






"""simple docstring"""







# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class        _SCREAMING_SNAKE_CASE						(  __snake_case							):





							"""simple docstring"""





							_SCREAMING_SNAKE_CASE    =42
							_SCREAMING_SNAKE_CASE    =None





def        SCREAMING_SNAKE_CASE       (      lowerCamelCase_ ,     lowerCamelCase_=0.999 ,     lowerCamelCase_="cosine" ,     ):
					if alpha_transform_type == "cosine":

										def alpha_bar_fn(lowerCamelCase_):
															return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(lowerCamelCase_):
															return math.exp(t * -12.0)

					else:
										raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}')

					a__          =  []
					for i in range(lowerCamelCase_):
										a__          =  i / num_diffusion_timesteps
										a__          =  (i + 1) / num_diffusion_timesteps
										betas.append(min(1 - alpha_bar_fn(lowerCamelCase_) / alpha_bar_fn(lowerCamelCase_) ,     lowerCamelCase_))
					return torch.tensor(lowerCamelCase_ ,     dtype=torch.floataa)







class        _SCREAMING_SNAKE_CASE						(  __snake_case       , __snake_case							):





							"""simple docstring"""





							_SCREAMING_SNAKE_CASE    =1




							@register_to_config
							def __init__(   self:     Optional[int]				,		__A:     int = 1000				,		__A:     float = 0.0_0_0_1				,		__A:     float = 0.0_2				,		__A:     str = "linear"				,		__A:     Optional[Union[np.ndarray, List[float]]] = None				,		__A:     bool = True				,		__A:     bool = True				,		__A:     int = 0				,		__A:     str = "epsilon"				,		__A:     float = 1.0				,		**__A:     List[Any]				,		):

												'''simple docstring'''

												if kwargs.get('''set_alpha_to_one'''				,		__A    ) is not None:
																	a__          =  (
																	    '''The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'''
																	)
																	deprecate('''set_alpha_to_one'''				,		'''1.0.0'''				,		__A				,		standard_warn=__A    )
																	a__          =  kwargs['''set_alpha_to_one''']
												if trained_betas is not None:
																	a__          =  torch.tensor(__A				,		dtype=torch.floataa    )
												elif beta_schedule == "linear":
																	a__          =  torch.linspace(__A				,		__A				,		__A				,		dtype=torch.floataa    )
												elif beta_schedule == "scaled_linear":
																	# this schedule is very specific to the latent diffusion model.
																	a__          =  (
																	    torch.linspace(beta_start**0.5				,		beta_end**0.5				,		__A				,		dtype=torch.floataa    ) ** 2
																	)
												elif beta_schedule == "squaredcos_cap_v2":
																	# Glide cosine schedule
																	a__          =  betas_for_alpha_bar(__A    )
												else:
																	raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'    )

												a__          =  1.0 - self.betas
												a__          =  torch.cumprod(self.alphas				,		dim=0    )

												# At every step in inverted ddim, we are looking into the next alphas_cumprod
												# For the final step, there is no next alphas_cumprod, and the index is out of bounds
												# `set_alpha_to_zero` decides whether we set this parameter simply to zero
												# in this case, self.step() just output the predicted noise
												# or whether we use the final alpha of the "non-previous" one.
												a__          =  torch.tensor(0.0    ) if set_alpha_to_zero else self.alphas_cumprod[-1]

												# standard deviation of the initial noise distribution
												a__          =  1.0

												# setable values
												a__          =  None
												a__          =  torch.from_numpy(np.arange(0				,		__A    ).copy().astype(np.intaa    )    )




							def  lowercase		(   self:     Tuple				,		__A:     torch.FloatTensor				,		__A:     Optional[int] = None    ):

												'''simple docstring'''

												return sample




							def  lowercase		(   self:     Tuple				,		__A:     int				,		__A:     Union[str, torch.device] = None    ):

												'''simple docstring'''

												if num_inference_steps > self.config.num_train_timesteps:
																	raise ValueError(
																	    F'`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'
																	    F' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'
																	    F' maximal {self.config.num_train_timesteps} timesteps.'    )

												a__          =  num_inference_steps
												a__          =  self.config.num_train_timesteps // self.num_inference_steps
												# creates integer timesteps by multiplying by ratio
												# casting to int to avoid issues when num_inference_step is power of 3
												a__          =  (np.arange(0				,		__A    ) * step_ratio).round().copy().astype(np.intaa    )
												a__          =  torch.from_numpy(__A    ).to(__A    )
												self.timesteps += self.config.steps_offset




							def  lowercase		(   self:     int				,		__A:     torch.FloatTensor				,		__A:     int				,		__A:     torch.FloatTensor				,		__A:     float = 0.0				,		__A:     bool = False				,		__A:     Optional[torch.FloatTensor] = None				,		__A:     bool = True				,		):

												'''simple docstring'''

												a__          =  timestep + self.config.num_train_timesteps // self.num_inference_steps

												# 2. compute alphas, betas
												# change original implementation to exactly match noise levels for analogous forward process
												a__          =  self.alphas_cumprod[timestep]
												a__          =  (
												    self.alphas_cumprod[prev_timestep]
												    if prev_timestep < self.config.num_train_timesteps
												    else self.final_alpha_cumprod
												)

												a__          =  1 - alpha_prod_t

												# 3. compute predicted original sample from predicted noise also called
												# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
												if self.config.prediction_type == "epsilon":
																	a__          =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
																	a__          =  model_output
												elif self.config.prediction_type == "sample":
																	a__          =  model_output
																	a__          =  (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
												elif self.config.prediction_type == "v_prediction":
																	a__          =  (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
																	a__          =  (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
												else:
																	raise ValueError(
																	    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'
																	    ''' `v_prediction`'''    )

												# 4. Clip or threshold "predicted x_0"
												if self.config.clip_sample:
																	a__          =  pred_original_sample.clamp(
																	    -self.config.clip_sample_range				,		self.config.clip_sample_range    )

												# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
												a__          =  (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

												# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
												a__          =  alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

												if not return_dict:
																	return (prev_sample, pred_original_sample)
												return DDIMSchedulerOutput(prev_sample=__A				,		pred_original_sample=__A    )





							def __len__(   self:     Optional[int]    ):

												'''simple docstring'''

												return self.config.num_train_timesteps










"""simple docstring"""







__a       :	Union[str, Any]             = range(2, 20 + 1)
__a       :	Any             = [10**k for k in range(ks[-1] + 1)]
__a       :	dict[int, dict[int, list[list[int]]]]             = {}





def        SCREAMING_SNAKE_CASE       (      lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_):
					a__          =  sum(a_i[j] for j in range(lowerCamelCase_ ,     len(lowerCamelCase_)))
					a__          =  sum(a_i[j] * base[j] for j in range(min(len(lowerCamelCase_) ,     lowerCamelCase_)))

					a__       ,a__          =  0, 0
					a__          =  n - i

					a__          =  memo.get(lowerCamelCase_)

					if sub_memo is not None:
										a__          =  sub_memo.get(lowerCamelCase_)

										if jumps is not None and len(lowerCamelCase_) > 0:
															# find and make the largest jump without going over
															a__          =  -1
															for _k in range(len(lowerCamelCase_) - 1 ,     -1 ,     -1):
																				if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																									a__          =  _k
																									break

															if max_jump >= 0:
																				a__       ,a__       ,a__          =  jumps[max_jump]
																				# since the difference between jumps is cached, add c
																				a__          =  diff + c
																				for j in range(min(lowerCamelCase_ ,     len(lowerCamelCase_))):
																									a__       ,a__          =  divmod(lowerCamelCase_ ,     10)
																				if new_c > 0:
																									add(lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_)

										else:
															a__          =  []
					else:
										a__          =  {c: []}
										a__          =  sub_memo

					if dn >= max_dn or c + diff >= base[k]:
										return diff, dn

					if k > ks[0]:
										while True:
															# keep doing smaller jumps
															a__       ,a__          =  next_term(lowerCamelCase_ ,     k - 1 ,     i + dn ,     lowerCamelCase_)
															diff += _diff
															dn += terms_jumped

															if dn >= max_dn or c + diff >= base[k]:
																				break
					else:
										# would be too small a jump, just compute sequential terms instead
										a__       ,a__          =  compute(lowerCamelCase_ ,     lowerCamelCase_ ,     i + dn ,     lowerCamelCase_)
										diff += _diff
										dn += terms_jumped

					a__          =  sub_memo[c]

					# keep jumps sorted by # of terms skipped
					a__          =  0
					while j < len(lowerCamelCase_):
										if jumps[j][1] > dn:
															break
										j += 1

					# cache the jump for this value digitsum(b) and c
					sub_memo[c].insert(lowerCamelCase_ ,     (diff, dn, k))
					return (diff, dn)





def        SCREAMING_SNAKE_CASE       (      lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_):
					if i >= n:
										return 0, i
					if k > len(lowerCamelCase_):
										a_i.extend([0 for _ in range(k - len(lowerCamelCase_))])

					# note: a_i -> b * 10^k + c
					# ds_b -> digitsum(b)
					# ds_c -> digitsum(c)
					a__          =  i
					a__       ,a__       ,a__          =  0, 0, 0
					for j in range(len(lowerCamelCase_)):
										if j >= k:
															ds_b += a_i[j]
										else:
															ds_c += a_i[j]

					while i < n:
										i += 1
										a__          =  ds_c + ds_b
										diff += addend
										a__          =  0
										for j in range(lowerCamelCase_):
															a__          =  a_i[j] + addend
															a__       ,a__          =  divmod(lowerCamelCase_ ,     10)

															ds_c += a_i[j]

										if addend > 0:
															break

					if addend > 0:
										add(lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_)
					return diff, i - start_i





def        SCREAMING_SNAKE_CASE       (      lowerCamelCase_ ,     lowerCamelCase_ ,     lowerCamelCase_):
					for j in range(lowerCamelCase_ ,     len(lowerCamelCase_)):
										a__          =  digits[j] + addend
										if s >= 10:
															a__       ,a__          =  divmod(lowerCamelCase_ ,     10)
															a__          =  addend // 10 + quotient
										else:
															a__          =  s
															a__          =  addend // 10

										if addend == 0:
															break

					while addend > 0:
										a__       ,a__          =  divmod(lowerCamelCase_ ,     10)
										digits.append(lowerCamelCase_)





def        SCREAMING_SNAKE_CASE       (      lowerCamelCase_ = 10**15):
					a__          =  [1]
					a__          =  1
					a__          =  0
					while True:
										a__       ,a__          =  next_term(lowerCamelCase_ ,     20 ,     i + dn ,     lowerCamelCase_)
										dn += terms_jumped
										if dn == n - i:
															break

					a__          =  0
					for j in range(len(lowerCamelCase_)):
										a_n += digits[j] * 10**j
					return a_n


if __name__ == "__main__":
	print(F'''{solution() = }''')


