




"""simple docstring"""


from __future__ import annotations

from math import gcd


def  UpperCAmelCase__	(snake_case__							: int		,       snake_case__							: int = 2		,       snake_case__							: int = 1		,       snake_case__							: int = 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(snake_case__							: int		,       snake_case__							: int		,       snake_case__							: int   ) -> int:
    return (pow(snake_case__		,       2   ) + step) % modulus

  for _ in range(snake_case__   ):
    # These track the position within the cycle detection logic.
    _snake_case							:		Optional[int]								=  seed
    _snake_case							:		str								=  seed

    while True:
      # At each iteration, the tortoise moves one step and the hare moves two.
      _snake_case							:		Any								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		Optional[Any]								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		int								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )

      # 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``.
      _snake_case							:		str								=  gcd(hare - tortoise		,       snake_case__   )

      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.
    _snake_case							:		Union[str, Any]								=  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

     A_      =    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''',
     )
     A_      =    parser.parse_args()

     A_      =    pollard_rho(args.num, attempts=args.attempts)
     if divisor is None:
          print(F'''{args.num} is probably prime''')
     else:
          A_      =    args.num // divisor
          print(F'''{args.num} = {divisor} * {quotient}''')








"""simple docstring"""


from typing import Optional, Tuple, Union

import flax
import flax.linen as nn
import jax
import jax.numpy as jnp
from flax.core.frozen_dict import FrozenDict

from ..configuration_utils import ConfigMixin, flax_register_to_config
from ..utils import BaseOutput
from .embeddings_flax import FlaxTimestepEmbedding, FlaxTimesteps
from .modeling_flax_utils import FlaxModelMixin
from .unet_ad_blocks_flax import (
    FlaxCrossAttnDownBlockaD,
    FlaxDownBlockaD,
    FlaxUNetMidBlockaDCrossAttn,
)






@flax.struct.dataclass
class  lowercase(					__a			):







 '''simple docstring'''





 lowercase__			 = 42
 lowercase__			 = 42







class  lowercase(					nn.Module			):







 '''simple docstring'''





 lowercase__			 = 42
 lowercase__			 = (16, 32, 96, 2_56)
 lowercase__			 = jnp.floataa


 def 			UpperCamelCase_       (    self:		Optional[int]		):




   '''simple docstring'''



   _snake_case							:		List[str]								=  nn.Conv(
       self.block_out_channels[0],				kernel_size=(3, 3),				padding=((1, 1), (1, 1)),				dtype=self.dtype,				)

   _snake_case							:		int								=  []
   for i in range(len(self.block_out_channels		) - 1		):
     _snake_case							:		int								=  self.block_out_channels[i]
     _snake_case							:		Tuple								=  self.block_out_channels[i + 1]
     _snake_case							:		Dict								=  nn.Conv(
         a_,				kernel_size=(3, 3),				padding=((1, 1), (1, 1)),				dtype=self.dtype,				)
     blocks.append(a_		)
     _snake_case							:		List[Any]								=  nn.Conv(
         a_,				kernel_size=(3, 3),				strides=(2, 2),				padding=((1, 1), (1, 1)),				dtype=self.dtype,				)
     blocks.append(a_		)
   _snake_case							:		Any								=  blocks

   _snake_case							:		Optional[Any]								=  nn.Conv(
       self.conditioning_embedding_channels,				kernel_size=(3, 3),				padding=((1, 1), (1, 1)),				kernel_init=nn.initializers.zeros_init(),				bias_init=nn.initializers.zeros_init(),				dtype=self.dtype,				)


 def __call__(    self:		Optional[Any],				a_:		Optional[Any]		):




   '''simple docstring'''



   _snake_case							:		int								=  self.conv_in(a_		)
   _snake_case							:		Optional[int]								=  nn.silu(a_		)

   for block in self.blocks:
     _snake_case							:		Tuple								=  block(a_		)
     _snake_case							:		int								=  nn.silu(a_		)

   _snake_case							:		Optional[int]								=  self.conv_out(a_		)

   return embedding







@flax_register_to_config
class  lowercase(					nn.Module	,      __a	,      __a			):







 '''simple docstring'''





 lowercase__			 = 32
 lowercase__			 = 4
 lowercase__			 = (
     "CrossAttnDownBlock2D",
     "CrossAttnDownBlock2D",
     "CrossAttnDownBlock2D",
     "DownBlock2D",
 )
 lowercase__			 = False
 lowercase__			 = (3_20, 6_40, 12_80, 12_80)
 lowercase__			 = 2
 lowercase__			 = 8
 lowercase__			 = None
 lowercase__			 = 12_80
 lowercase__			 = 0.0
 lowercase__			 = False
 lowercase__			 = jnp.floataa
 lowercase__			 = True
 lowercase__			 = 0
 lowercase__			 = "rgb"
 lowercase__			 = (16, 32, 96, 2_56)


 def 			UpperCamelCase_       (    self:		int,				a_:		jax.random.KeyArray		):




   '''simple docstring'''



   _snake_case							:		str								=  (1, self.in_channels, self.sample_size, self.sample_size)
   _snake_case							:		Optional[Any]								=  jnp.zeros(a_,				dtype=jnp.floataa		)
   _snake_case							:		List[str]								=  jnp.ones((1,),				dtype=jnp.intaa		)
   _snake_case							:		List[Any]								=  jnp.zeros((1, 1, self.cross_attention_dim),				dtype=jnp.floataa		)
   _snake_case							:		Any								=  (1, 3, self.sample_size * 8, self.sample_size * 8)
   _snake_case							:		Optional[int]								=  jnp.zeros(a_,				dtype=jnp.floataa		)

   _snake_case		, _snake_case							:		Tuple								=  jax.random.split(a_		)
   _snake_case							:		str								=  {"""params""": params_rng, """dropout""": dropout_rng}

   return self.init(a_,				a_,				a_,				a_,				a_		)["params"]


 def 			UpperCamelCase_       (    self:		Any		):




   '''simple docstring'''



   _snake_case							:		Optional[int]								=  self.block_out_channels
   _snake_case							:		Optional[int]								=  block_out_channels[0] * 4

   # If `num_attention_heads` is not defined (which is the case for most models)
   # it will default to `attention_head_dim`. This looks weird upon first reading it and it is.
   # The reason for this behavior is to correct for incorrectly named variables that were introduced
   # when this library was created. The incorrect naming was only discovered much later in https://github.com/huggingface/diffusers/issues/2011#issuecomment-1547958131
   # Changing `attention_head_dim` to `num_attention_heads` for 40,000+ configurations is too backwards breaking
   # which is why we correct for the naming here.
   _snake_case							:		int								=  self.num_attention_heads or self.attention_head_dim

   # input
   _snake_case							:		Union[str, Any]								=  nn.Conv(
       block_out_channels[0],				kernel_size=(3, 3),				strides=(1, 1),				padding=((1, 1), (1, 1)),				dtype=self.dtype,				)

   # time
   _snake_case							:		int								=  FlaxTimesteps(
       block_out_channels[0],				flip_sin_to_cos=self.flip_sin_to_cos,				freq_shift=self.config.freq_shift		)
   _snake_case							:		Any								=  FlaxTimestepEmbedding(a_,				dtype=self.dtype		)

   _snake_case							:		Optional[Any]								=  FlaxControlNetConditioningEmbedding(
       conditioning_embedding_channels=block_out_channels[0],				block_out_channels=self.conditioning_embedding_out_channels,				)

   _snake_case							:		List[str]								=  self.only_cross_attention
   if isinstance(a_,				a_		):
     _snake_case							:		List[Any]								=  (only_cross_attention,) * len(self.down_block_types		)

   if isinstance(a_,				a_		):
     _snake_case							:		Optional[Any]								=  (num_attention_heads,) * len(self.down_block_types		)

   # down
   _snake_case							:		List[str]								=  []
   _snake_case							:		Tuple								=  []

   _snake_case							:		int								=  block_out_channels[0]

   _snake_case							:		Optional[Any]								=  nn.Conv(
       a_,				kernel_size=(1, 1),				padding="""VALID""",				kernel_init=nn.initializers.zeros_init(),				bias_init=nn.initializers.zeros_init(),				dtype=self.dtype,				)
   controlnet_down_blocks.append(a_		)

   for i, down_block_type in enumerate(self.down_block_types		):
     _snake_case							:		List[Any]								=  output_channel
     _snake_case							:		Any								=  block_out_channels[i]
     _snake_case							:		List[str]								=  i == len(a_		) - 1

     if down_block_type == "CrossAttnDownBlock2D":
       _snake_case							:		Optional[int]								=  FlaxCrossAttnDownBlockaD(
           in_channels=a_,				out_channels=a_,				dropout=self.dropout,				num_layers=self.layers_per_block,				num_attention_heads=num_attention_heads[i],				add_downsample=not is_final_block,				use_linear_projection=self.use_linear_projection,				only_cross_attention=only_cross_attention[i],				dtype=self.dtype,				)
     else:
       _snake_case							:		List[Any]								=  FlaxDownBlockaD(
           in_channels=a_,				out_channels=a_,				dropout=self.dropout,				num_layers=self.layers_per_block,				add_downsample=not is_final_block,				dtype=self.dtype,				)

     down_blocks.append(a_		)

     for _ in range(self.layers_per_block		):
       _snake_case							:		List[Any]								=  nn.Conv(
           a_,				kernel_size=(1, 1),				padding="""VALID""",				kernel_init=nn.initializers.zeros_init(),				bias_init=nn.initializers.zeros_init(),				dtype=self.dtype,				)
       controlnet_down_blocks.append(a_		)

     if not is_final_block:
       _snake_case							:		List[Any]								=  nn.Conv(
           a_,				kernel_size=(1, 1),				padding="""VALID""",				kernel_init=nn.initializers.zeros_init(),				bias_init=nn.initializers.zeros_init(),				dtype=self.dtype,				)
       controlnet_down_blocks.append(a_		)

   _snake_case							:		str								=  down_blocks
   _snake_case							:		Union[str, Any]								=  controlnet_down_blocks

   # mid
   _snake_case							:		Tuple								=  block_out_channels[-1]
   _snake_case							:		Optional[int]								=  FlaxUNetMidBlockaDCrossAttn(
       in_channels=a_,				dropout=self.dropout,				num_attention_heads=num_attention_heads[-1],				use_linear_projection=self.use_linear_projection,				dtype=self.dtype,				)

   _snake_case							:		Tuple								=  nn.Conv(
       a_,				kernel_size=(1, 1),				padding="""VALID""",				kernel_init=nn.initializers.zeros_init(),				bias_init=nn.initializers.zeros_init(),				dtype=self.dtype,				)


 def __call__(    self:		str,				a_:		Any,				a_:		Tuple,				a_:		Any,				a_:		int,				a_:		float = 1.0,				a_:		bool = True,				a_:		bool = False,				):




   '''simple docstring'''



   _snake_case							:		Dict								=  self.controlnet_conditioning_channel_order
   if channel_order == "bgr":
     _snake_case							:		List[Any]								=  jnp.flip(a_,				axis=1		)

   # 1. time
   if not isinstance(a_,				jnp.ndarray		):
     _snake_case							:		Any								=  jnp.array([timesteps],				dtype=jnp.intaa		)
   elif isinstance(a_,				jnp.ndarray		) and len(timesteps.shape		) == 0:
     _snake_case							:		Union[str, Any]								=  timesteps.astype(dtype=jnp.floataa		)
     _snake_case							:		List[str]								=  jnp.expand_dims(a_,				0		)

   _snake_case							:		List[str]								=  self.time_proj(a_		)
   _snake_case							:		str								=  self.time_embedding(a_		)

   # 2. pre-process
   _snake_case							:		List[str]								=  jnp.transpose(a_,				(0, 2, 3, 1)		)
   _snake_case							:		List[Any]								=  self.conv_in(a_		)

   _snake_case							:		Union[str, Any]								=  jnp.transpose(a_,				(0, 2, 3, 1)		)
   _snake_case							:		Any								=  self.controlnet_cond_embedding(a_		)
   sample += controlnet_cond

   # 3. down
   _snake_case							:		List[str]								=  (sample,)
   for down_block in self.down_blocks:
     if isinstance(a_,				a_		):
       _snake_case		, _snake_case							:		Optional[Any]								=  down_block(a_,				a_,				a_,				deterministic=not train		)
     else:
       _snake_case		, _snake_case							:		Dict								=  down_block(a_,				a_,				deterministic=not train		)
     down_block_res_samples += res_samples

   # 4. mid
   _snake_case							:		Dict								=  self.mid_block(a_,				a_,				a_,				deterministic=not train		)

   # 5. contronet blocks
   _snake_case							:		Tuple								=  ()
   for down_block_res_sample, controlnet_block in zip(a_,				self.controlnet_down_blocks		):
     _snake_case							:		Any								=  controlnet_block(a_		)
     controlnet_down_block_res_samples += (down_block_res_sample,)

   _snake_case							:		List[Any]								=  controlnet_down_block_res_samples

   _snake_case							:		int								=  self.controlnet_mid_block(a_		)

   # 6. scaling
   _snake_case							:		int								=  [sample * conditioning_scale for sample in down_block_res_samples]
   mid_block_res_sample *= conditioning_scale

   if not return_dict:
     return (down_block_res_samples, mid_block_res_sample)

   return FlaxControlNetOutput(
       down_block_res_samples=a_,				mid_block_res_sample=a_		)


