
'''simple docstring'''
from copy import deepcopy

import torch
import torch.nn.functional as F
from torch.optim import AdamW
from torch.optim.lr_scheduler import LambdaLR
from torch.utils.data import DataLoader

from accelerate.accelerator import Accelerator
from accelerate.state import GradientState
from accelerate.test_utils import RegressionDataset, RegressionModel
from accelerate.utils import DistributedType, is_torch_version, set_seed







def        A_     (						__SCREAMING_SNAKE_CASE						:  Union[str, Any]			,     __SCREAMING_SNAKE_CASE						:  Tuple			,     __SCREAMING_SNAKE_CASE						:  Optional[Any]			,     __SCREAMING_SNAKE_CASE						:  Any )				->       Dict:





  """simple docstring"""

  for param, grad_param in zip(model_a.parameters()			,     model_b.parameters() ):
    if not param.requires_grad:
      continue
    if not did_step:
      # Grads should not be in sync
      assert (
          torch.allclose(param.grad			,     grad_param.grad ) is False
      ), F"Gradients in sync when they should not be at iteration {iteration}:\nmodel_a grad ({param.grad}) == model_b grad ({grad_param.grad})"
    else:
      # Grads should be in sync
      assert (
          torch.allclose(param.grad			,     grad_param.grad ) is True
      ), F"Gradients not in sync when they should be at iteration {iteration}:\nmodel_a grad ({param.grad}) != model_b grad ({grad_param.grad})"







def        A_     (						__SCREAMING_SNAKE_CASE						:  Tuple			,     __SCREAMING_SNAKE_CASE						:  Optional[Any]			,     __SCREAMING_SNAKE_CASE						:  Union[str, Any]			,     __SCREAMING_SNAKE_CASE						:  List[Any]			,     __SCREAMING_SNAKE_CASE						:  Any=True )				->       Any:





  """simple docstring"""

  model.train()
  __A		:     Any												=		model(__SCREAMING_SNAKE_CASE )
  __A		:     Any												=		F.mse_loss(__SCREAMING_SNAKE_CASE			,     target.to(output.device ) )
  if not do_backward:
    loss /= accelerator.gradient_accumulation_steps
    loss.backward()
  else:
    accelerator.backward(__SCREAMING_SNAKE_CASE )







def        A_     (						__SCREAMING_SNAKE_CASE						:  Optional[int]			,     __SCREAMING_SNAKE_CASE						:  Optional[int]=False )				->       Optional[Any]:





  """simple docstring"""

  set_seed(42 )
  __A		:     Union[str, Any]												=		RegressionModel()
  __A		:     Union[str, Any]												=		deepcopy(__SCREAMING_SNAKE_CASE )
  __A		:     List[str]												=		RegressionDataset(length=80 )
  __A		:     Tuple												=		DataLoader(__SCREAMING_SNAKE_CASE			,     batch_size=16 )
  model.to(accelerator.device )
  if sched:
    __A		:     Optional[int]												=		AdamW(params=model.parameters()			,     lr=1e-3 )
    __A		:     Optional[int]												=		AdamW(params=ddp_model.parameters()			,     lr=1e-3 )
    __A		:     Tuple												=		LambdaLR(__SCREAMING_SNAKE_CASE			,     lr_lambda=lambda __SCREAMING_SNAKE_CASE : epoch**0.65 )
    __A		:     List[Any]												=		LambdaLR(__SCREAMING_SNAKE_CASE			,     lr_lambda=lambda __SCREAMING_SNAKE_CASE : epoch**0.65 )
  # Make a copy of `model`
  if sched:
    __A							,					__A							,					__A							,					__A		:     str												=		accelerator.prepare(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
  else:
    __A							,					__A		:     List[str]												=		accelerator.prepare(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
  if sched:
    return (model, opt, sched, dataloader, ddp_model, ddp_opt, ddp_sched)
  return model, ddp_model, dataloader







def        A_     (						__SCREAMING_SNAKE_CASE						:  Tuple )				->       List[str]:





  """simple docstring"""

  __A							,					__A							,					__A		:     str												=		get_training_setup(__SCREAMING_SNAKE_CASE )
  # Use a single batch
  __A							,					__A		:     int												=		next(iter(__SCREAMING_SNAKE_CASE ) ).values()
  for iteration in range(3 ):
    # Gather the distributed inputs and targs for the base model
    __A							,					__A		:     Tuple												=		accelerator.gather((ddp_input, ddp_target) )
    __A							,					__A		:     Any												=		input.to(accelerator.device ), target.to(accelerator.device )
    # Perform our initial ground truth step in non "DDP"
    step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    # Do "gradient accumulation" (noop)
    if iteration % 2 == 0:
      # Accumulate grads locally
      with accelerator.no_sync(__SCREAMING_SNAKE_CASE ):
        step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    else:
      # Sync grads
      step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

    # Since `no_sync` is a noop, `ddp_model` and `model` grads should always be in sync
    check_model_parameters(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    for param, ddp_param in zip(model.parameters()			,     ddp_model.parameters() ):
      if not param.requires_grad:
        continue
      assert torch.allclose(
          param.grad			,     ddp_param.grad ), F"Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"

    # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration )
    __A		:     int												=		ddp_input[torch.randperm(len(__SCREAMING_SNAKE_CASE ) )]







def        A_     (						__SCREAMING_SNAKE_CASE						:  Tuple )				->       Dict:





  """simple docstring"""

  __A							,					__A							,					__A		:     Union[str, Any]												=		get_training_setup(__SCREAMING_SNAKE_CASE )
  # Use a single batch
  __A							,					__A		:     Optional[int]												=		next(iter(__SCREAMING_SNAKE_CASE ) ).values()
  for iteration in range(3 ):
    # Gather the distributed inputs and targs for the base model
    __A							,					__A		:     Tuple												=		accelerator.gather((ddp_input, ddp_target) )
    __A							,					__A		:     str												=		input.to(accelerator.device ), target.to(accelerator.device )
    # Perform our initial ground truth step in non "DDP"
    step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    # Do "gradient accumulation" (noop)
    if iteration % 2 == 0:
      # Accumulate grads locally
      with accelerator.no_sync(__SCREAMING_SNAKE_CASE ):
        step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    else:
      # Sync grads
      step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

    # DDP model and model should only be in sync when not (iteration % 2 == 0)
    for param, ddp_param in zip(model.parameters()			,     ddp_model.parameters() ):
      if not param.requires_grad:
        continue
      if iteration % 2 == 0:
        # Grads should not be in sync
        assert (
            torch.allclose(param.grad			,     ddp_param.grad ) is False
        ), F"Gradients in sync when they should not be:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"
      else:
        # Grads should be in sync
        assert (
            torch.allclose(param.grad			,     ddp_param.grad ) is True
        ), F"Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"

        # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration )
    __A		:     Optional[Any]												=		ddp_input[torch.randperm(len(__SCREAMING_SNAKE_CASE ) )]







def        A_     (						__SCREAMING_SNAKE_CASE						:  List[Any]=False			,     __SCREAMING_SNAKE_CASE						:  str=False )				->       Optional[int]:





  """simple docstring"""

  __A		:     Any												=		Accelerator(
      split_batches=__SCREAMING_SNAKE_CASE			,     dispatch_batches=__SCREAMING_SNAKE_CASE			,     gradient_accumulation_steps=2 )
  # Test that context manager behaves properly
  __A							,					__A							,					__A		:     Tuple												=		get_training_setup(__SCREAMING_SNAKE_CASE )
  for iteration, batch in enumerate(__SCREAMING_SNAKE_CASE ):
    __A							,					__A		:     Dict												=		batch.values()
    # Gather the distributed inputs and targs for the base model
    __A							,					__A		:     Dict												=		accelerator.gather((ddp_input, ddp_target) )
    __A							,					__A		:     Any												=		input.to(accelerator.device ), target.to(accelerator.device )
    # Perform our initial ground truth step in non "DDP"
    step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    # Do "gradient accumulation" (noop)
    with accelerator.accumulate(__SCREAMING_SNAKE_CASE ):
      step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

    # DDP model and model should only be in sync when not (iteration % 2 == 0)
    for param, ddp_param in zip(model.parameters()			,     ddp_model.parameters() ):
      if not param.requires_grad:
        continue
      if ((iteration + 1) % 2 == 0) or (iteration == len(__SCREAMING_SNAKE_CASE ) - 1):
        # Grads should be in sync
        assert (
            torch.allclose(param.grad			,     ddp_param.grad ) is True
        ), F"Gradients not in sync when they should be at iteration {iteration}:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"
      else:
        # Grads should not be in sync
        assert (
            torch.allclose(param.grad			,     ddp_param.grad ) is False
        ), F"Gradients in sync when they should not be at iteration {iteration}:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"

        # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration )
    __A		:     Any												=		ddp_input[torch.randperm(len(__SCREAMING_SNAKE_CASE ) )]
  GradientState._reset_state()







def        A_     (						__SCREAMING_SNAKE_CASE						:  List[str]=False			,     __SCREAMING_SNAKE_CASE						:  Tuple=False )				->       Tuple:





  """simple docstring"""

  __A		:     Tuple												=		Accelerator(
      split_batches=__SCREAMING_SNAKE_CASE			,     dispatch_batches=__SCREAMING_SNAKE_CASE			,     gradient_accumulation_steps=2 )
  # Test that context manager behaves properly
  __A							,					__A							,					__A							,					__A							,					__A							,					__A							,					__A		:     int												=		get_training_setup(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
  for iteration, batch in enumerate(__SCREAMING_SNAKE_CASE ):
    __A							,					__A		:     Optional[int]												=		batch.values()
    # Gather the distributed inputs and targs for the base model
    __A							,					__A		:     str												=		accelerator.gather((ddp_input, ddp_target) )
    __A							,					__A		:     Optional[int]												=		input.to(accelerator.device ), target.to(accelerator.device )
    # Perform our initial ground truth step in non "DDP"
    model.train()
    ddp_model.train()
    step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    opt.step()

    if ((iteration + 1) % 2 == 0) or ((iteration + 1) == len(__SCREAMING_SNAKE_CASE )):
      if split_batches:
        sched.step()
      else:
        for _ in range(accelerator.num_processes ):
          sched.step()
    opt.zero_grad()
    # Perform gradient accumulation under wrapper
    with accelerator.accumulate(__SCREAMING_SNAKE_CASE ):
      step_model(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
      ddp_opt.step()
      ddp_sched.step()
      ddp_opt.zero_grad()

    # Learning rates should be the same
    assert (
        opt.param_groups[0]["lr"] == ddp_opt.param_groups[0]["lr"]
    ), F"Learning rates found in each optimizer did not align\nopt: {opt.param_groups[0]['lr']}\nDDP opt: {ddp_opt.param_groups[0]['lr']}\n"
    __A		:     Any												=		(((iteration + 1) % 2) == 0) or ((iteration + 1) == len(__SCREAMING_SNAKE_CASE ))
    if accelerator.num_processes > 1:
      check_model_parameters(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration )
  GradientState._reset_state()







def        A_     (						)				->       List[str]:





  """simple docstring"""

  __A		:     Tuple												=		Accelerator()

  __A		:     Optional[Any]												=		RegressionDataset(length=80 )
  __A		:     int												=		DataLoader(__SCREAMING_SNAKE_CASE			,     batch_size=16 )
  __A		:     int												=		RegressionDataset(length=96 )
  __A		:     str												=		DataLoader(__SCREAMING_SNAKE_CASE			,     batch_size=16 )
  __A							,					__A		:     Any												=		accelerator.prepare(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
  assert accelerator.gradient_state.active_dataloader is None
  for iteration, _ in enumerate(__SCREAMING_SNAKE_CASE ):
    assert id(accelerator.gradient_state.active_dataloader ) == id(__SCREAMING_SNAKE_CASE )
    if iteration < len(__SCREAMING_SNAKE_CASE ) - 1:
      assert not accelerator.gradient_state.end_of_dataloader
      if iteration == 1:
        for batch_num, _ in enumerate(__SCREAMING_SNAKE_CASE ):
          assert id(accelerator.gradient_state.active_dataloader ) == id(__SCREAMING_SNAKE_CASE )
          if batch_num < len(__SCREAMING_SNAKE_CASE ) - 1:
            assert not accelerator.gradient_state.end_of_dataloader
          else:
            assert accelerator.gradient_state.end_of_dataloader
    else:
      assert accelerator.gradient_state.end_of_dataloader
  assert accelerator.gradient_state.active_dataloader is None







def        A_     (						)				->       int:





  """simple docstring"""

  __A		:     Union[str, Any]												=		Accelerator()
  __A		:     Union[str, Any]												=		accelerator.state
  if state.local_process_index == 0:
    print("""**Test `accumulate` gradient accumulation with dataloader break**""" )
  test_dataloader_break()
  if state.distributed_type == DistributedType.NO:
    if state.local_process_index == 0:
      print("""**Test NOOP `no_sync` context manager**""" )
    test_noop_sync(__SCREAMING_SNAKE_CASE )
  if state.distributed_type in (DistributedType.MULTI_GPU, DistributedType.MULTI_CPU):
    if state.local_process_index == 0:
      print("""**Test Distributed `no_sync` context manager**""" )
    test_distributed_sync(__SCREAMING_SNAKE_CASE )
  if state.distributed_type == DistributedType.MULTI_GPU:
    for split_batch in [True, False]:
      for dispatch_batches in [True, False]:
        if state.local_process_index == 0:
          print(
              """**Test `accumulate` gradient accumulation, """			,     F"`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"			,     )
        test_gradient_accumulation(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

    # Currently will break on torch 2.0 +, need to investigate why
  if is_torch_version("""<"""			,     """2.0""" ) or state.distributed_type == DistributedType.NO:
    if state.local_process_index == 0:
      print(
          """**Test `accumulate` gradient accumulation with optimizer and scheduler, """			,     """`split_batches=False`, `dispatch_batches=False`**"""			,     )
    test_gradient_accumulation_with_opt_and_scheduler()
    if state.distributed_type == DistributedType.MULTI_GPU:
      for split_batch in [True, False]:
        for dispatch_batches in [True, False]:
          if not split_batch and not dispatch_batches:
            continue
          if state.local_process_index == 0:
            print(
                """**Test `accumulate` gradient accumulation with optimizer and scheduler, """			,     F"`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"			,     )
          test_gradient_accumulation_with_opt_and_scheduler(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )







def        A_     (						__SCREAMING_SNAKE_CASE						:  int )				->       str:





  """simple docstring"""

  main()


if __name__ == "__main__":
     main()





'''simple docstring'''
def        A_     (						__SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  bool = False )				->       bool:





  """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_3170_4406_4679_8873_8596_1981 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		:     Optional[int]												=		[
      2047,
      137_3653,
      2532_6001,
      32_1503_1751,
      2_1523_0289_8747,
      3_4747_4966_0383,
      341_5500_7172_8321,
      1,
      382_5123_0565_4641_3051,
      1,
      1,
      3186_6585_7834_0311_5116_7461,
      3_3170_4406_4679_8873_8596_1981,
  ]

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





  """simple docstring"""

  assert not miller_rabin(561 )
  assert miller_rabin(563 )
  # 2047

  assert not miller_rabin(83_8201 )
  assert miller_rabin(83_8207 )
  # 1_373_653

  assert not miller_rabin(1731_6001 )
  assert miller_rabin(1731_6017 )
  # 25_326_001

  assert not miller_rabin(30_7838_6641 )
  assert miller_rabin(30_7838_6653 )
  # 3_215_031_751

  assert not miller_rabin(1_7130_4557_4801 )
  assert miller_rabin(1_7130_4557_4819 )
  # 2_152_302_898_747

  assert not miller_rabin(2_7797_9972_8307 )
  assert miller_rabin(2_7797_9972_8327 )
  # 3_474_749_660_383

  assert not miller_rabin(113_8500_2390_9441 )
  assert miller_rabin(113_8500_2390_9527 )
  # 341_550_071_728_321

  assert not miller_rabin(127_5041_0188_4880_4351 )
  assert miller_rabin(127_5041_0188_4880_4391 )
  # 3_825_123_056_546_413_051

  assert not miller_rabin(796_6646_4458_5077_8779_1867 )
  assert miller_rabin(796_6646_4458_5077_8779_1951 )
  # 318_665_857_834_031_151_167_461

  assert not miller_rabin(5528_4067_7446_6478_9766_0333 )
  assert miller_rabin(5528_4067_7446_6478_9766_0359 )
  # 3_317_044_064_679_887_385_961_981
  # upper limit for probabilistic test


if __name__ == "__main__":
     test_miller_rabin()



