


import mpmath  # for roots of unity
import numpy as np



class 							A   :
					'''simple docstring'''






					def __init__(self   :						Tuple				, _UpperCAmelCase   :						List[str]=None				, _UpperCAmelCase   :						List[Any]=None		)						->       int:




							"""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   lowerCamelCase__					(self   :						Any				, _UpperCAmelCase   :						Any		)						->       Any:




							"""simple docstring"""


							lowercase__					      =		[[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]
							#
							lowercase__					      =		self.c_max_length // 2
							while next_ncol > 0:
									lowercase__					      =		[[] for i in range(_UpperCAmelCase		)]
									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(_UpperCAmelCase		):
													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(_UpperCAmelCase		):
													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   lowerCamelCase__					(self   :						List[Any]		)						->       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(_UpperCAmelCase		)]
									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   :						Any		)						->       Dict:




							"""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 							A   (	UpperCAmelCase__			,  unittest.TestCase							):
					'''simple docstring'''






					A__      =			OpenAIGPTTokenizer
					A__      =			OpenAIGPTTokenizerFast
					A__      =			True
					A__      =			False

					def   lowerCamelCase__					(self   :						List[str]		)						->       int:




							"""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(_UpperCAmelCase				, range(len(_UpperCAmelCase		)		)		)		)
							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(_UpperCAmelCase		)		)
							with open(self.merges_file				, """w"""		) as fp:
									fp.write("""\n""".join(_UpperCAmelCase		)		)

					def   lowerCamelCase__					(self   :						Dict				, _UpperCAmelCase   :						List[Any]		)						->       Any:




							"""simple docstring"""


							return "lower newer", "lower newer"

					def   lowerCamelCase__					(self   :						Dict		)						->       Tuple:




							"""simple docstring"""


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

							lowercase__					      =		"""lower"""
							lowercase__					      =		["""low""", """er</w>"""]
							lowercase__					      =		tokenizer.tokenize(_UpperCAmelCase		)
							self.assertListEqual(_UpperCAmelCase				, _UpperCAmelCase		)

							lowercase__					      =		tokens + ["""<unk>"""]
							lowercase__					      =		[14, 15, 20]
							self.assertListEqual(tokenizer.convert_tokens_to_ids(_UpperCAmelCase		)				, _UpperCAmelCase		)

					def   lowerCamelCase__					(self   :						Optional[int]				, _UpperCAmelCase   :						Union[str, Any]=15		)						->       Optional[int]:




							"""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(_UpperCAmelCase				, **_UpperCAmelCase		)

											# 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(_UpperCAmelCase				, tokenizer_r.encode				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""		)

											# Simple input
											self.assertRaises(_UpperCAmelCase				, tokenizer_r.encode_plus				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""		)

											# Simple input
											self.assertRaises(
											    _UpperCAmelCase				, tokenizer_r.batch_encode_plus				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""				, )

											# Pair input
											self.assertRaises(_UpperCAmelCase				, tokenizer_r.encode				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""		)

											# Pair input
											self.assertRaises(_UpperCAmelCase				, tokenizer_r.encode_plus				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""		)

											# Pair input
											self.assertRaises(
											    _UpperCAmelCase				, tokenizer_r.batch_encode_plus				, _UpperCAmelCase				, max_length=_UpperCAmelCase				, padding="""max_length"""				, )


					def   lowerCamelCase__					(self   :						Tuple		)						->       Any:




							"""simple docstring"""


							pass






@require_ftfy
@require_spacy
@require_tokenizers
class 							A   (	UpperCAmelCase__							):
					'''simple docstring'''






					pass

