






'''simple docstring'''
from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize


class    _snake_case   (				snake_case					):

					"""simple docstring"""





					_UpperCamelCase		 =      1
					_UpperCamelCase		 =      2
					_UpperCamelCase		 =      3




					def __repr__(     self     )      ->	Any:
										return F'''{self.__class__.__name__}.{self.name}'''



def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )				->				float:






					"""simple docstring"""







					a_							,					a_									=   point
					return degrees(atana(y - miny					,  x - minx ) )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )				->				Direction:






					"""simple docstring"""







					a_							,					a_									=   starting
					a_							,					a_									=   via
					a_							,					a_									=   target
					a_									=   degrees(atana(ya - ya					,  xa - xa ) )
					via_angle %= 3_6_0
					a_									=   degrees(atana(ya - ya					,  xa - xa ) )
					target_angle %= 3_6_0
					# t-
					#  \ \
					#   \ v
					#    \|
					#     s
					# via_angle is always lower than target_angle, if direction is left.
					# If they are same, it means they are on a same line of convex hull.
					if target_angle > via_angle:
										return Direction.left
					elif target_angle == via_angle:
										return Direction.straight
					else:
										return Direction.right





def 							a	(   _UpperCAmelCase )				->				list[tuple[int, int]]:






					"""simple docstring"""







					if len(_UpperCAmelCase ) <= 2:
										# There is no convex hull
										raise ValueError('graham_scan: argument must contain more than 3 points.' )
					if len(_UpperCAmelCase ) == 3:
										return points
					# find the lowest and the most left point
					a_									=   0
					a_							,					a_									=   maxsize, maxsize
					for i, point in enumerate(_UpperCAmelCase ):
										a_									=   point[0]
										a_									=   point[1]
										if y < miny:
															a_									=   y
															a_									=   x
															a_									=   i
										if y == miny and x < minx:
															a_									=   x
															a_									=   i

    # remove the lowest and the most left point from points for preparing for sort
					points.pop(_UpperCAmelCase )

					a_									=   sorted(_UpperCAmelCase					,  key=lambda _UpperCAmelCase : angle_comparer(_UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase ) )
					# This insert actually costs complexity,
					# and you should instead add (minx, miny) into stack later.
					# I'm using insert just for easy understanding.
					sorted_points.insert(0					,  (minx, miny) )

					a_									=   deque()
					stack.append(sorted_points[0] )
					stack.append(sorted_points[1] )
					stack.append(sorted_points[2] )
					# In any ways, the first 3 points line are towards left.
					# Because we sort them the angle from minx, miny.
					a_									=   Direction.left

					for i in range(3					,  len(_UpperCAmelCase ) ):
										while True:
															a_									=   stack[-2]
															a_									=   stack[-1]
															a_									=   sorted_points[i]
															a_									=   check_direction(_UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )

															if next_direction == Direction.left:
																				a_									=   Direction.left
																				break
															if next_direction == Direction.straight:
																				if current_direction == Direction.left:
																									# We keep current_direction as left.
																									# Because if the straight line keeps as straight,
																									# we want to know if this straight line is towards left.
																									break
																				elif current_direction == Direction.right:
																									# If the straight line is towards right,
																									# every previous points on those straigh line is not convex hull.
																									stack.pop()
															if next_direction == Direction.right:
																				stack.pop()
										stack.append(sorted_points[i] )
					return list(_UpperCAmelCase )









'''simple docstring'''
import random
from typing import List, Optional, Union

import numpy as np
import torch

from ..state import AcceleratorState
from .constants import CUDA_DISTRIBUTED_TYPES
from .dataclasses import DistributedType, RNGType
from .imports import is_npu_available, is_tpu_available, is_xpu_available


if is_tpu_available(check_device=False):
						import torch_xla.core.xla_model as xm

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = False )				->				List[str]:






					"""simple docstring"""







					if device_specific:
										seed += AcceleratorState().process_index
					random.seed(_UpperCAmelCase )
					np.random.seed(_UpperCAmelCase )
					torch.manual_seed(_UpperCAmelCase )
					if is_xpu_available():
										torch.xpu.manual_seed_all(_UpperCAmelCase )
					elif is_npu_available():
										torch.npu.manual_seed_all(_UpperCAmelCase )
					else:
										torch.cuda.manual_seed_all(_UpperCAmelCase )
					# ^^ safe to call this function even if cuda is not available
					if is_tpu_available():
										xm.set_rng_state(_UpperCAmelCase )

def 							a	(   _UpperCAmelCase = None					,  _UpperCAmelCase = None )				->				Tuple:






					"""simple docstring"""







					if rng_type == RNGType.TORCH:
										a_									=   torch.get_rng_state()
					elif rng_type == RNGType.CUDA:
										a_									=   torch.cuda.get_rng_state()
					elif rng_type == RNGType.XLA:
										assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
										a_									=   torch.tensor(xm.get_rng_state() )
					elif rng_type == RNGType.NPU:
										assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
										a_									=   torch.npu.get_rng_state()
					elif rng_type == RNGType.XPU:
										assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
										a_									=   torch.xpu.get_rng_state()
					elif rng_type == RNGType.GENERATOR:
										assert generator is not None, "Need a generator to synchronize its seed."
										a_									=   generator.get_state()

					# Broadcast the rng state from device 0 to other devices
					a_									=   AcceleratorState()
					if state.distributed_type == DistributedType.TPU:
										a_									=   rng_state.to(xm.xla_device() )
										xm.collective_broadcast([rng_state] )
										xm.mark_step()
										a_									=   rng_state.cpu()
					elif (
					    state.distributed_type in CUDA_DISTRIBUTED_TYPES
					    or state.distributed_type == DistributedType.MULTI_NPU
					    or state.distributed_type == DistributedType.MULTI_XPU
					):
										a_									=   rng_state.to(state.device )
										torch.distributed.broadcast(_UpperCAmelCase					,  0 )
										a_									=   rng_state.cpu()
					elif state.distributed_type == DistributedType.MULTI_CPU:
										torch.distributed.broadcast(_UpperCAmelCase					,  0 )

					# Set the broadcast rng state
					if rng_type == RNGType.TORCH:
										torch.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.CUDA:
										torch.cuda.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.NPU:
										torch.npu.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.XPU:
										torch.xpu.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.XLA:
										xm.set_rng_state(rng_state.item() )
					elif rng_type == RNGType.GENERATOR:
										generator.set_state(_UpperCAmelCase )





def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = None )				->				Any:






					"""simple docstring"""







					for rng_type in rng_types:
										synchronize_rng_state(RNGType(_UpperCAmelCase )					,  generator=_UpperCAmelCase )

