





import mpmath  # for roots of unity
import numpy as np

class 					A     :



      def __init__(       self  ,	lowercase_=None  ,	lowercase_=None       )   -> List[Any]:



             '''simple docstring'''

             _snake_case   :				Dict  					=    list(poly_a or [0]       )[:]
             _snake_case   :				int  					=    list(poly_b or [0]       )[:]

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

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

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

             # The product
             _snake_case   :				Optional[int]  					=    self.__multiply()



      def  __a			(       self  ,	lowercase_       )   -> List[str]:



             '''simple docstring'''

             _snake_case   :				Dict  					=    [[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]
             #
             _snake_case   :				Optional[Any]  					=    self.c_max_length // 2
             while next_ncol > 0:
                    _snake_case   :				List[Any]  					=    [[] for i in range(lowercase_       )]
                    _snake_case   :				List[str]  					=    self.root**next_ncol

                    # First half of next step
                    _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
                    _snake_case   :				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
                    # Update
                    _snake_case   :				int  					=    new_dft
                    _snake_case   :				Tuple  					=    next_ncol // 2
             return dft[0]



      def  __a			(       self       )   -> Tuple:



             '''simple docstring'''

             _snake_case   :				Optional[int]  					=    self.__dft('''A'''       )
             _snake_case   :				Optional[Any]  					=    self.__dft('''B'''       )
             _snake_case   :				Union[str, 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
             _snake_case   :				Optional[int]  					=    2
             while next_ncol <= self.c_max_length:
                    _snake_case   :				Optional[int]  					=    [[] for i in range(lowercase_       )]
                    _snake_case   :				int  					=    self.root ** (next_ncol // 2)
                    _snake_case   :				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
                    _snake_case   :				Tuple  					=    new_inverse_c
                    next_ncol *= 2
             # Unpack
             _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       )   -> Optional[Any]:



             '''simple docstring'''

             _snake_case   :				Tuple  					=    '''A = ''' + ''' + '''.join(
                 F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]       )       )
             _snake_case   :				Union[str, Any]  					=    '''B = ''' + ''' + '''.join(
                 F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]       )       )
             _snake_case   :				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()













'''simple docstring'''

import gc
import unittest

from transformers import CTRLConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

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


if is_torch_available():
    import torch

    from transformers import (
        CTRL_PRETRAINED_MODEL_ARCHIVE_LIST,
        CTRLForSequenceClassification,
        CTRLLMHeadModel,
        CTRLModel,
    )







class __a			:





   def __init__(       self					:      Union[str, Any]					,lowerCamelCase					:      Optional[int]					,lowerCamelCase					:      Tuple=14					,lowerCamelCase					:      Optional[Any]=7					,lowerCamelCase					:      str=True					,lowerCamelCase					:      List[str]=True					,lowerCamelCase					:      Dict=True					,lowerCamelCase					:      Any=True					,lowerCamelCase					:      int=True					,lowerCamelCase					:      Dict=99					,lowerCamelCase					:      Dict=32					,lowerCamelCase					:      Optional[Any]=5					,lowerCamelCase					:      Tuple=4					,lowerCamelCase					:      Optional[int]=37					,lowerCamelCase					:      Optional[int]="gelu"					,lowerCamelCase					:      Optional[Any]=0.1					,lowerCamelCase					:      Tuple=0.1					,lowerCamelCase					:      Dict=512					,lowerCamelCase					:      int=16					,lowerCamelCase					:      Union[str, Any]=2					,lowerCamelCase					:      Tuple=0.02					,lowerCamelCase					:      str=3					,lowerCamelCase					:      Union[str, Any]=4					,lowerCamelCase					:      Any=None					,):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							parent
      __SCREAMING_SNAKE_CASE   				=							batch_size
      __SCREAMING_SNAKE_CASE   				=							seq_length
      __SCREAMING_SNAKE_CASE   				=							is_training
      __SCREAMING_SNAKE_CASE   				=							use_token_type_ids
      __SCREAMING_SNAKE_CASE   				=							use_input_mask
      __SCREAMING_SNAKE_CASE   				=							use_labels
      __SCREAMING_SNAKE_CASE   				=							use_mc_token_ids
      __SCREAMING_SNAKE_CASE   				=							vocab_size
      __SCREAMING_SNAKE_CASE   				=							hidden_size
      __SCREAMING_SNAKE_CASE   				=							num_hidden_layers
      __SCREAMING_SNAKE_CASE   				=							num_attention_heads
      __SCREAMING_SNAKE_CASE   				=							intermediate_size
      __SCREAMING_SNAKE_CASE   				=							hidden_act
      __SCREAMING_SNAKE_CASE   				=							hidden_dropout_prob
      __SCREAMING_SNAKE_CASE   				=							attention_probs_dropout_prob
      __SCREAMING_SNAKE_CASE   				=							max_position_embeddings
      __SCREAMING_SNAKE_CASE   				=							type_vocab_size
      __SCREAMING_SNAKE_CASE   				=							type_sequence_label_size
      __SCREAMING_SNAKE_CASE   				=							initializer_range
      __SCREAMING_SNAKE_CASE   				=							num_labels
      __SCREAMING_SNAKE_CASE   				=							num_choices
      __SCREAMING_SNAKE_CASE   				=							scope
      __SCREAMING_SNAKE_CASE   				=							self.vocab_size - 1





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size, self.seq_length]					,self.vocab_size     )

      __SCREAMING_SNAKE_CASE   				=							None
      if self.use_input_mask:
         __SCREAMING_SNAKE_CASE   				=							random_attention_mask([self.batch_size, self.seq_length]     )

      __SCREAMING_SNAKE_CASE   				=							None
      if self.use_token_type_ids:
         __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size, self.seq_length]					,self.type_vocab_size     )

      __SCREAMING_SNAKE_CASE   				=							None
      if self.use_mc_token_ids:
         __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size, self.num_choices]					,self.seq_length     )

      __SCREAMING_SNAKE_CASE   				=							None
      __SCREAMING_SNAKE_CASE   				=							None
      __SCREAMING_SNAKE_CASE   				=							None
      if self.use_labels:
         __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size]					,self.type_sequence_label_size     )
         __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size, self.seq_length]					,self.num_labels     )
         __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size]					,self.num_choices     )

      __SCREAMING_SNAKE_CASE   				=							self.get_config()

      __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.num_hidden_layers, self.num_attention_heads]					,2     )

      return (
          config,
          input_ids,
          input_mask,
          head_mask,
          token_type_ids,
          mc_token_ids,
          sequence_labels,
          token_labels,
          choice_labels,
      )





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      return CTRLConfig(
          vocab_size=self.vocab_size					,n_embd=self.hidden_size					,n_layer=self.num_hidden_layers					,n_head=self.num_attention_heads					,n_positions=self.max_position_embeddings					,pad_token_id=self.pad_token_id					,)





   def   UpperCAmelCase__  (       self					:      Tuple					,lowerCamelCase					:      Optional[Any]					,lowerCamelCase					:      Tuple					,lowerCamelCase					:      Any					,lowerCamelCase					:      List[str]					,lowerCamelCase					:      str					,*lowerCamelCase					:      Tuple     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							CTRLModel(config=lowerCamelCase     )
      model.to(lowerCamelCase     )
      model.eval()

      model(lowerCamelCase					,token_type_ids=lowerCamelCase					,head_mask=lowerCamelCase     )
      model(lowerCamelCase					,token_type_ids=lowerCamelCase     )
      __SCREAMING_SNAKE_CASE   				=							model(lowerCamelCase     )
      self.parent.assertEqual(result.last_hidden_state.shape					,(self.batch_size, self.seq_length, self.hidden_size)     )
      self.parent.assertEqual(len(result.past_key_values     )					,config.n_layer     )





   def   UpperCAmelCase__  (       self					:      Optional[int]					,lowerCamelCase					:      int					,lowerCamelCase					:      Optional[Any]					,lowerCamelCase					:      Optional[Any]					,lowerCamelCase					:      int					,lowerCamelCase					:      Dict					,*lowerCamelCase					:      int     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							CTRLLMHeadModel(lowerCamelCase     )
      model.to(lowerCamelCase     )
      model.eval()

      __SCREAMING_SNAKE_CASE   				=							model(lowerCamelCase					,token_type_ids=lowerCamelCase					,labels=lowerCamelCase     )
      self.parent.assertEqual(result.loss.shape					,()     )
      self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.seq_length, self.vocab_size)     )





   def   UpperCAmelCase__  (       self					:      List[Any]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.prepare_config_and_inputs()

      (
          (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  (
          __SCREAMING_SNAKE_CASE
      )				,  
      )   				=							config_and_inputs

      __SCREAMING_SNAKE_CASE   				=							{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """head_mask""": head_mask}

      return config, inputs_dict





   def   UpperCAmelCase__  (       self					:      Dict					,lowerCamelCase					:      int					,lowerCamelCase					:      str					,lowerCamelCase					:      Optional[Any]					,lowerCamelCase					:      Optional[Any]					,*lowerCamelCase					:      Optional[Any]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.num_labels
      __SCREAMING_SNAKE_CASE   				=							CTRLForSequenceClassification(lowerCamelCase     )
      model.to(lowerCamelCase     )
      model.eval()
      __SCREAMING_SNAKE_CASE   				=							ids_tensor([self.batch_size]					,self.type_sequence_label_size     )
      __SCREAMING_SNAKE_CASE   				=							model(lowerCamelCase					,token_type_ids=lowerCamelCase					,labels=lowerCamelCase     )
      self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.num_labels)     )







@require_torch
class __a			( _snake_case, _snake_case, _snake_case, unittest.TestCase      ):
   __UpperCamelCase :			str						   =						(CTRLModel, CTRLLMHeadModel, CTRLForSequenceClassification) if is_torch_available() else ()
   __UpperCamelCase :			Dict						   =						(CTRLLMHeadModel,) if is_torch_available() else ()
   __UpperCamelCase :			int						   =						(
       {
           'feature-extraction': CTRLModel,
           'text-classification': CTRLForSequenceClassification,
           'text-generation': CTRLLMHeadModel,
           'zero-shot': CTRLForSequenceClassification,
       }
       if is_torch_available()
       else {}
   )
   __UpperCamelCase :			List[str]						   =						True
   __UpperCamelCase :			Dict						   =						False
   __UpperCamelCase :			Tuple						   =						False





   def   UpperCAmelCase__  (       self					:      Dict					,lowerCamelCase					:      Any					,lowerCamelCase					:      str					,lowerCamelCase					:      List[str]					,lowerCamelCase					:      int					,lowerCamelCase					:      Dict     ):

      '''simple docstring'''

      if pipeline_test_casse_name == "ZeroShotClassificationPipelineTests":
         # Get `tokenizer does not have a padding token` error for both fast/slow tokenizers.
         # `CTRLConfig` was never used in pipeline tests, either because of a missing checkpoint or because a tiny
         # config could not be created.
         return True

      return False





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							CTRLModelTester(self     )
      __SCREAMING_SNAKE_CASE   				=							ConfigTester(self					,config_class=lowerCamelCase					,n_embd=37     )





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      super().tearDown()
      # clean-up as much as possible GPU memory occupied by PyTorch
      gc.collect()
      torch.cuda.empty_cache()





   def   UpperCAmelCase__  (       self					:      Optional[int]     ):

      '''simple docstring'''

      self.config_tester.run_common_tests()





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.model_tester.prepare_config_and_inputs()
      self.model_tester.create_and_check_ctrl_model(*lowerCamelCase     )





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.model_tester.prepare_config_and_inputs()
      self.model_tester.create_and_check_lm_head_model(*lowerCamelCase     )





   @unittest.skip("""Will be fixed soon by reducing the size of the model used for common tests."""     )
   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      pass





   @slow
   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      for model_name in CTRL_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
         __SCREAMING_SNAKE_CASE   				=							CTRLModel.from_pretrained(lowerCamelCase     )
         self.assertIsNotNone(lowerCamelCase     )





   @unittest.skip("""The model doesn't support left padding"""     )  # and it's not used enough to be worth fixing :)
   def   UpperCAmelCase__  (       self					:      Tuple     ):

      '''simple docstring'''

      pass







@require_torch
class __a			( unittest.TestCase      ):





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      super().tearDown()
      # clean-up as much as possible GPU memory occupied by PyTorch
      gc.collect()
      torch.cuda.empty_cache()





   @slow
   def   UpperCAmelCase__  (       self					:      Union[str, Any]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							CTRLLMHeadModel.from_pretrained("""ctrl"""     )
      model.to(lowerCamelCase     )
      __SCREAMING_SNAKE_CASE   				=							torch.tensor(
          [[1_1859, 0, 1611, 8]]					,dtype=torch.long					,device=lowerCamelCase     )  # Legal the president is
      __SCREAMING_SNAKE_CASE   				=							[
          1_1859,
          0,
          1611,
          8,
          5,
          150,
          2_6449,
          2,
          19,
          348,
          469,
          3,
          2595,
          48,
          2_0740,
          24_6533,
          24_6533,
          19,
          30,
          5,
      ]  # Legal the president is a good guy and I don't want to lose my job. \n \n I have a

      __SCREAMING_SNAKE_CASE   				=							model.generate(lowerCamelCase					,do_sample=lowerCamelCase     )
      self.assertListEqual(output_ids[0].tolist()					,lowerCamelCase     )





