
def        a_		(       __lowercase   :	int       ,					__lowercase   :	bool = False ) ->  bool:
			if n == 2:
						return True
			if not n % 2 or n < 2:
						return False
			if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
						return False
			if n > 3_317_044_064_679_887_385_961_981 and not allow_probable:
						raise ValueError(
						    'Warning: upper bound of deterministic test is exceeded. '
						    'Pass allow_probable=True to allow probabilistic test. '
						    'A return value of True indicates a probable prime.' )
			# array bounds provided by analysis
			_snake_case		=			[
			    2_047,
			    1_373_653,
			    25_326_001,
			    3_215_031_751,
			    2_152_302_898_747,
			    3_474_749_660_383,
			    341_550_071_728_321,
			    1,
			    3_825_123_056_546_413_051,
			    1,
			    1,
			    318_665_857_834_031_151_167_461,
			    3_317_044_064_679_887_385_961_981,
			]

			_snake_case		=			[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
			for idx, _p in enumerate(__lowercase       ,					1 ):
						if n < _p:
									# then we have our last prime to check
									_snake_case		=			primes[:idx]
									break
			_snake_case	,					_snake_case		=			n - 1, 0
			# break up n -1 into a power of 2 (s) and
			# remaining odd component
			# essentially, solve for d * 2 ** s == n - 1
			while d % 2 == 0:
						d //= 2
						s += 1
			for prime in plist:
						_snake_case		=			False
						for r in range(__lowercase ):
									_snake_case		=			pow(__lowercase       ,					d * 2**r       ,					__lowercase )
									# see article for analysis explanation for m
									if (r == 0 and m == 1) or ((m + 1) % n == 0):
												_snake_case		=			True
												# this loop will not determine compositeness
												break
						if pr:
									continue
						# if pr is False, then the above loop never evaluated to true,
						# and the n MUST be composite
						return False
			return True






def        a_		(       ) ->  None:
			assert not miller_rabin(561 )
			assert miller_rabin(563 )
			# 2047

			assert not miller_rabin(838_201 )
			assert miller_rabin(838_207 )
			# 1_373_653

			assert not miller_rabin(17_316_001 )
			assert miller_rabin(17_316_017 )
			# 25_326_001

			assert not miller_rabin(3_078_386_641 )
			assert miller_rabin(3_078_386_653 )
			# 3_215_031_751

			assert not miller_rabin(1_713_045_574_801 )
			assert miller_rabin(1_713_045_574_819 )
			# 2_152_302_898_747

			assert not miller_rabin(2_779_799_728_307 )
			assert miller_rabin(2_779_799_728_327 )
			# 3_474_749_660_383

			assert not miller_rabin(113_850_023_909_441 )
			assert miller_rabin(113_850_023_909_527 )
			# 341_550_071_728_321

			assert not miller_rabin(1_275_041_018_848_804_351 )
			assert miller_rabin(1_275_041_018_848_804_391 )
			# 3_825_123_056_546_413_051

			assert not miller_rabin(79_666_464_458_507_787_791_867 )
			assert miller_rabin(79_666_464_458_507_787_791_951 )
			# 318_665_857_834_031_151_167_461

			assert not miller_rabin(552_840_677_446_647_897_660_333 )
			assert miller_rabin(552_840_677_446_647_897_660_359 )
			# 3_317_044_064_679_887_385_961_981
			# upper limit for probabilistic test


if __name__ == "__main__":
			test_miller_rabin()

import os
import tempfile
import unittest
from pathlib import Path

from transformers import AutoConfig, is_torch_available
from transformers.testing_utils import require_torch, torch_device


if is_torch_available():
			from transformers import PyTorchBenchmark, PyTorchBenchmarkArguments




@require_torch
class    SCREAMING_SNAKE_CASE__     (	unittest.TestCase					):





	'''simple docstring'''



	def  A							(  self	:    List[Any]			,  lowercase	:    Dict	):


				'''simple docstring'''


				for model_result in results.values():
							for batch_size, sequence_length in zip(model_result['bs']			,  model_result['ss']	):
										_snake_case		=			model_result['result'][batch_size][sequence_length]
										self.assertIsNotNone(lowercase	)



	def  A							(  self	:    str	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    Any	):


				'''simple docstring'''


				_snake_case		=			'sgugger/tiny-distilbert-classification'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  only_pretrain_model=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    Optional[int]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  torchscript=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	@unittest.skipIf(torch_device == 'cpu'			,  'Cant do half precision'	)
	def  A							(  self	:    Optional[Any]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  fpaa=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    str	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			AutoConfig.from_pretrained(lowercase	)
				# set architectures equal to `None`
				_snake_case		=			None
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase			,  configs=[config]	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    Optional[Any]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result	)
				self.check_results_dict_not_empty(results.memory_train_result	)



	@unittest.skipIf(torch_device == 'cpu'			,  'Can\'t do half precision'	)
	def  A							(  self	:    str	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  fpaa=lowercase			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result	)
				self.check_results_dict_not_empty(results.memory_train_result	)



	def  A							(  self	:    Tuple	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			AutoConfig.from_pretrained(lowercase	)
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase			,  configs=[config]	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    Union[str, Any]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tinier_bart'
				_snake_case		=			AutoConfig.from_pretrained(lowercase	)
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase			,  configs=[config]	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result	)
				self.check_results_dict_not_empty(results.memory_inference_result	)



	def  A							(  self	:    Dict	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				_snake_case		=			AutoConfig.from_pretrained(lowercase	)
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase			,  configs=[config]	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result	)
				self.check_results_dict_not_empty(results.memory_train_result	)



	def  A							(  self	:    Dict	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tinier_bart'
				_snake_case		=			AutoConfig.from_pretrained(lowercase	)
				_snake_case		=			PyTorchBenchmarkArguments(
				    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  multi_process=lowercase			,  )
				_snake_case		=			PyTorchBenchmark(lowercase			,  configs=[config]	)
				_snake_case		=			benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result	)
				self.check_results_dict_not_empty(results.memory_train_result	)



	def  A							(  self	:    Optional[Any]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'
				with tempfile.TemporaryDirectory() as tmp_dir:
							_snake_case		=			PyTorchBenchmarkArguments(
							    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  save_to_csv=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  inference_time_csv_file=os.path.join(lowercase			,  'inf_time.csv'	)			,  train_memory_csv_file=os.path.join(lowercase			,  'train_mem.csv'	)			,  inference_memory_csv_file=os.path.join(lowercase			,  'inf_mem.csv'	)			,  train_time_csv_file=os.path.join(lowercase			,  'train_time.csv'	)			,  env_info_csv_file=os.path.join(lowercase			,  'env.csv'	)			,  multi_process=lowercase			,  )
							_snake_case		=			PyTorchBenchmark(lowercase	)
							benchmark.run()
							self.assertTrue(Path(os.path.join(lowercase			,  'inf_time.csv'	)	).exists()	)
							self.assertTrue(Path(os.path.join(lowercase			,  'train_time.csv'	)	).exists()	)
							self.assertTrue(Path(os.path.join(lowercase			,  'inf_mem.csv'	)	).exists()	)
							self.assertTrue(Path(os.path.join(lowercase			,  'train_mem.csv'	)	).exists()	)
							self.assertTrue(Path(os.path.join(lowercase			,  'env.csv'	)	).exists()	)





	def  A							(  self	:    Union[str, Any]	):


				'''simple docstring'''


				_snake_case		=			'sshleifer/tiny-gpt2'

				def _check_summary_is_not_empty(lowercase	:    Optional[Any]	):
							self.assertTrue(hasattr(lowercase			,  'sequential'	)	)
							self.assertTrue(hasattr(lowercase			,  'cumulative'	)	)
							self.assertTrue(hasattr(lowercase			,  'current'	)	)
							self.assertTrue(hasattr(lowercase			,  'total'	)	)

				with tempfile.TemporaryDirectory() as tmp_dir:
							_snake_case		=			PyTorchBenchmarkArguments(
							    models=[MODEL_ID]			,  training=lowercase			,  inference=lowercase			,  sequence_lengths=[8]			,  batch_sizes=[1]			,  log_filename=os.path.join(lowercase			,  'log.txt'	)			,  log_print=lowercase			,  trace_memory_line_by_line=lowercase			,  multi_process=lowercase			,  )
							_snake_case		=			PyTorchBenchmark(lowercase	)
							_snake_case		=			benchmark.run()
							_check_summary_is_not_empty(result.inference_summary	)
							_check_summary_is_not_empty(result.train_summary	)
							self.assertTrue(Path(os.path.join(lowercase			,  'log.txt'	)	).exists()	)