Parallel implementation of the computation of the sum of contiguous subsequences in an array using Cuda

Question

lets consider the following array: tab = [80,12,14,5,70,9,26,30,8,12,16,15] I want to compute the sum of all possible sequences of size 4 using cuda : for example :

S1=80+12+14+5=111
S2=12+14+5+70 =101
S3=14+5+70+9 =98
....

You have an efficient idea to parallise this task using Cuda. the previous table is just an example in my case i will use huge one.

Answer 1

We can do this in a single operation (thrust::transform) using thrust. In CUDA, this can be considered to be a fairly simple 1-D stencil operation.

A good description of a 1-D stencil operation can be found here on slides 49-58.

This is actually a simplified case, since the stencil width is 4 and it is only on one "side" of the center point.

Here's a worked example comparing the 2 approaches:

$ cat t88.cu
#include <thrust/device_vector.h>
#include <thrust/transform.h>
#include <thrust/iterator/zip_iterator.h>
#include <thrust/copy.h>
#include <iostream>

const int nTPB=256;
typedef float mytype;
const int ds = 1048576*32;

struct sum4
{
  template <typename T>
  __host__ __device__
  mytype operator()(const T t){
    return thrust::get<0>(t) + thrust::get<1>(t) + thrust::get<2>(t) + thrust::get<3>(t);
  }
};

template <typename T>
__global__ void sum4kernel(const T * __restrict__ in, T * __restrict__ out, const unsigned dsize)
{

  __shared__ T sdata[nTPB+3];
  unsigned idx = threadIdx.x+blockDim.x*blockIdx.x;
  if (idx < dsize) sdata[threadIdx.x] = in[idx];
  if ((threadIdx.x < 3) && ((idx+blockDim.x) < dsize)) sdata[threadIdx.x + blockDim.x] = in[idx + blockDim.x];
  __syncthreads();
  T temp = sdata[threadIdx.x];
  temp += sdata[threadIdx.x+1];
  temp += sdata[threadIdx.x+2];
  temp += sdata[threadIdx.x+3];
  if (idx < dsize - 4) out[idx] = temp;
}

int main(){

  mytype hdata1[] = {80,12,14,5,70,9,26,30,8,12,16,15};
  unsigned ds1 = sizeof(hdata1)/sizeof(hdata1[0]);
  mytype hres1[ds1-4];
  thrust::device_vector<mytype> ddata1(hdata1, hdata1+ds1);
  thrust::device_vector<mytype> dres1(ds1-4);
  thrust::transform(thrust::make_zip_iterator(thrust::make_tuple(ddata1.begin(), ddata1.begin()+1, ddata1.begin()+2, ddata1.begin()+3)), thrust::make_zip_iterator(thrust::make_tuple(ddata1.end()-3, ddata1.end()-2, ddata1.end()-1, ddata1.end())), dres1.begin(), sum4());
  thrust::copy(dres1.begin(), dres1.end(), std::ostream_iterator<mytype>(std::cout, ","));
  std::cout << std::endl;
  sum4kernel<<<(ds1+nTPB-1)/nTPB, nTPB>>>(thrust::raw_pointer_cast(ddata1.data()), thrust::raw_pointer_cast(dres1.data()), ds1);
  cudaMemcpy(hres1, thrust::raw_pointer_cast(dres1.data()), (ds1-4)*sizeof(mytype), cudaMemcpyDeviceToHost);
  for (int i = 0; i < ds1-4; i++)
    std::cout << hres1[i] << ",";
  std::cout << std::endl;

  thrust::device_vector<mytype> ddata2(ds, 1);
  thrust::device_vector<mytype> dres2(ds-4);

  cudaEvent_t start, stop;
  cudaEventCreate(&start); cudaEventCreate(&stop);

  cudaEventRecord(start);
  thrust::transform(thrust::make_zip_iterator(thrust::make_tuple(ddata2.begin(), ddata2.begin()+1, ddata2.begin()+2, ddata2.begin()+3)), thrust::make_zip_iterator(thrust::make_tuple(ddata2.end()-3, ddata2.end()-2, ddata2.end()-1, ddata2.end())), dres2.begin(), sum4());
  cudaEventRecord(stop);
  thrust::host_vector<mytype> hres2 = dres2;
  float et;
  cudaEventElapsedTime(&et, start, stop);
  std::cout << "thrust time: " << et << "ms" << std::endl;
// validate
  for (int i = 0; i < ds-4; i++) if (hres2[i] != 4) {std::cout << "thrust validation failure: " << i << "," << hres2[i] << std::endl; return 1;}
  cudaEventRecord(start);
  sum4kernel<<<(ds+nTPB-1)/nTPB, nTPB>>>(thrust::raw_pointer_cast(ddata2.data()), thrust::raw_pointer_cast(dres2.data()), ds);
  cudaEventRecord(stop);
  cudaMemcpy(&(hres2[0]), thrust::raw_pointer_cast(dres2.data()), (ds-4)*sizeof(mytype), cudaMemcpyDeviceToHost);
  cudaEventElapsedTime(&et, start, stop);
  std::cout << "cuda time: " << et << "ms" << std::endl;
  for (int i = 0; i < ds-4; i++) if (hres2[i] != 4) {std::cout << "cuda validation failure: " << i << "," << hres2[i] << std::endl; return 1;}
}


$ nvcc -arch=sm_61 -o t88 t88.cu
$ ./t88
111,101,98,110,135,73,76,66,
111,101,98,110,135,73,76,66,
thrust time: 0.902464ms
cuda time: 0.76288ms
$

For this particular GPU (Titan X Pascal) there is not much difference (~15%) between the thrust time for a 32M element data set and the CUDA time. We would expect this algorithm to be memory-bound.

For this pascal titan x, bandwidthTest reports about 345 GB/s of measureable memory bandwidth.

The CUDA implementation must load the entire data set size and store the entire data set size (approximately) = 2 operations per element, so the achieved bandwidth calculation for this CUDA code is:

(32*1048576 elements * 2 ops/element * 4 bytes/op) / 0.00076288 s = ~350GB/s

So it would appear that the CUDA implementation is achieving approximately the maximum available bandwidth.