
'''simple docstring'''





from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)

@flax.struct.dataclass
class     a :
				_snake_case		     =			42

				# setable values
				_snake_case		     =			42
				_snake_case		     =			42
				_snake_case		     =			42
				_snake_case		     =			None

				# running values
				_snake_case		     =			None




				@classmethod
				def 						__snake_case				(				cls						:					List[Any],     SCREAMING_SNAKE_CASE_						:					CommonSchedulerState,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray   ):
										return cls(common=SCREAMING_SNAKE_CASE_,     init_noise_sigma=SCREAMING_SNAKE_CASE_,     timesteps=SCREAMING_SNAKE_CASE_,     sigmas=SCREAMING_SNAKE_CASE_   )




@dataclass
class     a (					__magic_name__     ):
				_snake_case		     =			42




class     a (					__magic_name__					,__magic_name__     ):
				_snake_case		     =			[e.name for e in FlaxKarrasDiffusionSchedulers]

				_snake_case		     =			42




				@property
				def 						__snake_case				(				self						:					Any   ):
										return True




				@register_to_config
				def __init__(				self						:					Dict,     SCREAMING_SNAKE_CASE_						:					int = 10_00,     SCREAMING_SNAKE_CASE_						:					float = 0.0001,     SCREAMING_SNAKE_CASE_						:					float = 0.02,     SCREAMING_SNAKE_CASE_						:					str = "linear",     SCREAMING_SNAKE_CASE_						:					Optional[jnp.ndarray] = None,     SCREAMING_SNAKE_CASE_						:					str = "epsilon",     SCREAMING_SNAKE_CASE_						:					jnp.dtype = jnp.floataa,     ):
										snake_case							:  Dict			=     dtype




				def 						__snake_case				(				self						:					int,     SCREAMING_SNAKE_CASE_						:					Optional[CommonSchedulerState] = None   ):
										if common is None:
																snake_case							:  Optional[int]			=     CommonSchedulerState.create(self   )

										snake_case							:  str			=     jnp.arange(0,     self.config.num_train_timesteps   ).round()[::-1]
										snake_case							:  int			=     ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

										# standard deviation of the initial noise distribution
										snake_case							:  List[str]			=     sigmas.max()

										return LMSDiscreteSchedulerState.create(
										    common=SCREAMING_SNAKE_CASE_,     init_noise_sigma=SCREAMING_SNAKE_CASE_,     timesteps=SCREAMING_SNAKE_CASE_,     sigmas=SCREAMING_SNAKE_CASE_,     )




				def 						__snake_case				(				self						:					Tuple,     SCREAMING_SNAKE_CASE_						:					LMSDiscreteSchedulerState,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					int   ):
										((snake_case),       )							:  Any			=     jnp.where(state.timesteps == timestep,     size=1   )
										snake_case							:  Dict			=     step_index[0]

										snake_case							:  int			=     state.sigmas[step_index]
										snake_case							:  List[Any]			=     sample / ((sigma**2 + 1) ** 0.5)
										return sample




				def 						__snake_case				(				self						:					Optional[Any],     SCREAMING_SNAKE_CASE_						:					LMSDiscreteSchedulerState,     SCREAMING_SNAKE_CASE_						:					Tuple,     SCREAMING_SNAKE_CASE_						:					str,     SCREAMING_SNAKE_CASE_						:					Union[str, Any]   ):

										def lms_derivative(SCREAMING_SNAKE_CASE_						:					Tuple   ):
																snake_case							:  Any			=     1.0
																for k in range(SCREAMING_SNAKE_CASE_   ):
																						if current_order == k:
																												continue
																						prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
																return prod

										snake_case							:  Tuple			=     integrate.quad(SCREAMING_SNAKE_CASE_,     state.sigmas[t],     state.sigmas[t + 1],     epsrel=1e-4   )[0]

										return integrated_coeff




				def 						__snake_case				(				self						:					List[Any],     SCREAMING_SNAKE_CASE_						:					LMSDiscreteSchedulerState,     SCREAMING_SNAKE_CASE_						:					int,     SCREAMING_SNAKE_CASE_						:					Tuple = ()   ):
										snake_case							:  int			=     jnp.linspace(self.config.num_train_timesteps - 1,     0,     SCREAMING_SNAKE_CASE_,     dtype=self.dtype   )

										snake_case							:  str			=     jnp.floor(SCREAMING_SNAKE_CASE_   ).astype(jnp.intaa   )
										snake_case							:  Optional[Any]			=     jnp.ceil(SCREAMING_SNAKE_CASE_   ).astype(jnp.intaa   )

										snake_case							:  Dict			=     jnp.mod(SCREAMING_SNAKE_CASE_,     1.0   )

										snake_case							:  Any			=     ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
										snake_case							:  Optional[Any]			=     (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
										snake_case							:  Tuple			=     jnp.concatenate([sigmas, jnp.array([0.0],     dtype=self.dtype   )]   )

										snake_case							:  Tuple			=     timesteps.astype(jnp.intaa   )

										# initial running values
										snake_case							:  Dict			=     jnp.zeros((0,) + shape,     dtype=self.dtype   )

										return state.replace(
										    timesteps=SCREAMING_SNAKE_CASE_,     sigmas=SCREAMING_SNAKE_CASE_,     num_inference_steps=SCREAMING_SNAKE_CASE_,     derivatives=SCREAMING_SNAKE_CASE_,     )




				def 						__snake_case				(				self						:					Union[str, Any],     SCREAMING_SNAKE_CASE_						:					LMSDiscreteSchedulerState,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					int,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					int = 4,     SCREAMING_SNAKE_CASE_						:					bool = True,     ):
										if state.num_inference_steps is None:
																raise ValueError(
																    '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''   )

										snake_case							:  Dict			=     state.sigmas[timestep]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
																snake_case							:  List[str]			=     sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
																# * c_out + input * c_skip
																snake_case							:  str			=     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										else:
																raise ValueError(
																    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""   )

										# 2. Convert to an ODE derivative
										snake_case							:  Dict			=     (sample - pred_original_sample) / sigma
										snake_case							:  Any			=     state.replace(derivatives=jnp.append(state.derivatives,     SCREAMING_SNAKE_CASE_   )   )
										if len(state.derivatives   ) > order:
																snake_case							:  Tuple			=     state.replace(derivatives=jnp.delete(state.derivatives,     0   )   )

										# 3. Compute linear multistep coefficients
										snake_case							:  str			=     min(timestep + 1,     SCREAMING_SNAKE_CASE_   )
										snake_case							:  Tuple			=     [self.get_lms_coefficient(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_   ) for curr_order in range(SCREAMING_SNAKE_CASE_   )]

										# 4. Compute previous sample based on the derivatives path
										snake_case							:  int			=     sample + sum(
										    coeff * derivative for coeff, derivative in zip(SCREAMING_SNAKE_CASE_,     reversed(state.derivatives   )   )   )

										if not return_dict:
																return (prev_sample, state)

										return FlaxLMSSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_,     state=SCREAMING_SNAKE_CASE_   )




				def 						__snake_case				(				self						:					int,     SCREAMING_SNAKE_CASE_						:					LMSDiscreteSchedulerState,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     SCREAMING_SNAKE_CASE_						:					jnp.ndarray,     ):
										snake_case							:  int			=     state.sigmas[timesteps].flatten()
										snake_case							:  List[str]			=     broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE_,     noise.shape   )

										snake_case							:  Dict			=     original_samples + noise * sigma

										return noisy_samples




				def __len__(				self						:					Dict   ):
										return self.config.num_train_timesteps



'''simple docstring'''





import math
from timeit import timeit

def   A			(							A_				:       int							):
						snake_case							:  List[str]			=     0
						snake_case							:  Any			=     abs(A_							)
						while True:
												snake_case							:  List[Any]			=     n // 10
												digits += 1
												if n == 0:
																		break
						return digits

def   A			(							A_				:       int							):
						return 1 if n == 0 else math.floor(math.log(abs(A_							)     ,				10							) + 1							)

def   A			(							A_				:       int							):
						return len(str(abs(A_							)							)							)

def   A			(							):
						from collections.abc import Callable

						def benchmark_a_function(A_				:       Callable     ,				A_				:       int							) -> None:
												snake_case							:  Optional[int]			=     F"""{func.__name__}({value})"""
												snake_case							:  Optional[int]			=     timeit(F"""__main__.{call}"""     ,				setup='''import __main__'''							)
												print(F"""{call}: {func(A_							)} -- {timing} seconds"""							)

						for value in (262144, 1125899906842624, 1267650600228229401496703205376):
												for func in (num_digits, num_digits_fast, num_digits_faster):
																		benchmark_a_function(A_     ,				A_							)
												print()


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						benchmark()

