	=       decoder_ffn_dim
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       decoder_layers
         SCREAMING_SNAKE_CASE					:			str    	=       decoder_attention_heads
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       dropout
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       attention_dropout
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       activation_dropout
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       activation_function
         SCREAMING_SNAKE_CASE					:			Tuple    	=       init_std
         SCREAMING_SNAKE_CASE					:			int    	=       encoder_layerdrop
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       decoder_layerdrop
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       use_cache
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       encoder_layers
         SCREAMING_SNAKE_CASE					:			int    	=       scale_embedding  # scale factor will be sqrt(d_model) if True
         SCREAMING_SNAKE_CASE					:			str    	=       share_encoder_decoder_embeddings
         super().__init__(
             pad_token_id=lowercase__    ,							eos_token_id=lowercase__    ,							is_encoder_decoder=lowercase__    ,							decoder_start_token_id=lowercase__    ,							forced_eos_token_id=lowercase__    ,							**lowercase__    ,							)






class 				UpperCAmelCase (       _SCREAMING_SNAKE_CASE ):




    '''simple docstring'''







    @property
    # Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.inputs
    def       _UpperCamelCase    (       self )							-> Mapping[str, Mapping[int, str]]:
         if self.task in ["default", "seq2seq-lm"]:
              SCREAMING_SNAKE_CASE					:			Dict    	=       OrderedDict(
                  [
                      ('input_ids', {0: 'batch', 1: 'encoder_sequence'}),
                      ('attention_mask', {0: 'batch', 1: 'encoder_sequence'}),
                  ] )

              if self.use_past:
                   SCREAMING_SNAKE_CASE					:			List[Any]    	=       {0: 'batch'}
                   SCREAMING_SNAKE_CASE					:			Any    	=       {0: 'batch', 1: 'past_decoder_sequence + sequence'}
              else:
                   SCREAMING_SNAKE_CASE					:			str    	=       {0: 'batch', 1: 'decoder_sequence'}
                   SCREAMING_SNAKE_CASE					:			int    	=       {0: 'batch', 1: 'decoder_sequence'}

              if self.use_past:
                   self.fill_with_past_key_values_(lowercase__    ,							direction='inputs' )
         elif self.task == "causal-lm":
              # TODO: figure this case out.
              SCREAMING_SNAKE_CASE					:			List[Any]    	=       OrderedDict(
                  [
                      ('input_ids', {0: 'batch', 1: 'encoder_sequence'}),
                      ('attention_mask', {0: 'batch', 1: 'encoder_sequence'}),
                  ] )
              if self.use_past:
                   SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			Dict    	=       self.num_layers
                   for i in range(lowercase__ ):
                        SCREAMING_SNAKE_CASE					:			Dict    	=       {0: 'batch', 2: 'past_sequence + sequence'}
                        SCREAMING_SNAKE_CASE					:			Dict    	=       {0: 'batch', 2: 'past_sequence + sequence'}
         else:
              SCREAMING_SNAKE_CASE					:			Optional[int]    	=       OrderedDict(
                  [
                      ('input_ids', {0: 'batch', 1: 'encoder_sequence'}),
                      ('attention_mask', {0: 'batch', 1: 'encoder_sequence'}),
                      ('decoder_input_ids', {0: 'batch', 1: 'decoder_sequence'}),
                      ('decoder_attention_mask', {0: 'batch', 1: 'decoder_sequence'}),
                  ] )

         return common_inputs






    @property
    # Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.outputs
    def       _UpperCamelCase    (       self )							-> Mapping[str, Mapping[int, str]]:
         if self.task in ["default", "seq2seq-lm"]:
              SCREAMING_SNAKE_CASE					:			List[str]    	=       super().outputs
         else:
              SCREAMING_SNAKE_CASE					:			Tuple    	=       super(lowercase__    ,							self ).outputs
              if self.use_past:
                   SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self.num_layers
                   for i in range(lowercase__ ):
                        SCREAMING_SNAKE_CASE					:			int    	=       {0: 'batch', 2: 'past_sequence + sequence'}
                        SCREAMING_SNAKE_CASE					:			List[Any]    	=       {0: 'batch', 2: 'past_sequence + sequence'}
         return common_outputs






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = -1    ,							lowercase__ = False    ,							lowercase__ = None    ,							)							-> Mapping[str, Any]:
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       self._generate_dummy_inputs_for_encoder_and_decoder(
             lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )

         # Generate decoder inputs
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       seq_length if not self.use_past else 1
         SCREAMING_SNAKE_CASE					:			str    	=       self._generate_dummy_inputs_for_encoder_and_decoder(
             lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )
         SCREAMING_SNAKE_CASE					:			Tuple    	=       {F"""decoder_{name}""": tensor for name, tensor in decoder_inputs.items()}
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       dict(**lowercase__    ,							**lowercase__ )

         if self.use_past:
              if not is_torch_available():
                   raise ValueError('Cannot generate dummy past_keys inputs without PyTorch installed.' )
              else:
                   import torch
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			int    	=       common_inputs['input_ids'].shape
              SCREAMING_SNAKE_CASE					:			Tuple    	=       common_inputs['decoder_input_ids'].shape[1]
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			str    	=       self.num_attention_heads
              SCREAMING_SNAKE_CASE					:			int    	=       (
                  batch,
                  num_encoder_attention_heads,
                  encoder_seq_length,
                  self._config.hidden_size // num_encoder_attention_heads,
              )
              SCREAMING_SNAKE_CASE					:			str    	=       decoder_seq_length + 3
              SCREAMING_SNAKE_CASE					:			Tuple    	=       (
                  batch,
                  num_decoder_attention_heads,
                  decoder_past_length,
                  self._config.hidden_size // num_decoder_attention_heads,
              )

              SCREAMING_SNAKE_CASE					:			List[str]    	=       torch.cat(
                  [common_inputs['decoder_attention_mask'], torch.ones(lowercase__    ,							lowercase__ )]    ,							dim=1 )

              SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       []
              # If the number of encoder and decoder layers are present in the model configuration, both are considered
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			Dict    	=       self.num_layers
              SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       min(lowercase__    ,							lowercase__ )
              SCREAMING_SNAKE_CASE					:			Tuple    	=       max(lowercase__    ,							lowercase__ ) - min_num_layers
              SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       'encoder' if num_encoder_layers > num_decoder_layers else 'decoder'

              for _ in range(lowercase__ ):
                   common_inputs["past_key_values"].append(
                       (
                           torch.zeros(lowercase__ ),
                           torch.zeros(lowercase__ ),
                           torch.zeros(lowercase__ ),
                           torch.zeros(lowercase__ ),
                       ) )
              # TODO: test this.
              SCREAMING_SNAKE_CASE					:			str    	=       encoder_shape if remaining_side_name == 'encoder' else decoder_shape
              for _ in range(lowercase__    ,							lowercase__ ):
                   common_inputs["past_key_values"].append((torch.zeros(lowercase__ ), torch.zeros(lowercase__ )) )
         return common_inputs






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = -1    ,							lowercase__ = False    ,							lowercase__ = None    ,							)							-> Mapping[str, Any]:
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       self._generate_dummy_inputs_for_encoder_and_decoder(
             lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )

         if self.use_past:
              if not is_torch_available():
                   raise ValueError('Cannot generate dummy past_keys inputs without PyTorch installed.' )
              else:
                   import torch
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			Dict    	=       common_inputs['input_ids'].shape
              # Not using the same length for past_key_values
              SCREAMING_SNAKE_CASE					:			Dict    	=       seqlen + 2
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			str    	=       self.num_layers
              SCREAMING_SNAKE_CASE	,   SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self.num_attention_heads
              SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       (
                  batch,
                  num_encoder_attention_heads,
                  past_key_values_length,
                  self._config.hidden_size // num_encoder_attention_heads,
              )

              SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       common_inputs['attention_mask'].dtype
              SCREAMING_SNAKE_CASE					:			List[str]    	=       torch.cat(
                  [common_inputs['attention_mask'], torch.ones(lowercase__    ,							lowercase__    ,							dtype=lowercase__ )]    ,							dim=1 )
              SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       [
                  (torch.zeros(lowercase__ ), torch.zeros(lowercase__ )) for _ in range(lowercase__ )
              ]
         return common_inputs






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = -1    ,							lowercase__ = False    ,							lowercase__ = None    ,							)							-> Mapping[str, Any]:
         # Copied from OnnxConfig.generate_dummy_inputs
         # Did not use super(OnnxConfigWithPast, self).generate_dummy_inputs for code clarity.
         # If dynamic axis (-1) we forward with a fixed dimension of 2 samples to avoid optimizations made by ONNX
         SCREAMING_SNAKE_CASE					:			List[str]    	=       compute_effective_axis_dimension(
             lowercase__    ,							fixed_dimension=OnnxConfig.default_fixed_batch    ,							num_token_to_add=0 )

         # If dynamic axis (-1) we forward with a fixed dimension of 8 tokens to avoid optimizations made by ONNX
         SCREAMING_SNAKE_CASE					:			List[str]    	=       tokenizer.num_special_tokens_to_add(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Dict    	=       compute_effective_axis_dimension(
             lowercase__    ,							fixed_dimension=OnnxConfig.default_fixed_sequence    ,							num_token_to_add=lowercase__ )

         # Generate dummy inputs according to compute batch and sequence
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [' '.join([tokenizer.unk_token] ) * seq_length] * batch_size
         SCREAMING_SNAKE_CASE					:			Tuple    	=       dict(tokenizer(lowercase__    ,							return_tensors=lowercase__ ) )
         return common_inputs






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = -1    ,							lowercase__ = False    ,							lowercase__ = None    ,							)							-> Mapping[str, Any]:
         if self.task in ["default", "seq2seq-lm"]:
              SCREAMING_SNAKE_CASE					:			List[Any]    	=       self._generate_dummy_inputs_for_default_and_seqaseq_lm(
                  lowercase__    ,							batch_size=lowercase__    ,							seq_length=lowercase__    ,							is_pair=lowercase__    ,							framework=lowercase__ )

         else:
              SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self._generate_dummy_inputs_for_causal_lm(
                  lowercase__    ,							batch_size=lowercase__    ,							seq_length=lowercase__    ,							is_pair=lowercase__    ,							framework=lowercase__ )

         return common_inputs






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )							-> int:
         if self.task in ["default", "seq2seq-lm"]:
              SCREAMING_SNAKE_CASE					:			List[Any]    	=       super()._flatten_past_key_values_(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )
         else:
              SCREAMING_SNAKE_CASE					:			Any    	=       super(lowercase__    ,							self )._flatten_past_key_values_(
                  lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )






    @property
    def       _UpperCamelCase    (       self )							-> float:
         return 1E-4



