




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		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )      ->       List[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 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase=True    )      ->       Optional[Any]:
	model.train()
	a										=							model(__lowerCamelCase    )
	a										=							F.mse_loss(__lowerCamelCase							,			target.to(output.device    )    )
	if not do_backward:
		loss /= accelerator.gradient_accumulation_steps
		loss.backward()
	else:
		accelerator.backward(__lowerCamelCase    )





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





def 		__A		(	__lowerCamelCase    )      ->       Optional[Any]:
	# Test when on a single CPU or GPU that the context manager does nothing
	a				, a				, a										=							get_training_setup(__lowerCamelCase    )
	# Use a single batch
	a				, a										=							next(iter(__lowerCamelCase    )    ).values()
	for iteration in range(3    ):
		# Gather the distributed inputs and targs for the base model
		a				, a										=							accelerator.gather((ddp_input, ddp_target)    )
		a				, a										=							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										=							ddp_input[torch.randperm(len(__lowerCamelCase    )    )]





def 		__A		(	__lowerCamelCase    )      ->       Optional[Any]:
	# Test on distributed setup that context manager behaves properly
	a				, a				, a										=							get_training_setup(__lowerCamelCase    )
	# Use a single batch
	a				, a										=							next(iter(__lowerCamelCase    )    ).values()
	for iteration in range(3    ):
		# Gather the distributed inputs and targs for the base model
		a				, a										=							accelerator.gather((ddp_input, ddp_target)    )
		a				, a										=							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										=							ddp_input[torch.randperm(len(__lowerCamelCase    )    )]





def 		__A		(	__lowerCamelCase=False							,			__lowerCamelCase=False    )      ->       int:
	a										=							Accelerator(
	    split_batches=__lowerCamelCase							,			dispatch_batches=__lowerCamelCase							,			gradient_accumulation_steps=2    )
	# Test that context manager behaves properly
	a				, a				, a										=							get_training_setup(__lowerCamelCase    )
	for iteration, batch in enumerate(__lowerCamelCase    ):
		a				, a										=							batch.values()
		# Gather the distributed inputs and targs for the base model
		a				, a										=							accelerator.gather((ddp_input, ddp_target)    )
		a				, a										=							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										=							ddp_input[torch.randperm(len(__lowerCamelCase    )    )]
	GradientState._reset_state()





def 		__A		(	__lowerCamelCase=False							,			__lowerCamelCase=False    )      ->       Tuple:
	a										=							Accelerator(
	    split_batches=__lowerCamelCase							,			dispatch_batches=__lowerCamelCase							,			gradient_accumulation_steps=2    )
	# Test that context manager behaves properly
	a				, a				, a				, a				, a				, a				, a										=							get_training_setup(__lowerCamelCase							,			__lowerCamelCase    )
	for iteration, batch in enumerate(__lowerCamelCase    ):
		a				, a										=							batch.values()
		# Gather the distributed inputs and targs for the base model
		a				, a										=							accelerator.gather((ddp_input, ddp_target)    )
		a				, a										=							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										=							(((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 		__A		(	)      ->       Tuple:
	a										=							Accelerator()

	a										=							RegressionDataset(length=80    )
	a										=							DataLoader(__lowerCamelCase							,			batch_size=16    )
	a										=							RegressionDataset(length=96    )
	a										=							DataLoader(__lowerCamelCase							,			batch_size=16    )
	a				, a										=							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 		__A		(	)      ->       List[str]:
	a										=							Accelerator()
	a										=							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 		__A		(	__lowerCamelCase    )      ->       str:
	# For xla_spawn (TPUs)
	main()


if __name__ == "__main__":
		main()







from math import pi, sqrt





def 		__A		(	__lowerCamelCase    )      ->       float:
	if num <= 0:
		raise ValueError("""math domain error"""    )
	if num > 171.5:
		raise OverflowError("""math range error"""    )
	elif num - int(__lowerCamelCase    ) not in (0, 0.5):
		raise NotImplementedError("""num must be an integer or a half-integer"""    )
	elif num == 0.5:
		return sqrt(__lowerCamelCase    )
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1    )





def 		__A		(	)      ->       None:
	assert gamma(0.5    ) == sqrt(__lowerCamelCase    )
	assert gamma(1    ) == 1.0
	assert gamma(2    ) == 1.0


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		__UpperCamelCase					:       str    					=      1.0
		while num:
				__UpperCamelCase					:       Dict    					=      float(input("Gamma of: "))
				print(F'gamma({num}) = {gamma(num)}')
				print("\nEnter 0 to exit...")

