import mpmath  # for roots of unity
import numpy as np



class       UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self     ,       __lowerCAmelCase=None     ,       __lowerCAmelCase=None			)  ->  Union[str, Any]:
        # Input as list
        lowercase__    :   Tuple						= list(poly_a or [0]			)[:]
        lowercase__    :   int						= list(poly_b or [0]			)[:]

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

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

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

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

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  Any:
        lowercase__    :   List[str]						= [[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__    :   Optional[int]						= self.c_max_length // 2
        while next_ncol > 0:
         lowercase__    :   int						= [[] for i in range(__lowerCAmelCase			)]
         lowercase__    :   Any						= self.root**next_ncol

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

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

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       UpperCAmelCase  (						a__   ,						unittest.TestCase ):





       '''simple docstring'''



       SCREAMING_SNAKE_CASE 		=   OpenAIGPTTokenizer
       SCREAMING_SNAKE_CASE 		=   OpenAIGPTTokenizerFast
       SCREAMING_SNAKE_CASE 		=   True
       SCREAMING_SNAKE_CASE 		=   False

       def _lowerCAmelCase(						self			)  ->  Optional[int]:
        super().setUp()

        # Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
        lowercase__    :   Optional[Any]						= [
            '''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__    :   Optional[int]						= dict(zip(__lowerCAmelCase     ,       range(len(__lowerCAmelCase			)			)			)			)
        lowercase__    :   Union[str, Any]						= ['''#version: 0.2''', '''l o''', '''lo w''', '''e r</w>''', '''''']

        lowercase__    :   Optional[int]						= os.path.join(self.tmpdirname     ,       VOCAB_FILES_NAMES['''vocab_file''']			)
        lowercase__    :   Optional[int]						= 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 _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  Dict:
        return "lower newer", "lower newer"

       def _lowerCAmelCase(						self			)  ->  List[Any]:
        lowercase__    :   int						= OpenAIGPTTokenizer(self.vocab_file     ,       self.merges_file			)

        lowercase__    :   List[Any]						= '''lower'''
        lowercase__    :   Any						= ['''low''', '''er</w>''']
        lowercase__    :   Union[str, Any]						= tokenizer.tokenize(__lowerCAmelCase			)
        self.assertListEqual(__lowerCAmelCase     ,       __lowerCAmelCase			)

        lowercase__    :   Tuple						= tokens + ['''<unk>''']
        lowercase__    :   Optional[Any]						= [14, 15, 20]
        self.assertListEqual(tokenizer.convert_tokens_to_ids(__lowerCAmelCase			)     ,       __lowerCAmelCase			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase=15			)  ->  Optional[int]:
        for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
         with self.subTest(F"""{tokenizer.__class__.__name__} ({pretrained_name})"""			):
          lowercase__    :   List[str]						= self.rust_tokenizer_class.from_pretrained(__lowerCAmelCase     ,       **__lowerCAmelCase			)

          # Simple input
          lowercase__    :   List[str]						= '''This is a simple input'''
          lowercase__    :   Any						= ['''This is a simple input 1''', '''This is a simple input 2''']
          lowercase__    :   str						= ('''This is a simple input''', '''This is a pair''')
          lowercase__    :   str						= [
              ('''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 _lowerCAmelCase(						self			)  ->  Tuple:
        pass



@require_ftfy
@require_spacy
@require_tokenizers
class       UpperCAmelCase  (						a__ ):





       '''simple docstring'''



       pass

