






'''simple docstring'''







from __future__ import annotations

from math import pi, pow


def 						_UpperCamelCase							(     snake_case__							):
      if side_length < 0:
            raise ValueError("vol_cube() only accepts non-negative values"							)
      return pow(snake_case__							,			3							)


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or radius < 0:
            raise ValueError("vol_spherical_cap() only accepts non-negative values"							)
      # Volume is 1/3 pi * height squared * (3 * radius - height)
      return 1 / 3 * pi * pow(snake_case__							,			2							) * (3 * radius - height)


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__							):
      if radius_a < 0 or radius_a < 0 or centers_distance < 0:
            raise ValueError("vol_spheres_intersect() only accepts non-negative values"							)
      if centers_distance == 0:
            return vol_sphere(min(snake_case__							,			snake_case__							)							)

      __A		   =      (
          (radius_a - radius_a + centers_distance)
          * (radius_a + radius_a - centers_distance)
          / (2 * centers_distance)
      )
      __A		   =      (
          (radius_a - radius_a + centers_distance)
          * (radius_a + radius_a - centers_distance)
          / (2 * centers_distance)
      )

      return vol_spherical_cap(snake_case__							,			snake_case__							) + vol_spherical_cap(snake_case__							,			snake_case__							)


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__							):

      if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
            raise ValueError(
                "vol_spheres_union() only accepts non-negative values, non-zero radius"							)

      if centers_distance == 0:
            return vol_sphere(max(snake_case__							,			snake_case__							)							)

      return (
          vol_sphere(snake_case__							)
          + vol_sphere(snake_case__							)
          - vol_spheres_intersect(snake_case__							,			snake_case__							,			snake_case__							)
      )


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__							):
      if width < 0 or height < 0 or length < 0:
            raise ValueError("vol_cuboid() only accepts non-negative values"							)
      return float(width * height * length							)


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or area_of_base < 0:
            raise ValueError("vol_cone() only accepts non-negative values"							)
      return area_of_base * height / 3.0


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or radius < 0:
            raise ValueError("vol_right_circ_cone() only accepts non-negative values"							)
      return pi * pow(snake_case__							,			2							) * height / 3.0


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or area_of_base < 0:
            raise ValueError("vol_prism() only accepts non-negative values"							)
      return float(area_of_base * height							)


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or area_of_base < 0:
            raise ValueError("vol_pyramid() only accepts non-negative values"							)
      return area_of_base * height / 3.0


def 						_UpperCamelCase							(     snake_case__							):
      if radius < 0:
            raise ValueError("vol_sphere() only accepts non-negative values"							)
      # Volume is 4/3 * pi * radius cubed
      return 4 / 3 * pi * pow(snake_case__							,			3							)


def 						_UpperCamelCase							(     snake_case__							):
      if radius < 0:
            raise ValueError("vol_hemisphere() only accepts non-negative values"							)
      # Volume is radius cubed * pi * 2/3
      return pow(snake_case__							,			3							) * pi * 2 / 3


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if height < 0 or radius < 0:
            raise ValueError("vol_circular_cylinder() only accepts non-negative values"							)
      # Volume is radius squared * height * pi
      return pow(snake_case__							,			2							) * height * pi


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__							):
      # Volume - (outer_radius squared - inner_radius squared) * pi * height
      if inner_radius < 0 or outer_radius < 0 or height < 0:
            raise ValueError(
                "vol_hollow_circular_cylinder() only accepts non-negative values"							)
      if outer_radius <= inner_radius:
            raise ValueError("outer_radius must be greater than inner_radius"							)
      return pi * (pow(snake_case__							,			2							) - pow(snake_case__							,			2							)) * height


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__							):
      # Volume is 1/3 * pi * height *
      #           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
      if radius_a < 0 or radius_a < 0 or height < 0:
            raise ValueError("vol_conical_frustum() only accepts non-negative values"							)
      return (
          1
          / 3
          * pi
          * height
          * (pow(snake_case__							,			2							) + pow(snake_case__							,			2							) + radius_a * radius_a)
      )


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      if torus_radius < 0 or tube_radius < 0:
            raise ValueError("vol_torus() only accepts non-negative values"							)
      return 2 * pow(snake_case__							,			2							) * torus_radius * pow(snake_case__							,			2							)


def 						_UpperCamelCase							(     ):
      print("Volumes:"							)
      print(f"Cube: {vol_cube(2							) = }"							)  # = 8
      print(f"Cuboid: {vol_cuboid(2							,			2							,			2							) = }"							)  # = 8
      print(f"Cone: {vol_cone(2							,			2							) = }"							)  # ~= 1.33
      print(f"Right Circular Cone: {vol_right_circ_cone(2							,			2							) = }"							)  # ~= 8.38
      print(f"Prism: {vol_prism(2							,			2							) = }"							)  # = 4
      print(f"Pyramid: {vol_pyramid(2							,			2							) = }"							)  # ~= 1.33
      print(f"Sphere: {vol_sphere(2							) = }"							)  # ~= 33.5
      print(f"Hemisphere: {vol_hemisphere(2							) = }"							)  # ~= 16.75
      print(f"Circular Cylinder: {vol_circular_cylinder(2							,			2							) = }"							)  # ~= 25.1
      print(f"Torus: {vol_torus(2							,			2							) = }"							)  # ~= 157.9
      print(f"Conical Frustum: {vol_conical_frustum(2							,			2							,			4							) = }"							)  # ~= 58.6
      print(f"Spherical cap: {vol_spherical_cap(1							,			2							) = }"							)  # ~= 5.24
      print(f"Spheres intersetion: {vol_spheres_intersect(2							,			2							,			1							) = }"							)  # ~= 21.21
      print(f"Spheres union: {vol_spheres_union(2							,			2							,			1							) = }"							)  # ~= 45.81
      print(
          f"Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1							,			2							,			3							) = }"							)  # ~= 28.3


if __name__ == "__main__":
       main()










'''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()


