





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






def lowerCamelCase__   (							snake_case_     :  int	)				->    str:

   if not isinstance(snake_case_	,				snake_case_	):
      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								=       42_6880 * Decimal(1_0005	).sqrt()
   __snake_case								=       1
   __snake_case								=       1359_1409
   __snake_case								=       Decimal(snake_case_	)
   for k in range(1	,				snake_case_	):
      __snake_case								=       factorial(6 * k	) // (factorial(3 * k	) * factorial(snake_case_	) ** 3)
      linear_term += 5_4514_0134
      exponential_term *= -26_2537_4126_4076_8000
      partial_sum += Decimal(multinomial_term * linear_term	) / exponential_term
   return str(constant_term / partial_sum	)[:-1]


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








import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest

class 		SCREAMING_SNAKE_CASE__    (	_UpperCAmelCase  ):
      A_						:    Union[str, Any]							=   (DPMSolverSinglestepScheduler,)
      A_						:    Union[str, Any]							=   (('num_inference_steps', 25),)


      def        a			(self	:				Dict    ,      **a__	:				Tuple				):





         """simple docstring"""



         __snake_case								=       {
             '''num_train_timesteps''': 1000,
             '''beta_start''': 0.0_0_0_1,
             '''beta_end''': 0.0_2,
             '''beta_schedule''': '''linear''',
             '''solver_order''': 2,
             '''prediction_type''': '''epsilon''',
             '''thresholding''': False,
             '''sample_max_value''': 1.0,
             '''algorithm_type''': '''dpmsolver++''',
             '''solver_type''': '''midpoint''',
             '''lambda_min_clipped''': -float('''inf'''				),
             '''variance_type''': None,
         }

         config.update(**a__				)
         return config


      def        a			(self	:				str    ,      a__	:				Any=0    ,      **a__	:				Tuple				):





         """simple docstring"""



         __snake_case								=       dict(self.forward_default_kwargs				)
         __snake_case								=       kwargs.pop('''num_inference_steps'''    ,      a__				)
         __snake_case								=       self.dummy_sample
         __snake_case								=       0.1 * sample
         __snake_case								=       [residual + 0.2, residual + 0.1_5, residual + 0.1_0]

         for scheduler_class in self.scheduler_classes:
            __snake_case								=       self.get_scheduler_config(**a__				)
            __snake_case								=       scheduler_class(**a__				)
            scheduler.set_timesteps(a__				)
            # copy over dummy past residuals
            __snake_case								=       dummy_past_residuals[: scheduler.config.solver_order]

            with tempfile.TemporaryDirectory() as tmpdirname:
               scheduler.save_config(a__				)
               __snake_case								=       scheduler_class.from_pretrained(a__				)
               new_scheduler.set_timesteps(a__				)
               # copy over dummy past residuals
               __snake_case								=       dummy_past_residuals[: new_scheduler.config.solver_order]

            __snake_case	,     __snake_case								=       sample, sample
            for t in range(a__    ,      time_step + scheduler.config.solver_order + 1				):
               __snake_case								=       scheduler.step(a__    ,      a__    ,      a__    ,      **a__				).prev_sample
               __snake_case								=       new_scheduler.step(a__    ,      a__    ,      a__    ,      **a__				).prev_sample

               assert torch.sum(torch.abs(output - new_output				)				) < 1E-5, "Scheduler outputs are not identical"


      def        a			(self	:				Union[str, Any]				):





         """simple docstring"""



         pass


      def        a			(self	:				List[Any]    ,      a__	:				Dict=0    ,      **a__	:				List[str]				):





         """simple docstring"""



         __snake_case								=       dict(self.forward_default_kwargs				)
         __snake_case								=       kwargs.pop('''num_inference_steps'''    ,      a__				)
         __snake_case								=       self.dummy_sample
         __snake_case								=       0.1 * sample
         __snake_case								=       [residual + 0.2, residual + 0.1_5, residual + 0.1_0]

         for scheduler_class in self.scheduler_classes:
            __snake_case								=       self.get_scheduler_config()
            __snake_case								=       scheduler_class(**a__				)
            scheduler.set_timesteps(a__				)

            # copy over dummy past residuals (must be after setting timesteps)
            __snake_case								=       dummy_past_residuals[: scheduler.config.solver_order]

            with tempfile.TemporaryDirectory() as tmpdirname:
               scheduler.save_config(a__				)
               __snake_case								=       scheduler_class.from_pretrained(a__				)
               # copy over dummy past residuals
               new_scheduler.set_timesteps(a__				)

               # copy over dummy past residual (must be after setting timesteps)
               __snake_case								=       dummy_past_residuals[: new_scheduler.config.solver_order]

            __snake_case								=       scheduler.step(a__    ,      a__    ,      a__    ,      **a__				).prev_sample
            __snake_case								=       new_scheduler.step(a__    ,      a__    ,      a__    ,      **a__				).prev_sample

            assert torch.sum(torch.abs(output - new_output				)				) < 1E-5, "Scheduler outputs are not identical"


      def        a			(self	:				int    ,      a__	:				Tuple=None    ,      **a__	:				List[str]				):





         """simple docstring"""



         if scheduler is None:
            __snake_case								=       self.scheduler_classes[0]
            __snake_case								=       self.get_scheduler_config(**a__				)
            __snake_case								=       scheduler_class(**a__				)

         __snake_case								=       self.scheduler_classes[0]
         __snake_case								=       self.get_scheduler_config(**a__				)
         __snake_case								=       scheduler_class(**a__				)

         __snake_case								=       10
         __snake_case								=       self.dummy_model()
         __snake_case								=       self.dummy_sample_deter
         scheduler.set_timesteps(a__				)

         for i, t in enumerate(scheduler.timesteps				):
            __snake_case								=       model(a__    ,      a__				)
            __snake_case								=       scheduler.step(a__    ,      a__    ,      a__				).prev_sample

         return sample


      def        a			(self	:				str				):





         """simple docstring"""



         __snake_case								=       DPMSolverSinglestepScheduler(**self.get_scheduler_config()				)
         __snake_case								=       50
         __snake_case								=       self.dummy_model()
         __snake_case								=       self.dummy_sample_deter
         scheduler.set_timesteps(a__				)

         # make sure that the first t is uneven
         for i, t in enumerate(scheduler.timesteps[3:]				):
            __snake_case								=       model(a__    ,      a__				)
            __snake_case								=       scheduler.step(a__    ,      a__    ,      a__				).prev_sample

         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.2_5_7_4				) < 1E-3


      def        a			(self	:				int				):





         """simple docstring"""



         for timesteps in [25, 50, 100, 999, 1000]:
            self.check_over_configs(num_train_timesteps=a__				)


      def        a			(self	:				List[str]				):





         """simple docstring"""



         __snake_case								=       DPMSolverSinglestepScheduler(**self.get_scheduler_config()				)
         __snake_case								=       self.full_loop(scheduler=a__				)
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.2_7_9_1				) < 1E-3

         __snake_case								=       DEISMultistepScheduler.from_config(scheduler.config				)
         __snake_case								=       DPMSolverMultistepScheduler.from_config(scheduler.config				)
         __snake_case								=       UniPCMultistepScheduler.from_config(scheduler.config				)
         __snake_case								=       DPMSolverSinglestepScheduler.from_config(scheduler.config				)

         __snake_case								=       self.full_loop(scheduler=a__				)
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.2_7_9_1				) < 1E-3


      def        a			(self	:				List[str]				):





         """simple docstring"""



         self.check_over_configs(thresholding=a__				)
         for order in [1, 2, 3]:
            for solver_type in ["midpoint", "heun"]:
               for threshold in [0.5, 1.0, 2.0]:
                  for prediction_type in ["epsilon", "sample"]:
                     self.check_over_configs(
                         thresholding=a__    ,      prediction_type=a__    ,      sample_max_value=a__    ,      algorithm_type='''dpmsolver++'''    ,      solver_order=a__    ,      solver_type=a__    ,      )


      def        a			(self	:				Union[str, Any]				):





         """simple docstring"""



         for prediction_type in ["epsilon", "v_prediction"]:
            self.check_over_configs(prediction_type=a__				)


      def        a			(self	:				Union[str, Any]				):





         """simple docstring"""



         for algorithm_type in ["dpmsolver", "dpmsolver++"]:
            for solver_type in ["midpoint", "heun"]:
               for order in [1, 2, 3]:
                  for prediction_type in ["epsilon", "sample"]:
                     self.check_over_configs(
                         solver_order=a__    ,      solver_type=a__    ,      prediction_type=a__    ,      algorithm_type=a__    ,      )
                     __snake_case								=       self.full_loop(
                         solver_order=a__    ,      solver_type=a__    ,      prediction_type=a__    ,      algorithm_type=a__    ,      )
                     assert not torch.isnan(a__				).any(), "Samples have nan numbers"


      def        a			(self	:				List[str]				):





         """simple docstring"""



         self.check_over_configs(lower_order_final=a__				)
         self.check_over_configs(lower_order_final=a__				)


      def        a			(self	:				Optional[Any]				):





         """simple docstring"""



         self.check_over_configs(lambda_min_clipped=-float('''inf'''				)				)
         self.check_over_configs(lambda_min_clipped=-5.1				)


      def        a			(self	:				Tuple				):





         """simple docstring"""



         self.check_over_configs(variance_type=a__				)
         self.check_over_configs(variance_type='''learned_range'''				)


      def        a			(self	:				int				):





         """simple docstring"""



         for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1000]:
            self.check_over_forward(num_inference_steps=a__    ,      time_step=0				)


      def        a			(self	:				Optional[Any]				):





         """simple docstring"""



         __snake_case								=       self.full_loop()
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.2_7_9_1				) < 1E-3


      def        a			(self	:				int				):





         """simple docstring"""



         __snake_case								=       self.full_loop(use_karras_sigmas=a__				)
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.2_2_4_8				) < 1E-3


      def        a			(self	:				Tuple				):





         """simple docstring"""



         __snake_case								=       self.full_loop(prediction_type='''v_prediction'''				)
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.1_4_5_3				) < 1E-3


      def        a			(self	:				List[Any]				):





         """simple docstring"""



         __snake_case								=       self.full_loop(prediction_type='''v_prediction'''    ,      use_karras_sigmas=a__				)
         __snake_case								=       torch.mean(torch.abs(a__				)				)

         assert abs(result_mean.item() - 0.0_6_4_9				) < 1E-3


      def        a			(self	:				int				):





         """simple docstring"""



         __snake_case								=       self.scheduler_classes[0]
         __snake_case								=       self.get_scheduler_config(thresholding=a__    ,      dynamic_thresholding_ratio=0				)
         __snake_case								=       scheduler_class(**a__				)

         __snake_case								=       10
         __snake_case								=       self.dummy_model()
         __snake_case								=       self.dummy_sample_deter.half()
         scheduler.set_timesteps(a__				)

         for i, t in enumerate(scheduler.timesteps				):
            __snake_case								=       model(a__    ,      a__				)
            __snake_case								=       scheduler.step(a__    ,      a__    ,      a__				).prev_sample

         assert sample.dtype == torch.floataa

