

import mpmath  # for roots of unity
import numpy as np





class 				__lowerCAmelCase  :




  def __init__(       self							,     lowerCAmelCase=None							,     lowerCAmelCase=None      )						->				List[Any]:
        '''simple docstring'''






        _lowercase			 =list(poly_a or [0]      )[:]
        _lowercase			 =list(poly_b or [0]      )[:]

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

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

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

        # The product
        _lowercase			 =self.__multiply()




  def 						A__  (       self							,     lowerCAmelCase      )						->				List[str]:
        '''simple docstring'''






        _lowercase			 =[[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]
        #
        _lowercase			 =self.c_max_length // 2
        while next_ncol > 0:
              _lowercase			 =[[] for i in range(lowerCAmelCase      )]
              _lowercase			 =self.root**next_ncol

              # First half of next step
              _lowercase			 =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
              _lowercase			 =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
              _lowercase			 =new_dft
              _lowercase			 =next_ncol // 2
        return dft[0]




  def 						A__  (       self      )						->				List[str]:
        '''simple docstring'''






        _lowercase			 =self.__dft('A'      )
        _lowercase			 =self.__dft('B'      )
        _lowercase			 =[[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			 =2
        while next_ncol <= self.c_max_length:
              _lowercase			 =[[] for i in range(lowerCAmelCase      )]
              _lowercase			 =self.root ** (next_ncol // 2)
              _lowercase			 =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			 =new_inverse_c
              next_ncol *= 2
        # Unpack
        _lowercase			 =[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      )						->				List[Any]:
        '''simple docstring'''






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





import json
import os
import unittest

from transformers import OpenAIGPTTokenizer, OpenAIGPTTokenizerFast
from transformers.models.openai.tokenization_openai import VOCAB_FILES_NAMES
from transformers.testing_utils import require_ftfy, require_spacy, require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin





@require_tokenizers
class 				__lowerCAmelCase  (      SCREAMING_SNAKE_CASE    ,    unittest.TestCase							):
  _a		    =						OpenAIGPTTokenizer
  _a		    =						OpenAIGPTTokenizerFast
  _a		    =						True
  _a		    =						False




  def 						A__  (       self      )						->				Tuple:
        '''simple docstring'''






        super().setUp()

        # Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
        _lowercase			 =[
            'l',
            'o',
            'w',
            'e',
            'r',
            's',
            't',
            'i',
            'd',
            'n',
            'w</w>',
            'r</w>',
            't</w>',
            'lo',
            'low',
            'er</w>',
            'low</w>',
            'lowest</w>',
            'newer</w>',
            'wider</w>',
            '<unk>',
        ]
        _lowercase			 =dict(zip(lowerCAmelCase							,     range(len(lowerCAmelCase      )      )      )      )
        _lowercase			 =['#version: 0.2', 'l o', 'lo w', 'e r</w>', '']

        _lowercase			 =os.path.join(self.tmpdirname							,     VOCAB_FILES_NAMES['vocab_file']      )
        _lowercase			 =os.path.join(self.tmpdirname							,     VOCAB_FILES_NAMES['merges_file']      )
        with open(self.vocab_file							,     'w'      ) as fp:
              fp.write(json.dumps(lowerCAmelCase      )      )
        with open(self.merges_file							,     'w'      ) as fp:
              fp.write('\n'.join(lowerCAmelCase      )      )




  def 						A__  (       self							,     lowerCAmelCase      )						->				str:
        '''simple docstring'''






        return "lower newer", "lower newer"




  def 						A__  (       self      )						->				Tuple:
        '''simple docstring'''






        _lowercase			 =OpenAIGPTTokenizer(self.vocab_file							,     self.merges_file      )

        _lowercase			 ='lower'
        _lowercase			 =['low', 'er</w>']
        _lowercase			 =tokenizer.tokenize(lowerCAmelCase      )
        self.assertListEqual(lowerCAmelCase							,     lowerCAmelCase      )

        _lowercase			 =tokens + ['<unk>']
        _lowercase			 =[14, 15, 20]
        self.assertListEqual(tokenizer.convert_tokens_to_ids(lowerCAmelCase      )							,     lowerCAmelCase      )




  def 						A__  (       self							,     lowerCAmelCase=15      )						->				Union[str, Any]:
        '''simple docstring'''






        for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
              with self.subTest(F'''{tokenizer.__class__.__name__} ({pretrained_name})'''      ):
                    _lowercase			 =self.rust_tokenizer_class.from_pretrained(lowerCAmelCase							,     **lowerCAmelCase      )

                    # Simple input
                    _lowercase			 ='This is a simple input'
                    _lowercase			 =['This is a simple input 1', 'This is a simple input 2']
                    _lowercase			 =('This is a simple input', 'This is a pair')
                    _lowercase			 =[
                        ('This is a simple input 1', 'This is a simple input 2'),
                        ('This is a simple pair 1', 'This is a simple pair 2'),
                    ]

                    # Simple input tests
                    self.assertRaises(lowerCAmelCase							,     tokenizer_r.encode							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'      )

                    # Simple input
                    self.assertRaises(lowerCAmelCase							,     tokenizer_r.encode_plus							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'      )

                    # Simple input
                    self.assertRaises(
                        lowerCAmelCase							,     tokenizer_r.batch_encode_plus							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'							,     )

                    # Pair input
                    self.assertRaises(lowerCAmelCase							,     tokenizer_r.encode							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'      )

                    # Pair input
                    self.assertRaises(lowerCAmelCase							,     tokenizer_r.encode_plus							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'      )

                    # Pair input
                    self.assertRaises(
                        lowerCAmelCase							,     tokenizer_r.batch_encode_plus							,     lowerCAmelCase							,     max_length=lowerCAmelCase							,     padding='max_length'							,     )




  def 						A__  (       self      )						->				Dict:
        '''simple docstring'''






        pass





@require_ftfy
@require_spacy
@require_tokenizers
class 				__lowerCAmelCase  (      SCREAMING_SNAKE_CASE							):
  pass


