




"""simple docstring"""


import math
from enum import Enum
from typing import Optional, Union

from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR

from .utils import logging


A_      =    logging.get_logger(__name__)






class  lowercase(					__a			):







 '''simple docstring'''





 lowercase__			 = "linear"
 lowercase__			 = "cosine"
 lowercase__			 = "cosine_with_restarts"
 lowercase__			 = "polynomial"
 lowercase__			 = "constant"
 lowercase__			 = "constant_with_warmup"
 lowercase__			 = "piecewise_constant"







def  UpperCAmelCase__	(snake_case__							: Optimizer		,       snake_case__							: int = -1   ):
  """simple docstring"""

  return LambdaLR(snake_case__		,       lambda snake_case__   : 1		,       last_epoch=snake_case__   )


def  UpperCAmelCase__	(snake_case__							: Optimizer		,       snake_case__							: int		,       snake_case__							: int = -1   ):
  """simple docstring"""

  def lr_lambda(snake_case__							: int   ):
    if current_step < num_warmup_steps:
      return float(snake_case__   ) / float(max(1.0		,       snake_case__   )   )
    return 1.0

  return LambdaLR(snake_case__		,       snake_case__		,       last_epoch=snake_case__   )


def  UpperCAmelCase__	(snake_case__							: Optimizer		,       snake_case__							: str		,       snake_case__							: int = -1   ):
  """simple docstring"""

  _snake_case							:		Tuple								=  {}
  _snake_case							:		Union[str, Any]								=  step_rules.split(""","""   )
  for rule_str in rule_list[:-1]:
    _snake_case		, _snake_case							:		List[str]								=  rule_str.split(""":"""   )
    _snake_case							:		Optional[Any]								=  int(snake_case__   )
    _snake_case							:		Dict								=  float(snake_case__   )
    _snake_case							:		List[str]								=  value
  _snake_case							:		Any								=  float(rule_list[-1]   )

  def create_rules_function(snake_case__							: Dict		,       snake_case__							: List[str]   ):
    def rule_func(snake_case__							: int   ) -> float:
      _snake_case							:		List[str]								=  sorted(rules_dict.keys()   )
      for i, sorted_step in enumerate(snake_case__   ):
        if steps < sorted_step:
          return rules_dict[sorted_steps[i]]
      return last_lr_multiple

    return rule_func

  _snake_case							:		List[str]								=  create_rules_function(snake_case__		,       snake_case__   )

  return LambdaLR(snake_case__		,       snake_case__		,       last_epoch=snake_case__   )


def  UpperCAmelCase__	(snake_case__							: int		,       snake_case__							: int		,       snake_case__							: Optional[int]		,       snake_case__							: Any=-1   ):
  """simple docstring"""

  def lr_lambda(snake_case__							: int   ):
    if current_step < num_warmup_steps:
      return float(snake_case__   ) / float(max(1		,       snake_case__   )   )
    return max(
        0.0		,       float(num_training_steps - current_step   ) / float(max(1		,       num_training_steps - num_warmup_steps   )   )   )

  return LambdaLR(snake_case__		,       snake_case__		,       snake_case__   )


def  UpperCAmelCase__	(snake_case__							: Optimizer		,       snake_case__							: int		,       snake_case__							: int		,       snake_case__							: float = 0.5		,       snake_case__							: int = -1   ):
  """simple docstring"""

  def lr_lambda(snake_case__							: int   ):
    if current_step < num_warmup_steps:
      return float(snake_case__   ) / float(max(1		,       snake_case__   )   )
    _snake_case							:		Any								=  float(current_step - num_warmup_steps   ) / float(max(1		,       num_training_steps - num_warmup_steps   )   )
    return max(0.0		,       0.5 * (1.0 + math.cos(math.pi * float(snake_case__   ) * 2.0 * progress   ))   )

  return LambdaLR(snake_case__		,       snake_case__		,       snake_case__   )


def  UpperCAmelCase__	(snake_case__							: Optimizer		,       snake_case__							: int		,       snake_case__							: int		,       snake_case__							: int = 1		,       snake_case__							: int = -1   ):
  """simple docstring"""

  def lr_lambda(snake_case__							: Tuple   ):
    if current_step < num_warmup_steps:
      return float(snake_case__   ) / float(max(1		,       snake_case__   )   )
    _snake_case							:		int								=  float(current_step - num_warmup_steps   ) / float(max(1		,       num_training_steps - num_warmup_steps   )   )
    if progress >= 1.0:
      return 0.0
    return max(0.0		,       0.5 * (1.0 + math.cos(math.pi * ((float(snake_case__   ) * progress) % 1.0)   ))   )

  return LambdaLR(snake_case__		,       snake_case__		,       snake_case__   )


def  UpperCAmelCase__	(snake_case__							: Union[str, Any]		,       snake_case__							: Tuple		,       snake_case__							: List[str]		,       snake_case__							: Tuple=1e-7		,       snake_case__							: List[str]=1.0		,       snake_case__							: Union[str, Any]=-1   ):
  """simple docstring"""

  _snake_case							:		str								=  optimizer.defaults["""lr"""]
  if not (lr_init > lr_end):
    raise ValueError(F"lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})"   )

  def lr_lambda(snake_case__							: int   ):
    if current_step < num_warmup_steps:
      return float(snake_case__   ) / float(max(1		,       snake_case__   )   )
    elif current_step > num_training_steps:
      return lr_end / lr_init  # as LambdaLR multiplies by lr_init
    else:
      _snake_case							:		Optional[Any]								=  lr_init - lr_end
      _snake_case							:		Optional[Any]								=  num_training_steps - num_warmup_steps
      _snake_case							:		List[str]								=  1 - (current_step - num_warmup_steps) / decay_steps
      _snake_case							:		int								=  lr_range * pct_remaining**power + lr_end
      return decay / lr_init  # as LambdaLR multiplies by lr_init

  return LambdaLR(snake_case__		,       snake_case__		,       snake_case__   )


A_      =    {
    SchedulerType.LINEAR: get_linear_schedule_with_warmup,
    SchedulerType.COSINE: get_cosine_schedule_with_warmup,
    SchedulerType.COSINE_WITH_RESTARTS: get_cosine_with_hard_restarts_schedule_with_warmup,
    SchedulerType.POLYNOMIAL: get_polynomial_decay_schedule_with_warmup,
    SchedulerType.CONSTANT: get_constant_schedule,
    SchedulerType.CONSTANT_WITH_WARMUP: get_constant_schedule_with_warmup,
    SchedulerType.PIECEWISE_CONSTANT: get_piecewise_constant_schedule,
}






def  UpperCAmelCase__	(snake_case__							: Union[str, SchedulerType]		,       snake_case__							: Optimizer		,       snake_case__							: Optional[str] = None		,       snake_case__							: Optional[int] = None		,       snake_case__							: Optional[int] = None		,       snake_case__							: int = 1		,       snake_case__							: float = 1.0		,       snake_case__							: int = -1		,       ):
  """simple docstring"""

  _snake_case							:		Any								=  SchedulerType(snake_case__   )
  _snake_case							:		int								=  TYPE_TO_SCHEDULER_FUNCTION[name]
  if name == SchedulerType.CONSTANT:
    return schedule_func(snake_case__		,       last_epoch=snake_case__   )

  if name == SchedulerType.PIECEWISE_CONSTANT:
    return schedule_func(snake_case__		,       step_rules=snake_case__		,       last_epoch=snake_case__   )

  # All other schedulers require `num_warmup_steps`
  if num_warmup_steps is None:
    raise ValueError(F"{name} requires `num_warmup_steps`, please provide that argument."   )

  if name == SchedulerType.CONSTANT_WITH_WARMUP:
    return schedule_func(snake_case__		,       num_warmup_steps=snake_case__		,       last_epoch=snake_case__   )

  # All other schedulers require `num_training_steps`
  if num_training_steps is None:
    raise ValueError(F"{name} requires `num_training_steps`, please provide that argument."   )

  if name == SchedulerType.COSINE_WITH_RESTARTS:
    return schedule_func(
        snake_case__		,       num_warmup_steps=snake_case__		,       num_training_steps=snake_case__		,       num_cycles=snake_case__		,       last_epoch=snake_case__		,       )

  if name == SchedulerType.POLYNOMIAL:
    return schedule_func(
        snake_case__		,       num_warmup_steps=snake_case__		,       num_training_steps=snake_case__		,       power=snake_case__		,       last_epoch=snake_case__		,       )

  return schedule_func(
      snake_case__		,       num_warmup_steps=snake_case__		,       num_training_steps=snake_case__		,       last_epoch=snake_case__   )








"""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}''')


