如何使用 CUDA 生成随机排列

How to generate random permutations with CUDA(如何使用 CUDA 生成随机排列)

问题描述

我可以使用哪些并行算法从给定集合中生成随机排列?特别是适合 CUDA 的提案或论文链接会很有帮助.

What parallel algorithms could I use to generate random permutations from a given set? Especially proposals or links to papers suitable for CUDA would be helpful.

Fisher-Yates shuffle 的顺序版本.

A sequential version of this would be the Fisher-Yates shuffle.

例子:

令 S={1, 2, ..., 7} 为源索引集.目标是并行生成 n 个随机排列.n 个排列中的每一个都只包含每个源索引一次，例如{7, 6, ..., 1}.

Let S={1, 2, ..., 7} be the set of source indices. The goal is to generate n random permutations in parallel. Each of the n permutations contains each of the source indices exactly once, e.g. {7, 6, ..., 1}.

推荐答案

Fisher-Yates shuffle 可以并行化.例如，4 个并发工作人员只需要 3 次迭代即可对 8 个元素的向量进行混洗.在第一次迭代中，它们交换 0<->1, 2<->3, 4<->5, 6<->7;在第二次迭代 0<->2, 1<->3, 4<->5, 6<->7;并且在最后一次迭代 0<->4, 1<->5, 2<->6, 3<->7.

Fisher-Yates shuffle could be parallelized. For example, 4 concurrent workers need only 3 iterations to shuffle vector of 8 elements. On first iteration they swap 0<->1, 2<->3, 4<->5, 6<->7; on second iteration 0<->2, 1<->3, 4<->5, 6<->7; and on last iteration 0<->4, 1<->5, 2<->6, 3<->7.

这可以很容易地实现为 CUDA __device__ 代码(灵感来自标准 最小/最大减少):

This could be easily implemented as CUDA __device__ code (inspired by standard min/max reduction):

const int id  = threadIdx.x;
__shared__ int perm_shared[2 * BLOCK_SIZE];
perm_shared[2 * id]     = 2 * id;
perm_shared[2 * id + 1] = 2 * id + 1;
__syncthreads();

unsigned int shift = 1;
unsigned int pos = id * 2;  
while(shift <= BLOCK_SIZE)
{
    if (curand(&curand_state) & 1) swap(perm_shared, pos, pos + shift);
    shift = shift << 1;
    pos = (pos & ~shift) | ((pos & shift) >> 1);
    __syncthreads();
}

这里省略了curand初始化代码，方法swap(int *p, int i, int j)交换值p[i]和p[j].

Here the curand initialization code is omitted, and method swap(int *p, int i, int j) exchanges values p[i] and p[j].

请注意，上面的代码有以下假设:

Note that the code above has the following assumptions:

1. 排列的长度是 2 * BLOCK_SIZE，其中 BLOCK_SIZE 是 2 的幂.
2. 2 * BLOCK_SIZE 整数适合 __shared__ CUDA 设备的内存
3. BLOCK_SIZE 是 CUDA 块的有效大小(通常在 32 到 512 之间)

1. The length of permutation is 2 * BLOCK_SIZE, where BLOCK_SIZE is a power of 2.
2. 2 * BLOCK_SIZE integers fit into __shared__ memory of CUDA device
3. BLOCK_SIZE is a valid size of CUDA block (usually something between 32 and 512)

要生成多个排列，我建议使用不同的 CUDA 块.如果目标是排列 7 个元素(正如在原始问题中提到的那样)，那么我相信在单线程中完成它会更快.

To generate more than one permutation I would suggest to utilize different CUDA blocks. If the goal is to make permutation of 7 elements (as it was mentioned in the original question) then I believe it will be faster to do it in single thread.

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