


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






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

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

							a__    =  precision
							a__    =  ceil(precision / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
						snake_case							: Tuple      =   50
						print(f"""The first {n} digits of pi is: {pi(n)}""")








import os
import tempfile
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
						import torch
						from torch import nn

						from transformers import (
						    Adafactor,
						    AdamW,
						    get_constant_schedule,
						    get_constant_schedule_with_warmup,
						    get_cosine_schedule_with_warmup,
						    get_cosine_with_hard_restarts_schedule_with_warmup,
						    get_inverse_sqrt_schedule,
						    get_linear_schedule_with_warmup,
						    get_polynomial_decay_schedule_with_warmup,
						)






def 							__lowercase     (				__lowerCAmelCase							:       str      ,					__lowerCAmelCase							:       Any=1_0     ):
							a__    =  []
							for _ in range(__lowerCAmelCase     ):
														lrs.append(scheduler.get_lr()[0]     )
														scheduler.step()
							return lrs






def 							__lowercase     (				__lowerCAmelCase							:       Optional[int]      ,					__lowerCAmelCase							:       List[str]=1_0     ):
							a__    =  []
							for step in range(__lowerCAmelCase     ):
														lrs.append(scheduler.get_lr()[0]     )
														scheduler.step()
														if step == num_steps // 2:
																					with tempfile.TemporaryDirectory() as tmpdirname:
																												a__    =  os.path.join(__lowerCAmelCase      ,					'schedule.bin'     )
																												torch.save(scheduler.state_dict()      ,					__lowerCAmelCase     )

																												a__    =  torch.load(__lowerCAmelCase     )
																												scheduler.load_state_dict(__lowerCAmelCase     )
							return lrs







@require_torch
class  snake_case_     (unittest.TestCase   ):
					def 				lowerCamelCase__(   self     :Optional[int]    ,__snake_case     :List[Any]    ,__snake_case     :int    ,__snake_case     :Union[str, Any]   )      ->					int:
												self.assertEqual(len(__snake_case   )    ,len(__snake_case   )   )
												for a, b in zip(__snake_case    ,__snake_case   ):
																			self.assertAlmostEqual(__snake_case    ,__snake_case    ,delta=__snake_case   )
					def 				lowerCamelCase__(   self     :Optional[Any]   )      ->					str:
												a__    =  torch.tensor([0.1, -0.2, -0.1]    ,requires_grad=__snake_case   )
												a__    =  torch.tensor([0.4, 0.2, -0.5]   )
												a__    =  nn.MSELoss()
												# No warmup, constant schedule, no gradient clipping
												a__    =  AdamW(params=[w]    ,lr=2E-1    ,weight_decay=0.0   )
												for _ in range(1_00   ):
																			a__    =  criterion(__snake_case    ,__snake_case   )
																			loss.backward()
																			optimizer.step()
																			w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
																			w.grad.zero_()
												self.assertListAlmostEqual(w.tolist()    ,[0.4, 0.2, -0.5]    ,tol=1E-2   )



					def 				lowerCamelCase__(   self     :Tuple   )      ->					int:
												a__    =  torch.tensor([0.1, -0.2, -0.1]    ,requires_grad=__snake_case   )
												a__    =  torch.tensor([0.4, 0.2, -0.5]   )
												a__    =  nn.MSELoss()
												# No warmup, constant schedule, no gradient clipping
												a__    =  Adafactor(
												    params=[w]    ,lr=1E-2    ,eps=(1E-30, 1E-3)    ,clip_threshold=1.0    ,decay_rate=-0.8    ,betaa=__snake_case    ,weight_decay=0.0    ,relative_step=__snake_case    ,scale_parameter=__snake_case    ,warmup_init=__snake_case    ,)
												for _ in range(10_00   ):
																			a__    =  criterion(__snake_case    ,__snake_case   )
																			loss.backward()
																			optimizer.step()
																			w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
																			w.grad.zero_()
												self.assertListAlmostEqual(w.tolist()    ,[0.4, 0.2, -0.5]    ,tol=1E-2   )







@require_torch
class  snake_case_     (unittest.TestCase   ):
					UpperCAmelCase__      :					str					   =    nn.Linear(5_0			,		5_0   ) if is_torch_available() else None
					UpperCAmelCase__      :					Dict					   =    AdamW(m.parameters()			,		lr=1_0.0   ) if is_torch_available() else None
					UpperCAmelCase__      :					Optional[Any]					   =    1_0
					def 				lowerCamelCase__(   self     :Optional[Any]    ,__snake_case     :Optional[int]    ,__snake_case     :Tuple    ,__snake_case     :int    ,__snake_case     :Any=None   )      ->					Optional[Any]:
												self.assertEqual(len(__snake_case   )    ,len(__snake_case   )   )
												for a, b in zip(__snake_case    ,__snake_case   ):
																			self.assertAlmostEqual(__snake_case    ,__snake_case    ,delta=__snake_case    ,msg=__snake_case   )



					def 				lowerCamelCase__(   self     :Tuple   )      ->					List[Any]:
												a__    =  {'num_warmup_steps': 2, 'num_training_steps': 10}
												# schedulers doct format
												# function: (sched_args_dict, expected_learning_rates)
												a__    =  {
												    get_constant_schedule: ({}, [10.0] * self.num_steps),
												    get_constant_schedule_with_warmup: (
												        {'num_warmup_steps': 4},
												        [0.0, 2.5, 5.0, 7.5, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0],
												    ),
												    get_linear_schedule_with_warmup: (
												        {**common_kwargs},
												        [0.0, 5.0, 10.0, 8.75, 7.5, 6.25, 5.0, 3.75, 2.5, 1.25],
												    ),
												    get_cosine_schedule_with_warmup: (
												        {**common_kwargs},
												        [0.0, 5.0, 10.0, 9.61, 8.53, 6.91, 5.0, 3.08, 1.46, 0.38],
												    ),
												    get_cosine_with_hard_restarts_schedule_with_warmup: (
												        {**common_kwargs, 'num_cycles': 2},
												        [0.0, 5.0, 10.0, 8.53, 5.0, 1.46, 10.0, 8.53, 5.0, 1.46],
												    ),
												    get_polynomial_decay_schedule_with_warmup: (
												        {**common_kwargs, 'power': 2.0, 'lr_end': 1E-7},
												        [0.0, 5.0, 10.0, 7.6_56, 5.6_25, 3.9_06, 2.5, 1.4_06, 0.6_25, 0.1_56],
												    ),
												    get_inverse_sqrt_schedule: (
												        {'num_warmup_steps': 2},
												        [0.0, 5.0, 10.0, 8.1_65, 7.0_71, 6.3_25, 5.7_74, 5.3_45, 5.0, 4.7_14],
												    ),
												}

												for scheduler_func, data in scheds.items():
																			a__   ,      a__    =  data

																			a__    =  scheduler_func(self.optimizer    ,**__snake_case   )
																			self.assertEqual(len([scheduler.get_lr()[0]]   )    ,1   )
																			a__    =  unwrap_schedule(__snake_case    ,self.num_steps   )
																			self.assertListAlmostEqual(
																			    __snake_case    ,__snake_case    ,tol=1E-2    ,msg=F'failed for {scheduler_func} in normal scheduler'    ,)

																			a__    =  scheduler_func(self.optimizer    ,**__snake_case   )
																			if scheduler_func.__name__ != "get_constant_schedule":
																										LambdaScheduleWrapper.wrap_scheduler(__snake_case   )  # wrap to test picklability of the schedule
																			a__    =  unwrap_and_save_reload_schedule(__snake_case    ,self.num_steps   )
																			self.assertListEqual(__snake_case    ,__snake_case    ,msg=F'failed for {scheduler_func} in save and reload'   )







class  snake_case_     :
					def __init__(   self     :Tuple    ,__snake_case     :str   )      ->					Any:
												a__    =  fn
					def __call__(   self     :List[str]    ,*__snake_case     :Optional[Any]    ,**__snake_case     :Optional[int]   )      ->					Union[str, Any]:
												return self.fn(*__snake_case    ,**__snake_case   )



					@classmethod
					def 				lowerCamelCase__(   self     :Tuple    ,__snake_case     :Union[str, Any]   )      ->					Dict:
												a__    =  list(map(self    ,scheduler.lr_lambdas   )   )




