

'''simple docstring'''






from __future__ import annotations

from math import gcd


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

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

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

   # 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``.
   __lowercase							  = gcd(hare - tortoise     ,				A__      )

   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.
  __lowercase							  = 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__											=	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__											=	parser.parse_args()

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




'''simple docstring'''






# Copyright 2022 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import argparse
import os
import subprocess

from packaging.version import Version, parse

from accelerate.commands.config.config_args import default_config_file, load_config_from_file


lowerCAmelCase__											=	'''Run commands across TPU VMs for initial setup before running `accelerate launch`.'''


def 		_A     (    A__=None      ):






 """simple docstring"""



 if subparsers is not None:
  __lowercase							  = subparsers.add_parser('''tpu-config'''     ,				description=_description      )
 else:
  __lowercase							  = argparse.ArgumentParser('''Accelerate tpu-config command'''     ,				description=_description      )
 # Core arguments
 __lowercase							  = parser.add_argument_group(
     '''Config Arguments'''     ,				'''Arguments that can be configured through `accelerate config`.'''      )
 config_args.add_argument(
     '''--config_file'''     ,				type=A__     ,				default=A__     ,				help='''Path to the config file to use for accelerate.'''     ,				)
 config_args.add_argument(
     '''--tpu_name'''     ,				default=A__     ,				help='''The name of the TPU to use. If not specified, will use the TPU specified in the config file.'''     ,				)
 config_args.add_argument(
     '''--tpu_zone'''     ,				default=A__     ,				help='''The zone of the TPU to use. If not specified, will use the zone specified in the config file.'''     ,				)
 __lowercase							  = parser.add_argument_group('''TPU Arguments'''     ,				'''Arguments for options ran inside the TPU.'''      )
 pod_args.add_argument(
     '''--use_alpha'''     ,				action='''store_true'''     ,				help='''Whether to use `gcloud alpha` when running the TPU training script instead of `gcloud`.'''     ,				)
 pod_args.add_argument(
     '''--command_file'''     ,				default=A__     ,				help='''The path to the file containing the commands to run on the pod on startup.'''     ,				)
 pod_args.add_argument(
     '''--command'''     ,				action='''append'''     ,				nargs='''+'''     ,				help='''A command to run on the pod. Can be passed multiple times.'''     ,				)
 pod_args.add_argument(
     '''--install_accelerate'''     ,				action='''store_true'''     ,				help='''Whether to install accelerate on the pod. Defaults to False.'''     ,				)
 pod_args.add_argument(
     '''--accelerate_version'''     ,				default='''latest'''     ,				help='''The version of accelerate to install on the pod. If not specified, will use the latest pypi version. Specify \'dev\' to install from GitHub.'''     ,				)
 pod_args.add_argument(
     '''--debug'''     ,				action='''store_true'''     ,				help='''If set, will print the command that would be run instead of running it.'''      )

 if subparsers is not None:
  parser.set_defaults(func=A__      )
 return parser


def 		_A     (    A__      ):






 """simple docstring"""



 __lowercase							  = None

 # Get the default from the config file if it exists.
 if args.config_file is not None or os.path.isfile(A__      ):
  __lowercase							  = load_config_from_file(args.config_file      )
  if not args.command_file and defaults.command_file is not None and not args.command:
   __lowercase							  = defaults.command_file
  if not args.command and defaults.commands is not None:
   __lowercase							  = defaults.commands
  if not args.tpu_name:
   __lowercase							  = defaults.tpu_name
  if not args.tpu_zone:
   __lowercase							  = defaults.tpu_zone
 if args.accelerate_version == "dev":
  __lowercase							  = '''git+https://github.com/huggingface/accelerate.git'''
 elif args.accelerate_version == "latest":
  __lowercase							  = '''accelerate -U'''
 elif isinstance(parse(args.accelerate_version      )     ,				A__      ):
  __lowercase							  = F"accelerate=={args.accelerate_version}"

 if not args.command_file and not args.command:
  raise ValueError('''You must specify either a command file or a command to run on the pod.'''      )

 if args.command_file:
  with open(args.command_file     ,				'''r'''      ) as f:
   __lowercase							  = [f.read().splitlines()]

    # To turn list of lists into list of strings
 if isinstance(args.command[0]     ,				A__      ):
  __lowercase							  = [line for cmd in args.command for line in cmd]
 # Default to the shared folder and install accelerate
 __lowercase							  = ['''cd /usr/share''']
 if args.install_accelerate:
  new_cmd += [F"pip install {args.accelerate_version}"]
 new_cmd += args.command
 __lowercase							  = '''; '''.join(A__      )

 # Then send it to gcloud
 # Eventually try to use google-api-core to do this instead of subprocess
 __lowercase							  = ['''gcloud''']
 if args.use_alpha:
  cmd += ["alpha"]
 cmd += [
     "compute",
     "tpus",
     "tpu-vm",
     "ssh",
     args.tpu_name,
     "--zone",
     args.tpu_zone,
     "--command",
     args.command,
     "--worker",
     "all",
 ]
 if args.debug:
  print(F"Running {' '.join(A__      )}"      )
  return
 subprocess.run(A__      )
 print('''Successfully setup pod.'''      )






def 		_A     (    ):






 """simple docstring"""



 __lowercase							  = tpu_command_parser()
 __lowercase							  = parser.parse_args()

 tpu_command_launcher(A__      )

