Generate Cartesian Product using more than two lists on GPU

Question

I would like to know how to generate a Cartesian product of more than two lists using CUDA.

How do I make this code work with three or more lists?

It works with two lists but not with three, I tried /, % without success.

Its basic.

#include <thrust/device_vector.h>
    #include <thrust/pair.h>
    #include <thrust/copy.h>
    #include <iterator>
    
    __global__ void cartesian_product(const int *a, size_t a_size,
                                      const int *b, size_t b_size,
                                      const int *c, size_t c_size)
    {
      unsigned int idx = blockIdx.x * blockDim.x + threadIdx.x;
    
      if(idx < a_size * b_size * c_size) 
      {
        unsigned int a_idx = idx / a_size;
        unsigned int b_idx = idx % a_size;
        
        // ? 
        unsigned int c_idx = idx % a_size;
    
    
        
        printf("a[a_idx] and b[b_idx] and c[c_idx] are: %d %d %d\n\n",a[a_idx], b[b_idx], c[c_idx]);
        //1 3 5 , 1 3 6 , 1 4 5 , 1 4 6 , 2 3 5 , 2 3 6 , 2 4 5 , 2 4 6  
        //0 0 0 , 0 0 1 , 0 1 0 , 0 1 1 , 1 0 0 , 1 0 1 , 1 1 0 , 1 1 1
      }
    }
    
    int main()
    {
      
      
      // host_vector is stored in host memory while device_vector livesin GPU device memory.
      // a has storage for 2 integers
      thrust::device_vector<int> a(2);
      
      // initialize individual elements
      a[0] = 1; 
      a[1] = 2; 
     
    
      // b has storage for 2 integers
      thrust::device_vector<int> b(2);
      
      // initialize individual elements
      b[0] = 3; 
      b[1] = 4; 
     
    
       // d has storage for 2 integers
      thrust::device_vector<int> c(2);
      
      // initialize individual elements
      c[0] = 5; 
      c[1] = 6;
      
       
      unsigned int block_size = 256;
      unsigned int num_blocks = (8 + (block_size - 1)) / block_size;
    
    
      // raw_pointer_cast creates a "raw" pointer from a pointer-like type, simply returning the wrapped pointer, should it exist.
      cartesian_product<<<num_blocks, block_size>>>(thrust::raw_pointer_cast(a.data()), a.size(),
                                                    thrust::raw_pointer_cast(b.data()), b.size(),
                                                    thrust::raw_pointer_cast(c.data()), c.size());

      
      
      return 0;
    }

How do I get the right c_idx in the kernel and subsequent arrays if I want more than three lists?

Answer 1

It seems to me that you want "lexic indexing":

idx == (a_idx * b_size + b_idx) * c_size + c_idx

So you get your indices like this:

c_idx = idx % c_size;
b_idx = (idx / c_size) % b_size;
a_idx = (idx / c_size) / b_size;

This is easily generalizable to more dimensions. E.g. in four dimensions you have

idx == ((a_idx * b_size + b_idx) * c_size + c_idx) * d_size + d_idx

Then:

d_idx = idx % d_size;
c_idx = (idx / d_size) % c_size;
b_idx = ((idx / d_size) / c_size) % b_size;
a_idx = ((idx / d_size) / c_size) / b_size;

In C/C++ programming one likes to use this to calculate indices into an one-dimensional dynamic array representing a multidimensional dataset. In CUDA you normally don't need it as much, as CUDA gives you up to three-dimensional threadIdx/blockIdx/etc.. So for the Cartesian product of three arrays, you won't need this technique, but could just use the intrinsic CUDA features. Even in more than three the most performant solution will get two indices from two of the three dimensions of the kernel and use lexic indexing on the third one:

__global__ void cartesian_product_5d(const int *a, size_t a_size,
                                  const int *b, size_t b_size,
                                  const int *c, size_t c_size,
                                  const int *d, size_t d_size,
                                  const int *e, size_t e_size)
{
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    int d_idx = blockIdx.y * blockDim.y + threadIdx.y;
    int e_idx = blockIdx.z * blockDim.z + threadIdx.z;
    /* idx == (c_idx * b_size + b_idx) * a_size + a_idx */
    int a_idx = idx % a_size;
    int b_idx = (idx / a_size) % b_size;
    int c_idx = (idx / a_size) / b_size;

    /* ... */
}
 
int main()
{
    /* ... */
    dim3 threadsPerBlock(8, 8, 8);
    dim3 numBlocks((a_size + b_size + c_size + threadsPerBlock.x - 1) /
                   threadsPerBlock.x,
                   (d_size + threadsPerBlock.y - 1) / threadsPerBlock.y,
                   (e_size + threadsPerBlock.z - 1) / threadsPerBlock.z);
    cartesian_product_5d<<<numBlocks, threadsPerBlock>>>(/* ... */);
    /* ... */
}