



'''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 							__UpperCAmelCase				(				UpperCamelCase__				:int   ,				UpperCamelCase__				:bool = False			)		->						int:
				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 							__UpperCAmelCase				(				UpperCamelCase__				:Optional[RNGType] = None   ,				UpperCamelCase__				:Optional[torch.Generator] = None			)		->						Tuple:
				# Get the proper rng state
				if rng_type == RNGType.TORCH:
								snake_case__      :   List[str]      =    torch.get_rng_state()
				elif rng_type == RNGType.CUDA:
								snake_case__      :   Dict      =    torch.cuda.get_rng_state()
				elif rng_type == RNGType.XLA:
								assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
								snake_case__      :   Tuple      =    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."
								snake_case__      :   Dict      =    torch.npu.get_rng_state()
				elif rng_type == RNGType.XPU:
								assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
								snake_case__      :   int      =    torch.xpu.get_rng_state()
				elif rng_type == RNGType.GENERATOR:
								assert generator is not None, "Need a generator to synchronize its seed."
								snake_case__      :   List[Any]      =    generator.get_state()

				# Broadcast the rng state from device 0 to other devices
				snake_case__      :   Tuple      =    AcceleratorState()
				if state.distributed_type == DistributedType.TPU:
								snake_case__      :   int      =    rng_state.to(xm.xla_device()			)
								xm.collective_broadcast([rng_state]			)
								xm.mark_step()
								snake_case__      :   Dict      =    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
				):
								snake_case__      :   Optional[Any]      =    rng_state.to(state.device			)
								torch.distributed.broadcast(UpperCamelCase__   ,				0			)
								snake_case__      :   Dict      =    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 							__UpperCAmelCase				(				UpperCamelCase__				:List[Union[str, RNGType]]   ,				UpperCamelCase__				:Optional[torch.Generator] = None			)		->						Union[str, Any]:
				for rng_type in rng_types:
								synchronize_rng_state(RNGType(UpperCamelCase__			)   ,				generator=UpperCamelCase__			)





'''simple docstring'''





from itertools import count
from math import asin, pi, sqrt






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float  )   ->				float:







     """simple docstring"""
     return (
         (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
     ) / 4






def SCREAMING_SNAKE_CASE__  (				snake_case       :				int  )   ->				float:







     """simple docstring"""
     a					:							List[str]							= (circles_number + 1 - sqrt(2 * circles_number  )) / (
         2 * (circles_number**2 + 1)
     )
     a					:							int							= circles_number * intersection_y

     a					:							List[Any]							= intersection_x * intersection_y / 2
     a					:							List[str]							= circle_bottom_arc_integral(
         1 / 2  ) - circle_bottom_arc_integral(snake_case  )

     return triangle_area + concave_region_area






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float = 1 / 1_000  )   ->				int:







     """simple docstring"""
     a					:							str							= (1 - pi / 4) / 4

     for n in count(1  ):
          if concave_triangle_area(snake_case  ) / l_section_area < fraction:
               return n

     return -1


if __name__ == "__main__":
      print(f'''{solution() = }''')

