



'''simple docstring'''





def lowerCAmelCase    (__A    ,      __A = False):



     """simple docstring"""



     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
     _a           =    [
         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,
     ]

     _a           =    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
     for idx, _p in enumerate(__A    ,      1):
          if n < _p:
               # then we have our last prime to check
               _a           =    primes[:idx]
               break
     _a    ,       _a           =    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:
          _a           =    False
          for r in range(__A):
               _a           =    pow(__A    ,      d * 2**r    ,      __A)
               # see article for analysis explanation for m
               if (r == 0 and m == 1) or ((m + 1) % n == 0):
                    _a           =    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 lowerCAmelCase    ():



     """simple docstring"""



     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()







'''simple docstring'''






import unittest

import torch
from torch import nn

from accelerate.test_utils import require_cuda
from accelerate.utils.memory import find_executable_batch_size, release_memory


def    _snake_case  (	)		->       Union[str, Any]:
							raise RuntimeError('''CUDA out of memory.'''			)




class 						a__							(				nn.Module    ):





							'''simple docstring'''






							def __init__(						self  )			->				int:
														super().__init__()
														lowerCAmelCase__			  =      nn.Linear(3   ,       4  )
														lowerCAmelCase__			  =      nn.BatchNormad(4  )
														lowerCAmelCase__			  =      nn.Linear(4   ,       5  )







							def     __SCREAMING_SNAKE_CASE				(						self   ,       lowerCamelCase_  )			->				Optional[Any]:
														return self.lineara(self.batchnorm(self.lineara(lowerCamelCase_  )  )  )




class 						a__							(				unittest.TestCase    ):





							'''simple docstring'''






							def     __SCREAMING_SNAKE_CASE				(						self  )			->				str:
														lowerCAmelCase__			  =      []

														@find_executable_batch_size(starting_batch_size=1_28  )
														def mock_training_loop_function(lowerCamelCase_  ):
																					nonlocal batch_sizes
																					batch_sizes.append(lowerCamelCase_  )
																					if batch_size != 8:
																												raise_fake_out_of_memory()

														mock_training_loop_function()
														self.assertListEqual(lowerCamelCase_   ,       [1_28, 64, 32, 16, 8]  )







							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Optional[int]:
														lowerCAmelCase__			  =      []

														@find_executable_batch_size(starting_batch_size=1_28  )
														def mock_training_loop_function(lowerCamelCase_   ,       lowerCamelCase_  ):
																					nonlocal batch_sizes
																					batch_sizes.append(lowerCamelCase_  )
																					if batch_size != 8:
																												raise_fake_out_of_memory()
																					return batch_size, arga

														lowerCAmelCase__  ,   lowerCAmelCase__			  =      mock_training_loop_function('''hello'''  )
														self.assertListEqual(lowerCamelCase_   ,       [1_28, 64, 32, 16, 8]  )
														self.assertListEqual([bs, arga]   ,       [8, '''hello''']  )







							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Tuple:
														@find_executable_batch_size(starting_batch_size=0  )
														def mock_training_loop_function(lowerCamelCase_  ):
																					pass

														with self.assertRaises(lowerCamelCase_  ) as cm:
																					mock_training_loop_function()
																					self.assertIn('''No executable batch size found, reached zero.'''   ,       cm.exception.args[0]  )







							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Dict:
														@find_executable_batch_size(starting_batch_size=16  )
														def mock_training_loop_function(lowerCamelCase_  ):
																					if batch_size > 0:
																												raise_fake_out_of_memory()
																					pass

														with self.assertRaises(lowerCamelCase_  ) as cm:
																					mock_training_loop_function()
																					self.assertIn('''No executable batch size found, reached zero.'''   ,       cm.exception.args[0]  )







							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Optional[int]:
														@find_executable_batch_size(starting_batch_size=1_28  )
														def mock_training_loop_function(lowerCamelCase_   ,       lowerCamelCase_   ,       lowerCamelCase_  ):
																					if batch_size != 8:
																												raise raise_fake_out_of_memory()

														with self.assertRaises(lowerCamelCase_  ) as cm:
																					mock_training_loop_function(1_28   ,       '''hello'''   ,       '''world'''  )
																					self.assertIn('''Batch size was passed into `f`'''   ,       cm.exception.args[0]  )
																					self.assertIn('''`f(arg1=\'hello\', arg2=\'world\')'''   ,       cm.exception.args[0]  )







							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Union[str, Any]:
														@find_executable_batch_size(starting_batch_size=16  )
														def mock_training_loop_function(lowerCamelCase_  ):
																					raise ValueError('''Oops, we had an error!'''  )

														with self.assertRaises(lowerCamelCase_  ) as cm:
																					mock_training_loop_function()
																					self.assertIn('''Oops, we had an error!'''   ,       cm.exception.args[0]  )







							@require_cuda
							def     __SCREAMING_SNAKE_CASE				(						self  )			->				Optional[Any]:
														lowerCAmelCase__			  =      torch.cuda.memory_allocated()
														lowerCAmelCase__			  =      ModelForTest()
														model.cuda()
														self.assertGreater(torch.cuda.memory_allocated()   ,       lowerCamelCase_  )
														lowerCAmelCase__			  =      release_memory(lowerCamelCase_  )
														self.assertEqual(torch.cuda.memory_allocated()   ,       lowerCamelCase_  )