


'''simple docstring'''
import mpmath  # for roots of unity
import numpy as np
class      lowercase			:

		"""simple docstring"""

		def __init__(	self					,     UpperCamelCase_=None					,     UpperCamelCase_=None							):

							'''simple docstring'''


							UpperCamelCase__     :List[Any]							      =				list(poly_a or [0]							)[:]
							UpperCamelCase__     :Optional[int]							      =				list(poly_b or [0]							)[:]

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

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

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

							# The product
							UpperCamelCase__     :Optional[Any]							      =				self.__multiply()




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_							):

							'''simple docstring'''


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

												# First half of next step
												UpperCamelCase__     :List[Any]							      =				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
												UpperCamelCase__     :Optional[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
												UpperCamelCase__     :Any							      =				new_dft
												UpperCamelCase__     :Union[str, Any]							      =				next_ncol // 2
							return dft[0]




		def 					lowerCAmelCase__       (	self							):

							'''simple docstring'''


							UpperCamelCase__     :Dict							      =				self.__dft('''A'''							)
							UpperCamelCase__     :int							      =				self.__dft('''B'''							)
							UpperCamelCase__     :List[str]							      =				[[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
							UpperCamelCase__     :List[Any]							      =				2
							while next_ncol <= self.c_max_length:
												UpperCamelCase__     :Optional[Any]							      =				[[] for i in range(UpperCamelCase_							)]
												UpperCamelCase__     :Optional[Any]							      =				self.root ** (next_ncol // 2)
												UpperCamelCase__     :Union[str, 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
												UpperCamelCase__     :str							      =				new_inverse_c
												next_ncol *= 2
							# Unpack
							UpperCamelCase__     :Union[str, 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							):

							'''simple docstring'''


							UpperCamelCase__     :Union[str, Any]							      =				'''A = ''' + ''' + '''.join(
							    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
							UpperCamelCase__     :Dict							      =				'''B = ''' + ''' + '''.join(
							    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
							UpperCamelCase__     :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 json
import logging
import os
import sys
from time import time
from unittest.mock import patch

from transformers.testing_utils import TestCasePlus, require_torch_tpu


logging.basicConfig(level=logging.DEBUG)

__snake_case							   =  logging.getLogger()


def     a   (    __a     )						->			Dict:



					'''simple docstring'''






					UpperCamelCase__     :str							      =				{}
					UpperCamelCase__     :Dict							      =				os.path.join(__a				,      '''all_results.json'''     )
					if os.path.exists(__a     ):
										with open(__a				,      '''r'''     ) as f:
															UpperCamelCase__     :int							      =				json.load(__a     )
					else:
										raise ValueError(f'''can\'t find {path}'''     )
					return results


__snake_case							   =  logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)







@require_torch_tpu
class      lowercase			(							A__      ):

		"""simple docstring"""

		def 					lowerCAmelCase__       (	self							):

							'''simple docstring'''


							import xla_spawn

							UpperCamelCase__     :Any							      =				self.get_auto_remove_tmp_dir()
							UpperCamelCase__     :List[str]							      =				F'''
            ./examples/pytorch/text-classification/run_glue.py
            --num_cores=8
            ./examples/pytorch/text-classification/run_glue.py
            --model_name_or_path distilbert-base-uncased
            --output_dir {tmp_dir}
            --overwrite_output_dir
            --train_file ./tests/fixtures/tests_samples/MRPC/train.csv
            --validation_file ./tests/fixtures/tests_samples/MRPC/dev.csv
            --do_train
            --do_eval
            --debug tpu_metrics_debug
            --per_device_train_batch_size=2
            --per_device_eval_batch_size=1
            --learning_rate=1e-4
            --max_steps=10
            --warmup_steps=2
            --seed=42
            --max_seq_length=128
            '''.split()

							with patch.object(UpperCamelCase_					,     '''argv'''					,     UpperCamelCase_							):
												UpperCamelCase__     :List[Any]							      =				time()
												xla_spawn.main()
												UpperCamelCase__     :List[Any]							      =				time()

												UpperCamelCase__     :Tuple							      =				get_results(UpperCamelCase_							)
												self.assertGreaterEqual(result['''eval_accuracy''']					,     0.75							)

												# Assert that the script takes less than 500 seconds to make sure it doesn't hang.
												self.assertLess(end - start					,     500							)




		def 					lowerCAmelCase__       (	self							):

							'''simple docstring'''


							import xla_spawn

							UpperCamelCase__     :Tuple							      =				'''
            ./tests/test_trainer_tpu.py
            --num_cores=8
            ./tests/test_trainer_tpu.py
            '''.split()
							with patch.object(UpperCamelCase_					,     '''argv'''					,     UpperCamelCase_							):
												xla_spawn.main()