



"""simple docstring"""


from __future__ import annotations

import math







def  _a	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



				_UpperCAmelCase					=    u
				for i in range(1					,     _SCREAMING_SNAKE_CASE				):
								_UpperCAmelCase					=    temp * (u - i)
				return temp







def  _a	(      ):






				'''simple docstring'''



				_UpperCAmelCase					=    int(input('''enter the numbers of values: '''				)				)
				_UpperCAmelCase					=    []
				for _ in range(_SCREAMING_SNAKE_CASE				):
								y.append([]				)
				for i in range(_SCREAMING_SNAKE_CASE				):
								for j in range(_SCREAMING_SNAKE_CASE				):
												y[i].append(_SCREAMING_SNAKE_CASE				)
												_UpperCAmelCase					=    0

				print('''enter the values of parameters in a list: '''				)
				_UpperCAmelCase					=    list(map(_SCREAMING_SNAKE_CASE					,     input().split()				)				)

				print('''enter the values of corresponding parameters: '''				)
				for i in range(_SCREAMING_SNAKE_CASE				):
								_UpperCAmelCase					=    float(input()				)

				_UpperCAmelCase					=    int(input('''enter the value to interpolate: '''				)				)
				_UpperCAmelCase					=    (value - x[0]) / (x[1] - x[0])

				# for calculating forward difference table

				for i in range(1					,     _SCREAMING_SNAKE_CASE				):
								for j in range(n - i				):
												_UpperCAmelCase					=    y[j + 1][i - 1] - y[j][i - 1]

				_UpperCAmelCase					=    y[0][0]
				for i in range(1					,     _SCREAMING_SNAKE_CASE				):
								summ += (ucal(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				) * y[0][i]) / math.factorial(_SCREAMING_SNAKE_CASE				)

				print(f'the value at {value} is {summ}'				)


if __name__ == "__main__":
					main()








"""simple docstring"""


import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment
@require_huggingface_suite
class 			_a (					unittest.TestCase):
			"""simple docstring"""



			def  lowercase__						(		self     :    Tuple   )->int:
							_UpperCAmelCase					=    inspect.getfile(accelerate.test_utils   )
							_UpperCAmelCase					=    os.path.sep.join(
							    mod_file.split(os.path.sep   )[:-1] + ['''scripts''', '''external_deps''', '''test_metrics.py''']   )

							from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

							_UpperCAmelCase					=    test_metrics



			@require_cpu
			def  lowercase__						(		self     :    Any   )->int:
							debug_launcher(self.test_metrics.main				,   num_processes=1   )



			@require_cpu
			def  lowercase__						(		self     :    List[str]   )->List[str]:
							debug_launcher(self.test_metrics.main   )



			@require_single_gpu
			def  lowercase__						(		self     :    List[Any]   )->Dict:
							self.test_metrics.main()



			@require_multi_gpu
			def  lowercase__						(		self     :    str   )->int:
							print(F'Found {torch.cuda.device_count()} devices.'   )
							_UpperCAmelCase					=    ['''torchrun''', F'--nproc_per_node={torch.cuda.device_count()}', self.test_file_path]
							with patch_environment(omp_num_threads=1   ):
											execute_subprocess_async(__UpperCamelCase				,   env=os.environ.copy()   )



