




'''simple docstring'''
def     snake_case_  (       a__		:     list[list[int]]   ,a__		:     list[list[int]]      ):



    """simple docstring"""




    __lowercase          =						[]
    __lowercase          =						len(a__      )
    for i in range(a__      ):
        __lowercase          =						[]
        for j in range(a__      ):
            __lowercase          =						0
            for k in range(a__      ):
                __lowercase          =						val + matrix_a[i][k] * matrix_b[k][j]
            list_a.append(a__      )
        matrix_c.append(a__      )
    return matrix_c
def     snake_case_  (       a__		:     int      ):



    """simple docstring"""




    return [[int(row == column      ) for column in range(a__      )] for row in range(a__      )]
def     snake_case_  (       a__		:     int      ):



    """simple docstring"""




    if n <= 1:
        return n
    __lowercase          =						identity(2      )
    __lowercase          =						[[1, 1], [1, 0]]
    __lowercase          =						n - 1
    while n > 0:
        if n % 2 == 1:
            __lowercase          =						multiply(a__   ,a__      )
        __lowercase          =						multiply(a__   ,a__      )
        __lowercase          =						int(n / 2      )
    return res_matrix[0][0]
def     snake_case_  (       a__		:     int      ):



    """simple docstring"""




    if n <= 1:
        return n
    __lowercase          =						0
    __lowercase          =						1
    for _ in range(2   ,n + 1      ):
        __lowercase    ,__lowercase          =						fiba, fiba + fiba
    return fiba
def     snake_case_  (       ):



    """simple docstring"""




    for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
        __lowercase          =						int("""""".join(c for c in ordinal if c in """0123456789"""      )      )  # 1000th --> 1000
        print(
            f'{ordinal} fibonacci number using matrix exponentiation is '
            f'{nth_fibonacci_matrix(a__      )} and using bruteforce is '
            f'{nth_fibonacci_bruteforce(a__      )}\n'      )
    # from timeit import timeit
    # print(timeit("nth_fibonacci_matrix(1000000)",
    #              "from main import nth_fibonacci_matrix", number=5))
    # print(timeit("nth_fibonacci_bruteforce(1000000)",
    #              "from main import nth_fibonacci_bruteforce", number=5))
    # 2.3342058970001744
    # 57.256506615000035


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()










'''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     snake_case_  (       a__		:     int   ,a__		:     bool = False      ):



    """simple docstring"""




    if device_specific:
        seed += AcceleratorState().process_index
    random.seed(a__      )
    np.random.seed(a__      )
    torch.manual_seed(a__      )
    if is_xpu_available():
        torch.xpu.manual_seed_all(a__      )
    elif is_npu_available():
        torch.npu.manual_seed_all(a__      )
    else:
        torch.cuda.manual_seed_all(a__      )
    # ^^ safe to call this function even if cuda is not available
    if is_tpu_available():
        xm.set_rng_state(a__      )
def     snake_case_  (       a__		:     Optional[RNGType] = None   ,a__		:     Optional[torch.Generator] = None      ):



    """simple docstring"""




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

    # Broadcast the rng state from device 0 to other devices
    __lowercase          =						AcceleratorState()
    if state.distributed_type == DistributedType.TPU:
        __lowercase          =						rng_state.to(xm.xla_device()      )
        xm.collective_broadcast([rng_state]      )
        xm.mark_step()
        __lowercase          =						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
    ):
        __lowercase          =						rng_state.to(state.device      )
        torch.distributed.broadcast(a__   ,0      )
        __lowercase          =						rng_state.cpu()
    elif state.distributed_type == DistributedType.MULTI_CPU:
        torch.distributed.broadcast(a__   ,0      )

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



def     snake_case_  (       a__		:     List[Union[str, RNGType]]   ,a__		:     Optional[torch.Generator] = None      ):



    """simple docstring"""




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




