gfortran 如何将 random_seed 增加 2^128

Question

gfortran page on random_seed 说当使用 OMP 线程时，每个线程将其种子递增 2^128。我想知道如何手动将种子增加 2^128。我写了一个小测试程序将主种子全部设置为 0，然后查看种子是什么，但我不明白我在看什么。我想知道的是我在子例程 increment_by_2_tothe_128

中放入的内容

program main
  implicit none

  character(len=32)    :: arg
  integer              :: n
  integer              :: i
  integer              :: nthreads
  integer, allocatable :: seed(:, :)
  integer, allocatable :: master_seed(:)
  real,    allocatable :: rn(:)

  call get_command_argument(1, arg)
  read(arg, *) nthreads

  call random_seed(size=n)
  allocate(seed(n, nthreads))
  allocate(master_seed(n))
  allocate(rn(nthreads))
  master_seed = 0
  seed = 0
  call random_seed(put=master_seed)

  ! call increment_by_2_tothe_128(n)

  call omp_set_num_threads(nthreads)

  !$OMP PARALLEL DO
  do i=1,nthreads
     call random_number(rn(i))
     call random_seed(get=seed(:,i))
  end do

  do i=1,nthreads
     print *, i
     print *, rn(i)
     print *, seed(:,i)
  end do

end program main


subroutine increment_by_2_tothe_128(n)
  implicit none
  integer, intent(in) :: n
  integer             :: current_seed(n)
  integer             :: increment_seed(n)
  call random_seed(get=current_seed)
  ! what goes here:
  ! incrememt_seed = current_seed + 2**128
  call random_seed(put=increment_seed)
end subroutine increment_by_2_tothe_128

Answer 1

您不能手动执行此操作。您需要访问随机数生成器才能执行此操作，但内部结构不会向 Fortran 程序员公开。而且你显然不能调用生成器 2^128 次。

如果您需要进行移位，您需要使用一些伪随机数生成器，它确实公开了内部结构和同时允许这种移位。例如，它可以是 gfortran 内部使用的 xoroshiro PRNG family。这些生成器具有针对此转换的专门功能：

All generators, being based on linear recurrences, provide jump functions that make it possible to simulate any number of calls to the next-state function in constant time, once a suitable jump polynomial has been computed. We provide ready-made jump functions for a number of calls equal to the square root of the period, to make it easy generating non-overlapping sequences for parallel computations, and equal to the cube of the fourth root of the period, to make it possible to generate independent sequences on different parallel processors.

这些生成器通常用 C 实现，但 Fortran 实现 also exist（subroutine rng_jump 是跳转函数，免责声明：link 转到我的存储库，不保证质量）。

gfortran 如何将 random_seed 增加 2^128

gfortran how do I increment random_seed by 2^128

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