"""simple docstring"""




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

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput

@dataclass
class       a_      (     __UpperCamelCase			):

					'''simple docstring'''





					UpperCamelCase_ :	torch.FloatTensor
					UpperCamelCase_ :	torch.FloatTensor

class       a_      (     __UpperCamelCase ,		__UpperCamelCase			):

					'''simple docstring'''





					UpperCamelCase_ :	Dict			=    1




					@register_to_config
					def __init__(	self						:     Optional[int]  ,						snake_case__						:     int = 2000  ,						snake_case__						:     float = 0.15  ,						snake_case__						:     float = 0.01  ,						snake_case__						:     float = 1348.0  ,						snake_case__						:     float = 1E-5  ,						snake_case__						:     int = 1  ,						):
							# standard deviation of the initial noise distribution
							lowerCAmelCase__        =   sigma_max

							# setable values
							lowerCAmelCase__        =   None

							self.set_sigmas(snake_case__  ,						snake_case__  ,						snake_case__  ,						snake_case__     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Union[str, Any]  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     Optional[int] = None     ):
							return sample




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Optional[Any]  ,						snake_case__						:     int  ,						snake_case__						:     float = None  ,						snake_case__						:     Union[str, torch.device] = None     ):
							lowerCAmelCase__        =   sampling_eps if sampling_eps is not None else self.config.sampling_eps

							lowerCAmelCase__        =   torch.linspace(1  ,						snake_case__  ,						snake_case__  ,						device=snake_case__     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Optional[Any]  ,						snake_case__						:     int  ,						snake_case__						:     float = None  ,						snake_case__						:     float = None  ,						snake_case__						:     float = None     ):
							lowerCAmelCase__        =   sigma_min if sigma_min is not None else self.config.sigma_min
							lowerCAmelCase__        =   sigma_max if sigma_max is not None else self.config.sigma_max
							lowerCAmelCase__        =   sampling_eps if sampling_eps is not None else self.config.sampling_eps
							if self.timesteps is None:
									self.set_timesteps(snake_case__  ,						snake_case__     )

							lowerCAmelCase__        =   sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
							lowerCAmelCase__        =   torch.exp(torch.linspace(math.log(snake_case__     )  ,						math.log(snake_case__     )  ,						snake_case__     )     )
							lowerCAmelCase__        =   torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Optional[int]  ,						snake_case__						:     int  ,						snake_case__						:     int     ):
							return torch.where(
							    timesteps == 0  ,						torch.zeros_like(t.to(timesteps.device     )     )  ,						self.discrete_sigmas[timesteps - 1].to(timesteps.device     )  ,						)




					def 						_SCREAMING_SNAKE_CASE						(	self						:     int  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     int  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     Optional[torch.Generator] = None  ,						snake_case__						:     bool = True  ,						):
							if self.timesteps is None:
									raise ValueError(
									    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""     )

							lowerCAmelCase__        =   timestep * torch.ones(
							    sample.shape[0]  ,						device=sample.device     )  # torch.repeat_interleave(timestep, sample.shape[0])
							lowerCAmelCase__        =   (timestep * (len(self.timesteps     ) - 1)).long()

							# mps requires indices to be in the same device, so we use cpu as is the default with cuda
							lowerCAmelCase__        =   timesteps.to(self.discrete_sigmas.device     )

							lowerCAmelCase__        =   self.discrete_sigmas[timesteps].to(sample.device     )
							lowerCAmelCase__        =   self.get_adjacent_sigma(snake_case__  ,						snake_case__     ).to(sample.device     )
							lowerCAmelCase__        =   torch.zeros_like(snake_case__     )
							lowerCAmelCase__        =   (sigma**2 - adjacent_sigma**2) ** 0.5

							# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
							# also equation 47 shows the analog from SDE models to ancestral sampling methods
							lowerCAmelCase__        =   diffusion.flatten()
							while len(diffusion.shape     ) < len(sample.shape     ):
									lowerCAmelCase__        =   diffusion.unsqueeze(-1     )
							lowerCAmelCase__        =   drift - diffusion**2 * model_output

							#  equation 6: sample noise for the diffusion term of
							lowerCAmelCase__        =   randn_tensor(
							    sample.shape  ,						layout=sample.layout  ,						generator=snake_case__  ,						device=sample.device  ,						dtype=sample.dtype     )
							lowerCAmelCase__        =   sample - drift  # subtract because `dt` is a small negative timestep
							# TODO is the variable diffusion the correct scaling term for the noise?
							lowerCAmelCase__        =   prev_sample_mean + diffusion * noise  # add impact of diffusion field g

							if not return_dict:
									return (prev_sample, prev_sample_mean)

							return SdeVeOutput(prev_sample=snake_case__  ,						prev_sample_mean=snake_case__     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     List[Any]  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     Optional[torch.Generator] = None  ,						snake_case__						:     bool = True  ,						):
							if self.timesteps is None:
									raise ValueError(
									    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""     )

							# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
							# sample noise for correction
							lowerCAmelCase__        =   randn_tensor(sample.shape  ,						layout=sample.layout  ,						generator=snake_case__     ).to(sample.device     )

							# compute step size from the model_output, the noise, and the snr
							lowerCAmelCase__        =   torch.norm(model_output.reshape(model_output.shape[0]  ,						-1     )  ,						dim=-1     ).mean()
							lowerCAmelCase__        =   torch.norm(noise.reshape(noise.shape[0]  ,						-1     )  ,						dim=-1     ).mean()
							lowerCAmelCase__        =   (self.config.snr * noise_norm / grad_norm) ** 2 * 2
							lowerCAmelCase__        =   step_size * torch.ones(sample.shape[0]     ).to(sample.device     )
							# self.repeat_scalar(step_size, sample.shape[0])

							# compute corrected sample: model_output term and noise term
							lowerCAmelCase__        =   step_size.flatten()
							while len(step_size.shape     ) < len(sample.shape     ):
									lowerCAmelCase__        =   step_size.unsqueeze(-1     )
							lowerCAmelCase__        =   sample + step_size * model_output
							lowerCAmelCase__        =   prev_sample_mean + ((step_size * 2) ** 0.5) * noise

							if not return_dict:
									return (prev_sample,)

							return SchedulerOutput(prev_sample=snake_case__     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     List[str]  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     torch.FloatTensor  ,						snake_case__						:     torch.FloatTensor  ,						):
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							lowerCAmelCase__        =   timesteps.to(original_samples.device     )
							lowerCAmelCase__        =   self.discrete_sigmas.to(original_samples.device     )[timesteps]
							lowerCAmelCase__        =   (
							    noise * sigmas[:, None, None, None]
							    if noise is not None
							    else torch.randn_like(snake_case__     ) * sigmas[:, None, None, None]
							)
							lowerCAmelCase__        =   noise + original_samples
							return noisy_samples




					def __len__(	self						:     List[Any]     ):
							return self.config.num_train_timesteps





"""simple docstring"""




from __future__ import annotations

from math import gcd







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__ = 2			,  lowerCamelCase__ = 1			,  lowerCamelCase__ = 3			,  ):





		"""simple docstring"""




		if num < 2:
				raise ValueError("""The input value cannot be less than 2"""     )

		# Because of the relationship between ``f(f(x))`` and ``f(x)``, this
		# algorithm struggles to find factors that are divisible by two.
		# As a workaround, we specifically check for two and even inputs.
		#   See: https://math.stackexchange.com/a/2856214/165820
		if num > 2 and num % 2 == 0:
				return 2

		# Pollard's Rho algorithm requires a function that returns pseudorandom
		# values between 0 <= X < ``num``.  It doesn't need to be random in the
		# sense that the output value is cryptographically secure or difficult
		# to calculate, it only needs to be random in the sense that all output
		# values should be equally likely to appear.
		# For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
		# However, the success of Pollard's algorithm isn't guaranteed and is
		# determined in part by the initial seed and the chosen random function.
		# To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
		# where ``C`` is a value that we can modify between each attempt.
		def rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     ) -> int:
				return (pow(lowerCamelCase__			,  2     ) + step) % modulus

		for _ in range(lowerCamelCase__     ):
				# These track the position within the cycle detection logic.
				lowerCAmelCase__        =   seed
				lowerCAmelCase__        =   seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						lowerCAmelCase__        =   rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     )
						lowerCAmelCase__        =   rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     )
						lowerCAmelCase__        =   rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     )

						# At some point both the tortoise and the hare will enter a cycle whose
						# length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
						# the tortoise and hare will end up on the same value modulo ``p``.
						# We can detect when this happens because the position difference between
						# the tortoise and the hare will share a common divisor with ``num``.
						lowerCAmelCase__        =   gcd(hare - tortoise			,  lowerCamelCase__     )

						if divisor == 1:
								# No common divisor yet, just keep searching.
								continue
						else:
								# We found a common divisor!
								if divisor == num:
										# Unfortunately, the divisor is ``num`` itself and is useless.
										break
								else:
										# The divisor is a nontrivial factor of ``num``!
										return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
				lowerCAmelCase__        =   hare

				# The new step value for the random function can just be incremented.
				# At first the results will be similar to what the old function would
				# have produced, but the value will quickly diverge after a bit.
				step += 1

		# We haven't found a divisor within the requested number of attempts.
		# We were unlucky or ``num`` itself is actually prime.
		return None


if __name__ == "__main__":
			import argparse

			__lowerCAmelCase    :							Union[str, Any]													=						argparse.ArgumentParser()
			parser.add_argument(
			    "num",
			    type=int,
			    help="The value to find a divisor of",
			)
			parser.add_argument(
			    "--attempts",
			    type=int,
			    default=3,
			    help="The number of attempts before giving up",
			)
			__lowerCAmelCase    :							List[str]													=						parser.parse_args()

			__lowerCAmelCase    :							Dict													=						pollard_rho(args.num, attempts=args.attempts)
			if divisor is None:
						print(F"{args.num} is probably prime")
			else:
						__lowerCAmelCase    :							List[str]													=						args.num // divisor
						print(F"{args.num} = {divisor} * {quotient}")




