


"""simple docstring"""





import tempfile
import unittest

from transformers import TaConfig, is_torch_available
from transformers.testing_utils import (
    require_sentencepiece,
    require_tokenizers,
    require_torch,
    slow,
    torch_device,
)

from ...generation.test_utils import GenerationTesterMixin
from ...test_modeling_common import ModelTesterMixin, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
 import torch

 from transformers import AutoTokenizer, UMTaForConditionalGeneration, UMTaForQuestionAnswering, UMTaModel



class 						snake_case_:






     def __init__(		self     :    Dict    , UpperCamelCase_     :    Any    , UpperCamelCase_     :    int=9_9    , UpperCamelCase_     :    str=1_3    , UpperCamelCase_     :    Union[str, Any]=7    , UpperCamelCase_     :    Optional[int]=9    , UpperCamelCase_     :    Optional[Any]=True    , UpperCamelCase_     :    Dict=True    , UpperCamelCase_     :    Optional[int]=False    , UpperCamelCase_     :    int=3_2    , UpperCamelCase_     :    List[Any]=5    , UpperCamelCase_     :    int=4    , UpperCamelCase_     :    int=3_7    , UpperCamelCase_     :    Dict=8    , UpperCamelCase_     :    str=0.1    , UpperCamelCase_     :    List[str]=0.002    , UpperCamelCase_     :    List[Any]=1    , UpperCamelCase_     :    str=0    , UpperCamelCase_     :    Union[str, Any]=0    , UpperCamelCase_     :    int=None    , UpperCamelCase_     :    Any=None    , ):
           lowerCAmelCase    :		Union[str, Any]				=      parent
           lowerCAmelCase    :		Any				=      batch_size
           lowerCAmelCase    :		str				=      encoder_seq_length
           lowerCAmelCase    :		int				=      decoder_seq_length
           # For common tests
           lowerCAmelCase    :		str				=      self.decoder_seq_length
           lowerCAmelCase    :		int				=      is_training
           lowerCAmelCase    :		Optional[Any]				=      use_attention_mask
           lowerCAmelCase    :		Optional[int]				=      use_labels
           lowerCAmelCase    :		Any				=      vocab_size
           lowerCAmelCase    :		Tuple				=      hidden_size
           lowerCAmelCase    :		Any				=      num_hidden_layers
           lowerCAmelCase    :		str				=      num_attention_heads
           lowerCAmelCase    :		Any				=      d_ff
           lowerCAmelCase    :		List[str]				=      relative_attention_num_buckets
           lowerCAmelCase    :		Union[str, Any]				=      dropout_rate
           lowerCAmelCase    :		str				=      initializer_factor
           lowerCAmelCase    :		Tuple				=      eos_token_id
           lowerCAmelCase    :		Dict				=      pad_token_id
           lowerCAmelCase    :		List[Any]				=      decoder_start_token_id
           lowerCAmelCase    :		Tuple				=      None
           lowerCAmelCase    :		List[Any]				=      decoder_layers






     def    lowerCamelCase__   (		self     :    Any ):
           return TaConfig.from_pretrained('''google/umt5-base''' )






     def    lowerCamelCase__   (		self     :    Dict    , UpperCamelCase_     :    str    , UpperCamelCase_     :    Tuple    , UpperCamelCase_     :    List[Any]    , UpperCamelCase_     :    List[Any]=None    , UpperCamelCase_     :    Union[str, Any]=None    , UpperCamelCase_     :    Tuple=None    , UpperCamelCase_     :    List[str]=None    , UpperCamelCase_     :    Optional[int]=None    , ):
           if attention_mask is None:
                 lowerCAmelCase    :		str				=      input_ids.ne(config.pad_token_id )
           if decoder_attention_mask is None:
                 lowerCAmelCase    :		Dict				=      decoder_input_ids.ne(config.pad_token_id )
           if head_mask is None:
                 lowerCAmelCase    :		Dict				=      torch.ones(config.num_hidden_layers    , config.num_attention_heads    , device=UpperCamelCase_ )
           if decoder_head_mask is None:
                 lowerCAmelCase    :		Optional[int]				=      torch.ones(config.num_decoder_layers    , config.num_attention_heads    , device=UpperCamelCase_ )
           if cross_attn_head_mask is None:
                 lowerCAmelCase    :		str				=      torch.ones(
                     config.num_decoder_layers    , config.num_attention_heads    , device=UpperCamelCase_ )
           return {
               "input_ids": input_ids,
               "decoder_input_ids": decoder_input_ids,
               "attention_mask": attention_mask,
               "decoder_attention_mask": decoder_attention_mask,
               "head_mask": head_mask,
               "decoder_head_mask": decoder_head_mask,
               "cross_attn_head_mask": cross_attn_head_mask,
           }






     def    lowerCamelCase__   (		self     :    Union[str, Any] ):
           lowerCAmelCase    :		Optional[Any]				=      ids_tensor([self.batch_size, self.encoder_seq_length]    , self.vocab_size )
           lowerCAmelCase    :		List[Any]				=      ids_tensor([self.batch_size, self.decoder_seq_length]    , self.vocab_size )

           # we need to clamp the input ids here to avoid having pad token in between
           # this is because for NllbMoe the position_ids are prepared such that
           # all pad tokens have pos id = 2 and rest are between 2..seq_length
           # and the seq_length here is seq_length - num_pad_tokens
           # but when using past, there is no way of knowing if the past input ids had
           # pad tokens in them, which results in incorrect seq_lenth and which in turn results in
           # position_ids being off by num_pad_tokens in past input
           lowerCAmelCase    :		Optional[Any]				=      input_ids.clamp(self.pad_token_id + 1 )
           lowerCAmelCase    :		Dict				=      decoder_input_ids.clamp(self.pad_token_id + 1 )

           lowerCAmelCase    :		Dict				=      self.get_config()
           lowerCAmelCase    :		Union[str, Any]				=      config.num_attention_heads
           lowerCAmelCase    :		Any				=      self.prepare_inputs_dict(UpperCamelCase_    , UpperCamelCase_    , UpperCamelCase_ )
           return config, input_dict






     def    lowerCamelCase__   (		self     :    Tuple ):
           lowerCAmelCase,					lowerCAmelCase    :		Optional[int]				=      self.prepare_config_and_inputs()
           return config, inputs_dict






     def    lowerCamelCase__   (		self     :    Optional[int] ):
           return TaConfig(
               vocab_size=1_6_6    , d_model=self.hidden_size    , d_ff=self.d_ff    , d_kv=self.hidden_size // self.num_attention_heads    , num_layers=self.num_hidden_layers    , num_decoder_layers=self.decoder_layers    , num_heads=self.num_attention_heads    , relative_attention_num_buckets=self.relative_attention_num_buckets    , dropout_rate=self.dropout_rate    , initializer_factor=self.initializer_factor    , eos_token_id=self.eos_token_id    , bos_token_id=self.pad_token_id    , pad_token_id=self.pad_token_id    , decoder_start_token_id=self.decoder_start_token_id    , )






     def    lowerCamelCase__   (		self     :    Tuple ):
           return TaConfig(
               vocab_size=self.vocab_size    , d_model=self.hidden_size    , d_ff=self.d_ff    , d_kv=self.hidden_size // self.num_attention_heads    , num_layers=self.num_hidden_layers    , num_decoder_layers=self.decoder_layers    , num_heads=self.num_attention_heads    , relative_attention_num_buckets=self.relative_attention_num_buckets    , dropout_rate=self.dropout_rate    , initializer_factor=self.initializer_factor    , eos_token_id=self.eos_token_id    , bos_token_id=self.pad_token_id    , pad_token_id=self.pad_token_id    , decoder_start_token_id=self.decoder_start_token_id    , )






     def    lowerCamelCase__   (		self     :    Dict    , UpperCamelCase_     :    Union[str, Any]    , UpperCamelCase_     :    Any    , UpperCamelCase_     :    Any    , UpperCamelCase_     :    Optional[Any]    , UpperCamelCase_     :    Optional[int]    , UpperCamelCase_     :    Dict    , ):
           lowerCAmelCase    :		List[str]				=      UMTaModel(config=UpperCamelCase_ )
           model.to(UpperCamelCase_ )
           model.eval()
           lowerCAmelCase    :		Dict				=      model(
               input_ids=UpperCamelCase_    , decoder_input_ids=UpperCamelCase_    , attention_mask=UpperCamelCase_    , decoder_attention_mask=UpperCamelCase_    , )
           lowerCAmelCase    :		Any				=      model(input_ids=UpperCamelCase_    , decoder_input_ids=UpperCamelCase_ )
           lowerCAmelCase    :		str				=      result.last_hidden_state
           lowerCAmelCase    :		int				=      result.past_key_values
           lowerCAmelCase    :		Dict				=      result.encoder_last_hidden_state

           self.parent.assertEqual(encoder_output.size()    , (self.batch_size, self.encoder_seq_length, self.hidden_size) )
           self.parent.assertEqual(decoder_output.size()    , (self.batch_size, self.decoder_seq_length, self.hidden_size) )
           # There should be `num_layers` key value embeddings stored in decoder_past
           self.parent.assertEqual(len(UpperCamelCase_ )    , config.num_layers )
           # There should be a self attn key, a self attn value, a cross attn key and a cross attn value stored in each decoder_past tuple
           self.parent.assertEqual(len(decoder_past[0] )    , 4 )






     def    lowerCamelCase__   (		self     :    List[str]    , UpperCamelCase_     :    Union[str, Any]    , UpperCamelCase_     :    Tuple    , UpperCamelCase_     :    Tuple    , UpperCamelCase_     :    Tuple    , UpperCamelCase_     :    List[str]    , UpperCamelCase_     :    str    , ):
           lowerCAmelCase    :		Any				=      UMTaModel(config=UpperCamelCase_ ).get_decoder().to(UpperCamelCase_ ).eval()
           # first forward pass
           lowerCAmelCase    :		int				=      model(UpperCamelCase_    , use_cache=UpperCamelCase_ )
           lowerCAmelCase    :		List[Any]				=      model(UpperCamelCase_ )
           lowerCAmelCase    :		Union[str, Any]				=      model(UpperCamelCase_    , use_cache=UpperCamelCase_ )

           self.parent.assertTrue(len(UpperCamelCase_ ) == len(UpperCamelCase_ ) )
           self.parent.assertTrue(len(UpperCamelCase_ ) == len(UpperCamelCase_ ) + 1 )

           lowerCAmelCase,					lowerCAmelCase    :		List[str]				=      outputs.to_tuple()

           # create hypothetical next token and extent to next_input_ids
           lowerCAmelCase    :		Dict				=      ids_tensor((self.batch_size, 1)    , config.vocab_size )

           # append to next input_ids and
           lowerCAmelCase    :		List[Any]				=      torch.cat([input_ids, next_tokens]    , dim=-1 )

           lowerCAmelCase    :		str				=      model(UpperCamelCase_ )['''last_hidden_state''']
           lowerCAmelCase    :		Union[str, Any]				=      model(UpperCamelCase_    , past_key_values=UpperCamelCase_ )['''last_hidden_state''']

           # select random slice
           lowerCAmelCase    :		int				=      ids_tensor((1,)    , output_from_past.shape[-1] ).item()
           lowerCAmelCase    :		Any				=      output_from_no_past[:, -1, random_slice_idx].detach()
           lowerCAmelCase    :		List[Any]				=      output_from_past[:, 0, random_slice_idx].detach()

           # test that outputs are equal for slice
           self.parent.assertTrue(torch.allclose(UpperCamelCase_    , UpperCamelCase_    , atol=1E-3 ) )






     def    lowerCamelCase__   (		self     :    Any    , UpperCamelCase_     :    Optional[int]    , UpperCamelCase_     :    Optional[int]    , ):
           lowerCAmelCase    :		Optional[int]				=      UMTaModel(config=UpperCamelCase_ ).to(UpperCamelCase_ ).half().eval()
           lowerCAmelCase    :		Union[str, Any]				=      model(**UpperCamelCase_ )['''last_hidden_state''']
           self.parent.assertFalse(torch.isnan(UpperCamelCase_ ).any().item() )



@require_torch
class 						snake_case_(				a__							,    a__							,    a__							,    unittest.TestCase	):
     __UpperCamelCase     =    (
         (UMTaModel, UMTaForConditionalGeneration, UMTaForQuestionAnswering) if is_torch_available() else ()
     )
     __UpperCamelCase     =    (UMTaForConditionalGeneration,) if is_torch_available() else ()
     __UpperCamelCase     =    (
         {
             '''conversational''': UMTaForConditionalGeneration,
             '''feature-extraction''': UMTaModel,
             '''summarization''': UMTaForConditionalGeneration,
             '''text2text-generation''': UMTaForConditionalGeneration,
             '''translation''': UMTaForConditionalGeneration,
             '''question-answering''': UMTaForQuestionAnswering,
         }
         if is_torch_available()
         else {}
     )
     __UpperCamelCase     =    True
     __UpperCamelCase     =    False
     __UpperCamelCase     =    False
     __UpperCamelCase     =    True
     __UpperCamelCase     =    True
     # The small UMT5 model needs higher percentages for CPU/MP tests
     __UpperCamelCase     =    [0.8, 0.9]






     def    lowerCamelCase__   (		self     :    Optional[int] ):
           lowerCAmelCase    :		Any				=      UMTaModelTester(self )






     @unittest.skip('''Test has a segmentation fault on torch 1.8.0''' )
     def    lowerCamelCase__   (		self     :    Tuple ):
           lowerCAmelCase    :		Tuple				=      self.model_tester.prepare_config_and_inputs()
           lowerCAmelCase    :		Union[str, Any]				=      UMTaModel(config_and_inputs[0] ).to(UpperCamelCase_ )
           with tempfile.TemporaryDirectory() as tmpdirname:
                 torch.onnx.export(
                     UpperCamelCase_    , (config_and_inputs[1], config_and_inputs[3], config_and_inputs[2])    , F'''{tmpdirname}/t5_test.onnx'''    , export_params=UpperCamelCase_    , opset_version=9    , input_names=['''input_ids''', '''decoder_input_ids''']    , )






     @unittest.skipIf(torch_device == '''cpu'''    , '''Cant do half precision''' )
     def    lowerCamelCase__   (		self     :    Any ):
           lowerCAmelCase    :		int				=      self.model_tester.prepare_config_and_inputs()
           self.model_tester.create_and_check_model_fpaa_forward(*UpperCamelCase_ )






     def    lowerCamelCase__   (		self     :    List[Any] ):
           lowerCAmelCase    :		Dict				=      ['''encoder_attentions''', '''decoder_attentions''', '''cross_attentions''']
           lowerCAmelCase    :		List[str]				=      self.model_tester.prepare_config_and_inputs()
           lowerCAmelCase    :		str				=      config_and_inputs[0]
           lowerCAmelCase    :		List[str]				=      UMTaForConditionalGeneration(UpperCamelCase_ ).eval()
           model.to(UpperCamelCase_ )

           lowerCAmelCase    :		str				=      {
               '''head_mask''': torch.zeros(config.num_layers    , config.num_heads    , device=UpperCamelCase_ ),
               '''decoder_head_mask''': torch.zeros(config.num_decoder_layers    , config.num_heads    , device=UpperCamelCase_ ),
               '''cross_attn_head_mask''': torch.zeros(config.num_decoder_layers    , config.num_heads    , device=UpperCamelCase_ ),
           }

           for attn_name, (name, mask) in zip(UpperCamelCase_    , head_masking.items() ):
                 lowerCAmelCase    :		Tuple				=      {name: mask}
                 # Explicitly pass decoder_head_mask as it is required from T5 model when head_mask specified
                 if name == "head_mask":
                       lowerCAmelCase    :		List[str]				=      torch.ones(
                           config.num_decoder_layers    , config.num_heads    , device=UpperCamelCase_ )

                 lowerCAmelCase    :		List[str]				=      model.generate(
                     config_and_inputs[1]['''input_ids''']    , num_beams=1    , max_length=3    , output_attentions=UpperCamelCase_    , return_dict_in_generate=UpperCamelCase_    , **UpperCamelCase_    , )
                 # We check the state of decoder_attentions and cross_attentions just from the last step
                 lowerCAmelCase    :		int				=      out[attn_name] if attn_name == attention_names[0] else out[attn_name][-1]
                 self.assertEqual(sum([w.sum().item() for w in attn_weights] )    , 0.0 )






     @unittest.skip('''Does not work on the tiny model as we keep hitting edge cases.''' )
     def    lowerCamelCase__   (		self     :    Any ):
           pass



@require_torch
@require_sentencepiece
@require_tokenizers
class 						snake_case_(				unittest.TestCase	):






     @slow
     @unittest.skip(
         '''Unless we stop stripping left and right by default for all special tokens, the expected ids obtained here will not match the original ones. Wait for https://github.com/huggingface/transformers/pull/23909 to be merged''' )
     def    lowerCamelCase__   (		self     :    int ):
           lowerCAmelCase    :		int				=      UMTaForConditionalGeneration.from_pretrained('''google/umt5-small'''    , return_dict=UpperCamelCase_ ).to(UpperCamelCase_ )
           lowerCAmelCase    :		int				=      AutoTokenizer.from_pretrained('''google/umt5-small'''    , use_fast=UpperCamelCase_    , legacy=UpperCamelCase_ )
           lowerCAmelCase    :		List[Any]				=      [
               '''Bonjour monsieur <extra_id_0> bien <extra_id_1>.''',
               '''No se como puedo <extra_id_0>.''',
               '''This is the reason why we <extra_id_0> them.''',
               '''The <extra_id_0> walks in <extra_id_1>, seats''',
               '''A <extra_id_0> walks into a bar and orders a <extra_id_1> with <extra_id_2> pinch of <extra_id_3>.''',
           ]
           lowerCAmelCase    :		List[str]				=      tokenizer(UpperCamelCase_    , return_tensors='''pt'''    , padding=UpperCamelCase_ ).input_ids
           # fmt: off
           lowerCAmelCase    :		Optional[Any]				=      torch.tensor(
               [
                   [ 3_8_5_3_0, 2_1_0_7_0_3, 2_5_6_2_9_9, 1_4_1_0, 2_5_6_2_9_8, 2_7_4, 1, 0,0, 0, 0, 0, 0, 0, 0, 0,0, 0],
                   [   8_2_6, 3_2_1, 6_7_1, 2_5_9_2_2, 2_5_6_2_9_9, 2_7_4, 1, 0,0, 0, 0, 0, 0, 0, 0, 0,0, 0],
                   [  1_4_6_0, 3_3_9, 3_1_2, 1_9_0_1_4, 1_0_6_2_0, 7_5_8, 2_5_6_2_9_9, 2_3_5_5,2_7_4, 1, 0, 0, 0, 0, 0, 0,0, 0],
                   [   5_1_7, 2_5_6_2_9_9, 1_4_8_6_9, 2_8_1, 3_0_1, 2_5_6_2_9_8, 2_7_5, 1_1_9_9_8_3,1, 0, 0, 0, 0, 0, 0, 0,0, 0],
                   [   3_2_0, 2_5_6_2_9_9, 1_4_8_6_9, 2_8_1, 2_2_3_4, 2_8_9, 2_2_7_5, 3_3_3,6_1_3_9_1, 2_8_9, 2_5_6_2_9_8, 5_4_3, 2_5_6_2_9_7, 1_6_8_7_1_4, 3_2_9, 2_5_6_2_9_6,2_7_4, 1],
               ] )
           # fmt: on
           torch.testing.assert_allclose(UpperCamelCase_    , UpperCamelCase_ )

           lowerCAmelCase    :		str				=      model.generate(input_ids.to(UpperCamelCase_ ) )
           lowerCAmelCase    :		Optional[Any]				=      [
               '''<pad><extra_id_0> et<extra_id_1> [eod] <extra_id_2><extra_id_55>.. [eod] 💐 💐 💐 💐 💐 💐 💐 💐 💐 💐 💐 <extra_id_56>ajšietosto<extra_id_56>lleux<extra_id_19><extra_id_6>ajšie</s>''',
               '''<pad><extra_id_0>.<extra_id_1>.,<0x0A>...spech <0x0A><extra_id_20> <extra_id_21></s><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad>''',
               '''<pad><extra_id_0> are not going to be a part of the world. We are not going to be a part of<extra_id_1> and<extra_id_2><0x0A><extra_id_48>.<extra_id_48></s><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad>''',
               '''<pad><extra_id_0> door<extra_id_1>, the door<extra_id_2> 피해[/</s><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad>''',
               '''<pad><extra_id_0>nyone who<extra_id_1> drink<extra_id_2> a<extra_id_3> alcohol<extra_id_4> A<extra_id_5> A. This<extra_id_6> I<extra_id_7><extra_id_52><extra_id_53></s><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad>''',
           ]
           lowerCAmelCase    :		Tuple				=      tokenizer.batch_decode(UpperCamelCase_ )
           self.assertEqual(UpperCamelCase_    , UpperCamelCase_ )






"""simple docstring"""





import mpmath  # for roots of unity
import numpy as np



class 						snake_case_:






     def __init__(		self     :    str    , UpperCamelCase_     :    int=None    , UpperCamelCase_     :    List[str]=None ):
           # Input as list
           lowerCAmelCase    :		str				=      list(poly_a or [0] )[:]
           lowerCAmelCase    :		Any				=      list(poly_b or [0] )[:]

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

           while self.polyB[-1] == 0:
                 self.polyB.pop()
           lowerCAmelCase    :		Union[str, Any]				=      len(self.polyB )

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

           # The product
           lowerCAmelCase    :		int				=      self.__multiply()






     def    lowerCamelCase__   (		self     :    List[str]    , UpperCamelCase_     :    str ):
           lowerCAmelCase    :		Optional[Any]				=      [[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
           # Corner case
           if len(UpperCamelCase_ ) <= 1:
                 return dft[0]
           #
           lowerCAmelCase    :		Tuple				=      self.c_max_length // 2
           while next_ncol > 0:
                 lowerCAmelCase    :		Dict				=      [[] for i in range(UpperCamelCase_ )]
                 lowerCAmelCase    :		List[Any]				=      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(UpperCamelCase_ ):
                             new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j] )
                       current_root *= root
                 # Second half of next step
                 lowerCAmelCase    :		int				=      1
                 for j in range(self.c_max_length // (next_ncol * 2) ):
                       for i in range(UpperCamelCase_ ):
                             new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j] )
                       current_root *= root
                 # Update
                 lowerCAmelCase    :		Optional[Any]				=      new_dft
                 lowerCAmelCase    :		Union[str, Any]				=      next_ncol // 2
           return dft[0]






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


