



'''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 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )      ->				str:
		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 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_=True  )      ->				Optional[Any]:
		model.train()
		_a					:				Tuple				=							model(lowerCAmelCase_  )
		_a					:				Tuple				=							F.mse_loss(lowerCAmelCase_						,      target.to(output.device  )  )
		if not do_backward:
				loss /= accelerator.gradient_accumulation_steps
				loss.backward()
		else:
				accelerator.backward(lowerCAmelCase_  )



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



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				Tuple:
		# Test when on a single CPU or GPU that the context manager does nothing
		_a	, _a	, _a					:				str				=							get_training_setup(lowerCAmelCase_  )
		# Use a single batch
		_a	, _a					:				int				=							next(iter(lowerCAmelCase_  )  ).values()
		for iteration in range(3  ):
				# Gather the distributed inputs and targs for the base model
				_a	, _a					:				int				=							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(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				# Do "gradient accumulation" (noop)
				if iteration % 2 == 0:
						# Accumulate grads locally
						with accelerator.no_sync(lowerCAmelCase_  ):
								step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				else:
						# Sync grads
						step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )

				# Since `no_sync` is a noop, `ddp_model` and `model` grads should always be in sync
				check_model_parameters(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				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					:				Dict				=							ddp_input[torch.randperm(len(lowerCAmelCase_  )  )]



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				str:
		# Test on distributed setup that context manager behaves properly
		_a	, _a	, _a					:				Tuple				=							get_training_setup(lowerCAmelCase_  )
		# Use a single batch
		_a	, _a					:				Union[str, Any]				=							next(iter(lowerCAmelCase_  )  ).values()
		for iteration in range(3  ):
				# Gather the distributed inputs and targs for the base model
				_a	, _a					:				str				=							accelerator.gather((ddp_input, ddp_target)  )
				_a	, _a					:				Dict				=							input.to(accelerator.device  ), target.to(accelerator.device  )
				# Perform our initial ground truth step in non "DDP"
				step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				# Do "gradient accumulation" (noop)
				if iteration % 2 == 0:
						# Accumulate grads locally
						with accelerator.no_sync(lowerCAmelCase_  ):
								step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				else:
						# Sync grads
						step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )

				# 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					:				Dict				=							ddp_input[torch.randperm(len(lowerCAmelCase_  )  )]



def 					__lowerCamelCase					(				lowerCAmelCase_=False						,      lowerCAmelCase_=False  )      ->				List[Any]:
		_a					:				str				=							Accelerator(
		    split_batches=lowerCAmelCase_						,      dispatch_batches=lowerCAmelCase_						,      gradient_accumulation_steps=2  )
		# Test that context manager behaves properly
		_a	, _a	, _a					:				List[str]				=							get_training_setup(lowerCAmelCase_  )
		for iteration, batch in enumerate(lowerCAmelCase_  ):
				_a	, _a					:				Union[str, Any]				=							batch.values()
				# Gather the distributed inputs and targs for the base model
				_a	, _a					:				Optional[Any]				=							accelerator.gather((ddp_input, ddp_target)  )
				_a	, _a					:				Union[str, Any]				=							input.to(accelerator.device  ), target.to(accelerator.device  )
				# Perform our initial ground truth step in non "DDP"
				step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				# Do "gradient accumulation" (noop)
				with accelerator.accumulate(lowerCAmelCase_  ):
						step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )

				# 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(lowerCAmelCase_  ) - 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					:				Union[str, Any]				=							ddp_input[torch.randperm(len(lowerCAmelCase_  )  )]
		GradientState._reset_state()



def 					__lowerCamelCase					(				lowerCAmelCase_=False						,      lowerCAmelCase_=False  )      ->				Union[str, Any]:
		_a					:				List[Any]				=							Accelerator(
		    split_batches=lowerCAmelCase_						,      dispatch_batches=lowerCAmelCase_						,      gradient_accumulation_steps=2  )
		# Test that context manager behaves properly
		_a	, _a	, _a	, _a	, _a	, _a	, _a					:				Tuple				=							get_training_setup(lowerCAmelCase_						,      lowerCAmelCase_  )
		for iteration, batch in enumerate(lowerCAmelCase_  ):
				_a	, _a					:				List[str]				=							batch.values()
				# Gather the distributed inputs and targs for the base model
				_a	, _a					:				Dict				=							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"
				model.train()
				ddp_model.train()
				step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				opt.step()

				if ((iteration + 1) % 2 == 0) or ((iteration + 1) == len(lowerCAmelCase_  )):
						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(lowerCAmelCase_  ):
						step_model(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
						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					:				int				=							(((iteration + 1) % 2) == 0) or ((iteration + 1) == len(lowerCAmelCase_  ))
				if accelerator.num_processes > 1:
						check_model_parameters(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
				# Shuffle ddp_input on each iteration
				torch.manual_seed(1337 + iteration  )
		GradientState._reset_state()



def 					__lowerCamelCase					(				)      ->				Tuple:
		_a					:				List[str]				=							Accelerator()

		_a					:				Union[str, Any]				=							RegressionDataset(length=80  )
		_a					:				str				=							DataLoader(lowerCAmelCase_						,      batch_size=16  )
		_a					:				Any				=							RegressionDataset(length=96  )
		_a					:				Union[str, Any]				=							DataLoader(lowerCAmelCase_						,      batch_size=16  )
		_a	, _a					:				str				=							accelerator.prepare(lowerCAmelCase_						,      lowerCAmelCase_  )
		assert accelerator.gradient_state.active_dataloader is None
		for iteration, _ in enumerate(lowerCAmelCase_  ):
				assert id(accelerator.gradient_state.active_dataloader  ) == id(lowerCAmelCase_  )
				if iteration < len(lowerCAmelCase_  ) - 1:
						assert not accelerator.gradient_state.end_of_dataloader
						if iteration == 1:
								for batch_num, _ in enumerate(lowerCAmelCase_  ):
										assert id(accelerator.gradient_state.active_dataloader  ) == id(lowerCAmelCase_  )
										if batch_num < len(lowerCAmelCase_  ) - 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 					__lowerCamelCase					(				)      ->				Tuple:
		_a					:				Union[str, Any]				=							Accelerator()
		_a					:				Dict				=							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(lowerCAmelCase_  )
		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(lowerCAmelCase_  )
		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(lowerCAmelCase_						,      lowerCAmelCase_  )

    # 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(lowerCAmelCase_						,      lowerCAmelCase_  )



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				Any:
		# For xla_spawn (TPUs)
		main()


if __name__ == "__main__":
							main()









'''simple docstring'''

__lowerCAmelCase						      =       range(2, 20 + 1)
__lowerCAmelCase						      =       [10**k for k in range(ks[-1] + 1)]
__lowerCAmelCase						      =       {}



def 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )      ->				Optional[Any]:
		_a					:				Optional[int]				=							sum(a_i[j] for j in range(lowerCAmelCase_						,      len(lowerCAmelCase_  )  )  )
		_a					:				List[str]				=							sum(a_i[j] * base[j] for j in range(min(len(lowerCAmelCase_  )						,      lowerCAmelCase_  )  )  )

		_a	, _a					:				Any				=							0, 0
		_a					:				Any				=							n - i

		_a					:				List[Any]				=							memo.get(lowerCAmelCase_  )

		if sub_memo is not None:
				_a					:				Tuple				=							sub_memo.get(lowerCAmelCase_  )

				if jumps is not None and len(lowerCAmelCase_  ) > 0:
						# find and make the largest jump without going over
						_a					:				Any				=							-1
						for _k in range(len(lowerCAmelCase_  ) - 1						,      -1						,      -1  ):
								if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
										_a					:				Any				=							_k
										break

						if max_jump >= 0:
								_a	, _a	, _a					:				Tuple				=							jumps[max_jump]
								# since the difference between jumps is cached, add c
								_a					:				Union[str, Any]				=							diff + c
								for j in range(min(lowerCAmelCase_						,      len(lowerCAmelCase_  )  )  ):
										_a	, _a					:				Dict				=							divmod(lowerCAmelCase_						,      10  )
								if new_c > 0:
										add(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )

				else:
						_a					:				Tuple				=							[]
		else:
				_a					:				Any				=							{c: []}
				_a					:				Optional[Any]				=							sub_memo

		if dn >= max_dn or c + diff >= base[k]:
				return diff, dn

		if k > ks[0]:
				while True:
						# keep doing smaller jumps
						_a	, _a					:				Dict				=							next_term(lowerCAmelCase_						,      k - 1						,      i + dn						,      lowerCAmelCase_  )
						diff += _diff
						dn += terms_jumped

						if dn >= max_dn or c + diff >= base[k]:
								break
		else:
				# would be too small a jump, just compute sequential terms instead
				_a	, _a					:				Any				=							compute(lowerCAmelCase_						,      lowerCAmelCase_						,      i + dn						,      lowerCAmelCase_  )
				diff += _diff
				dn += terms_jumped

		_a					:				Tuple				=							sub_memo[c]

		# keep jumps sorted by # of terms skipped
		_a					:				Any				=							0
		while j < len(lowerCAmelCase_  ):
				if jumps[j][1] > dn:
						break
				j += 1

		# cache the jump for this value digitsum(b) and c
		sub_memo[c].insert(lowerCAmelCase_						,      (diff, dn, k)  )
		return (diff, dn)



def 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )      ->				str:
		if i >= n:
				return 0, i
		if k > len(lowerCAmelCase_  ):
				a_i.extend([0 for _ in range(k - len(lowerCAmelCase_  )  )]  )

		# note: a_i -> b * 10^k + c
		# ds_b -> digitsum(b)
		# ds_c -> digitsum(c)
		_a					:				Any				=							i
		_a	, _a	, _a					:				Optional[int]				=							0, 0, 0
		for j in range(len(lowerCAmelCase_  )  ):
				if j >= k:
						ds_b += a_i[j]
				else:
						ds_c += a_i[j]

		while i < n:
				i += 1
				_a					:				Any				=							ds_c + ds_b
				diff += addend
				_a					:				int				=							0
				for j in range(lowerCAmelCase_  ):
						_a					:				Optional[Any]				=							a_i[j] + addend
						_a	, _a					:				Tuple				=							divmod(lowerCAmelCase_						,      10  )

						ds_c += a_i[j]

				if addend > 0:
						break

		if addend > 0:
				add(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )
		return diff, i - start_i



def 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )      ->				int:
		for j in range(lowerCAmelCase_						,      len(lowerCAmelCase_  )  ):
				_a					:				Optional[Any]				=							digits[j] + addend
				if s >= 10:
						_a	, _a					:				List[str]				=							divmod(lowerCAmelCase_						,      10  )
						_a					:				List[str]				=							addend // 10 + quotient
				else:
						_a					:				Optional[Any]				=							s
						_a					:				Optional[Any]				=							addend // 10

				if addend == 0:
						break

		while addend > 0:
				_a	, _a					:				List[str]				=							divmod(lowerCAmelCase_						,      10  )
				digits.append(lowerCAmelCase_  )



def 					__lowerCamelCase					(				lowerCAmelCase_ = 10**15  )      ->				int:
		_a					:				Dict				=							[1]
		_a					:				int				=							1
		_a					:				Tuple				=							0
		while True:
				_a	, _a					:				str				=							next_term(lowerCAmelCase_						,      20						,      i + dn						,      lowerCAmelCase_  )
				dn += terms_jumped
				if dn == n - i:
						break

		_a					:				Union[str, Any]				=							0
		for j in range(len(lowerCAmelCase_  )  ):
				a_n += digits[j] * 10**j
		return a_n


if __name__ == "__main__":
							print(f"""{solution() = }""")




