





from __future__ import annotations

import math





def lowerCAmelCase__(__snake_case ,__snake_case							)       ->   float:







	'''simple docstring'''







	lowerCamelCase__              =	u
	for i in range(1 ,__snake_case							):
		lowerCamelCase__              =	temp * (u - i)
	return temp





def lowerCAmelCase__()       ->   None:







	'''simple docstring'''







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

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

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

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

	# for calculating forward difference table

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

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

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


if __name__ == "__main__":
			main()










import contextlib
from multiprocessing import Pool, RLock

from tqdm.auto import tqdm

from ..utils import experimental, logging


_a						=   logging.get_logger(__name__)






class       __A					:

			'''simple docstring'''







			lowerCAmelCase_							  =		None





@experimental
def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case							)       ->   Tuple:







	'''simple docstring'''







	if ParallelBackendConfig.backend_name is None:
		return _map_with_multiprocessing_pool(
		    __snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case							)

	return _map_with_joblib(__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case							)





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case							)       ->   int:







	'''simple docstring'''







	lowerCamelCase__              =	num_proc if num_proc <= len(__snake_case							) else len(__snake_case							)
	lowerCamelCase__              =	[]  # We organize the splits ourselve (contiguous splits)
	for index in range(__snake_case							):
		lowerCamelCase__              =	len(__snake_case							) // num_proc
		lowerCamelCase__              =	len(__snake_case							) % num_proc
		lowerCamelCase__              =	div * index + min(__snake_case ,__snake_case							)
		lowerCamelCase__              =	start + div + (1 if index < mod else 0)
		split_kwds.append((function, iterable[start:end], types, index, disable_tqdm, desc)							)

	if len(__snake_case							) != sum(len(i[1]							) for i in split_kwds							):
		raise ValueError(
		    F'Error dividing inputs iterable among processes. '
		    F'Total number of objects {len(__snake_case							)}, '
		    F'length: {sum(len(i[1]							) for i in split_kwds							)}'							)

	logger.info(
	    F'Spawning {num_proc} processes for {len(__snake_case							)} objects in slices of {[len(i[1]							) for i in split_kwds]}'							)
	lowerCamelCase__       ,			lowerCamelCase__              =	None, None
	if not disable_tqdm:
		lowerCamelCase__       ,			lowerCamelCase__              =	(RLock(),), tqdm.set_lock
	with Pool(__snake_case ,initargs=__snake_case ,initializer=__snake_case							) as pool:
		lowerCamelCase__              =	pool.map(__snake_case ,__snake_case							)
	logger.info(F'Finished {num_proc} processes'							)
	lowerCamelCase__              =	[obj for proc_res in mapped for obj in proc_res]
	logger.info(F'Unpacked {len(__snake_case							)} objects'							)

	return mapped





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case							)       ->   List[str]:







	'''simple docstring'''







	import joblib

	with joblib.parallel_backend(ParallelBackendConfig.backend_name ,n_jobs=__snake_case							):
		return joblib.Parallel()(
		    joblib.delayed(__snake_case							)((function, obj, types, None, True, None)							) for obj in iterable							)





@experimental
@contextlib.contextmanager
def lowerCAmelCase__(__snake_case							)       ->   int:







	'''simple docstring'''







	lowerCamelCase__              =	backend_name

	if backend_name == "spark":
		from joblibspark import register_spark

		register_spark()

		# TODO: call create_cache_and_write_probe if "download" in steps
		# TODO: raise NotImplementedError when Dataset.map etc is called

	try:
		yield
	finally:
		lowerCamelCase__              =	None



