




'''simple docstring'''





from typing import Dict

from transformers import EvalPrediction, HfArgumentParser, TrainingArguments, is_torch_available
from transformers.testing_utils import (
    TestCasePlus,
    execute_subprocess_async,
    get_torch_dist_unique_port,
    require_torch_multi_gpu,
    require_torch_neuroncore,
)
from transformers.training_args import ParallelMode
from transformers.utils import logging


UpperCamelCase_						:      str       =						logging.get_logger(__name__)


if is_torch_available():
			import torch
			from torch import nn
			from torch.utils.data import Dataset

			from transformers import Trainer

			class        _a    (						__lowerCAmelCase							):






								def __init__(			self ,_SCREAMING_SNAKE_CASE = 101   )							->      Tuple:
													_snake_case							=				length






								def __len__(			self   )							->      List[Any]:
													return self.length






								def __getitem__(			self ,_SCREAMING_SNAKE_CASE   )							->      int:
													return i







			class        _a    :






								def __call__(			self ,_SCREAMING_SNAKE_CASE   )							->      List[str]:
													return {"input_ids": torch.tensor(_SCREAMING_SNAKE_CASE   ), "labels": torch.tensor(_SCREAMING_SNAKE_CASE   )}







			class        _a    (						nn.Module							):






								def __init__(			self   )							->      List[Any]:
													super().__init__()
													# Add some (unused) params otherwise DDP will complain.
													_snake_case							=				nn.Linear(120 ,80   )






								def     _lowercase     (			self ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE=None   )							->      Tuple:
													if labels is not None:
																		return torch.tensor(0.0 ,device=input_ids.device   ), input_ids
													else:
																		return input_ids

class        _a    (						__lowerCAmelCase							):






					@require_torch_neuroncore
					def     _lowercase     (			self   )							->      int:
										_snake_case							=				f"""--nproc_per_node=2
            --master_port={get_torch_dist_unique_port()}
            {self.test_file_dir}/test_trainer_distributed.py
        """.split()
										_snake_case							=				self.get_auto_remove_tmp_dir()
										_snake_case							=				f"""--output_dir {output_dir}""".split()
										_snake_case							=				["torchrun"] + distributed_args + args
										execute_subprocess_async(_SCREAMING_SNAKE_CASE ,env=self.get_env()   )
										# successful return here == success - any errors would have caused an error in the sub-call







class        _a    (						__lowerCAmelCase							):






					@require_torch_multi_gpu
					def     _lowercase     (			self   )							->      Tuple:
										_snake_case							=				f"""--nproc_per_node={torch.cuda.device_count()}
            --master_port={get_torch_dist_unique_port()}
            {self.test_file_dir}/test_trainer_distributed.py
        """.split()
										_snake_case							=				self.get_auto_remove_tmp_dir()
										_snake_case							=				f"""--output_dir {output_dir}""".split()
										_snake_case							=				["torchrun"] + distributed_args + args
										execute_subprocess_async(_SCREAMING_SNAKE_CASE ,env=self.get_env()   )
										# successful return here == success - any errors would have caused an error in the sub-call


if __name__ == "__main__":
			# The script below is meant to be run under torch.distributed, on a machine with multiple GPUs:
			#
			# PYTHONPATH="src" python -m torch.distributed.run --nproc_per_node 2 --output_dir output_dir ./tests/test_trainer_distributed.py

			UpperCamelCase_						:      Union[str, Any]       =						HfArgumentParser((TrainingArguments,))
			UpperCamelCase_						:      int       =						parser.parse_args_into_dataclasses()[0]

			logger.warning(
			    F'Process rank: {training_args.local_rank}, device: {training_args.device}, n_gpu: {training_args.n_gpu}, '
			    F'distributed training: {training_args.parallel_mode != ParallelMode.NOT_DISTRIBUTED}'
			)

			# Essentially, what we want to verify in the distributed case is that we get all samples back,
			# in the right order. (this is crucial for prediction for instance)
			for dataset_length in [101, 40, 7]:
						UpperCamelCase_						:      str       =						DummyDataset(dataset_length)





						def      __a     (       _UpperCamelCase:   EvalPrediction   )						->			Dict:

											"""simple docstring"""




											_snake_case							=				list(range(len(_UpperCamelCase   )   )   )
											_snake_case							=				p.predictions.tolist() == sequential and p.label_ids.tolist() == sequential
											if not success and training_args.local_rank == 0:
																logger.warning(
																    "Predictions and/or labels do not match expected results:\n  - predictions: "
																    F"""{p.predictions.tolist()}\n  - labels: {p.label_ids.tolist()}\n  - expected: {sequential}"""   )
											return {"success": success}

						UpperCamelCase_						:      Optional[Any]       =						Trainer(
						    model=DummyModel(),
						    args=training_args,
						    data_collator=DummyDataCollator(),
						    eval_dataset=dataset,
						    compute_metrics=compute_metrics,
						)
						UpperCamelCase_						:      List[Any]       =						trainer.evaluate()
						logger.info(metrics)
						if metrics["eval_success"] is not True:
									logger.error(metrics)
									exit(1)

						UpperCamelCase_						:      Union[str, Any]       =						trainer.predict(dataset)
						logger.info(p.metrics)
						if p.metrics["test_success"] is not True:
									logger.error(p.metrics)
									exit(1)

						UpperCamelCase_						:      Dict       =						2

						UpperCamelCase_						:      Dict       =						trainer.evaluate()
						logger.info(metrics)
						if metrics["eval_success"] is not True:
									logger.error(metrics)
									exit(1)

						UpperCamelCase_						:      Dict       =						trainer.predict(dataset)
						logger.info(p.metrics)
						if p.metrics["test_success"] is not True:
									logger.error(p.metrics)
									exit(1)





						UpperCamelCase_						:      Dict       =						None








'''simple docstring'''





from decimal import Decimal, getcontext
from math import ceil, factorial





def      __a     (       _UpperCamelCase:   int   )						->			str:

     """simple docstring"""




     if not isinstance(_UpperCamelCase ,						_UpperCamelCase   ):
          raise TypeError("Undefined for non-integers"   )
     elif precision < 1:
          raise ValueError("Undefined for non-natural numbers"   )

     _snake_case							=				precision
     _snake_case							=				ceil(precision / 14   )
     _snake_case							=				426_880 * Decimal(10_005   ).sqrt()
     _snake_case							=				1
     _snake_case							=				13_591_409
     _snake_case							=				Decimal(_UpperCamelCase   )
     for k in range(1 ,						_UpperCamelCase   ):
          _snake_case							=				factorial(6 * k   ) // (factorial(3 * k   ) * factorial(_UpperCamelCase   ) ** 3)
          linear_term += 545_140_134
          exponential_term *= -262_537_412_640_768_000
          partial_sum += Decimal(multinomial_term * linear_term   ) / exponential_term
     return str(constant_term / partial_sum   )[:-1]


if __name__ == "__main__":
   UpperCamelCase_						:      Any       =						50
   print(F'The first {n} digits of pi is: {pi(n)}')


