






'''simple docstring'''







import math


def 						_UpperCamelCase							(     snake_case__							):
      __A		   =      math.log(2							,			10							) * number
      __A		   =      round((log_number - int(snake_case__							))							,			15							)

      return difference


def 						_UpperCamelCase							(     snake_case__ = 678_910							):
      __A		   =      90
      __A		   =      0

      __A		   =      math.log(1.23							,			10							)
      __A		   =      math.log(1.24							,			10							)
      __A		   =      0

      while position < number:
            __A		   =      log_difference(snake_case__							)

            if difference >= upper_limit:
                  power_iterator += 93

            elif difference < lower_limit:
                  power_iterator += 196

            else:
                  __A		   =      power_iterator
                  power_iterator += 196
                  position += 1

      return previous_power


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       print(F"""{solution() = }""")









'''simple docstring'''







import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp


def 						_UpperCamelCase							(     ):
      __A		   =      ArgumentParser(
          description=(
              "PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"
          )							)

      # Optional arguments for the launch helper
      parser.add_argument("--num_cores"							,			type=snake_case__							,			default=1							,			help="Number of TPU cores to use (1 or 8)."							)

      # positional
      parser.add_argument(
          "training_script"							,			type=snake_case__							,			help=(
              "The full path to the single TPU training "
              "program/script to be launched in parallel, "
              "followed by all the arguments for the "
              "training script"
          )							,			)

      # rest from the training program
      parser.add_argument("training_script_args"							,			nargs=snake_case__							)

      return parser.parse_args()


def 						_UpperCamelCase							(     ):
      __A		   =      parse_args()

      # Import training_script as a module.
      __A		   =      Path(args.training_script							)
      sys.path.append(str(script_fpath.parent.resolve()							)							)
      __A		   =      script_fpath.stem
      __A		   =      importlib.import_module(snake_case__							)

      # Patch sys.argv
      __A		   =      [args.training_script] + args.training_script_args + ["--tpu_num_cores", str(args.num_cores							)]

      xmp.spawn(mod._mp_fn							,			args=()							,			nprocs=args.num_cores							)


if __name__ == "__main__":
       main()


