






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

import sys

def 							a	(   _UpperCAmelCase )				->				int:






					"""simple docstring"""







					if n < 0:
										raise ValueError('Negative arguments are not supported' )
					return _fib(_UpperCAmelCase )[0]

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






					"""simple docstring"""







					if n == 0:  # (F(0), F(1))
										return (0, 1)

					# F(2n) = F(n)[2F(n+1) − F(n)]
					# F(2n+1) = F(n+1)^2+F(n)^2
					a_							,					a_									=   _fib(n // 2 )
					a_									=   a * (b * 2 - a)
					a_									=   a * a + b * b
					return (d, c + d) if n % 2 else (c, d)


if __name__ == "__main__":
						__lowerCAmelCase							=int(sys.argv[1])
						print(f'''fibonacci({n}) is {fibonacci(n)}''')









'''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 )

