Sample solution

#include <cmath>
#include <printf.hpp>
#include <hpc/cuda/check.hpp>
#include <hpc/cuda/copy.hpp>
#include <hpc/cuda/densevector.hpp>
#include <hpc/matvec/densevector.hpp>

constexpr std::size_t N = 8192;
constexpr std::size_t THREADS_PER_BLOCK 1024
constexpr std::size_t NUM_BLOCKS =
   (N + THREADS_PER_BLOCK - 1) / THREADS_PER_BLOCK;

template<typename TX, typename TY>
TX dot(std::size_t n, const TX* x, std::ptrdiff_t incX,
      TY* y, std::size_t incY) {
   TX res = 0;
   for (std::size_t index = 0; index < n; ++index) {
      res += x[index * incX] * y[index * incY];
   }
   return res;
}

template<typename T>
__global__ void asum(std::size_t n, const T* x, T* sums) {
   __shared__ double sums_per_block[THREADS_PER_BLOCK];
   std::size_t index = threadIdx.x + blockIdx.x * blockDim.x;
   std::size_t me = threadIdx.x;
   if (index < n) {
      sums_per_block[me] = x[index];
   } else {
      sums_per_block[me] = 0;
   }
   /* aggregate sum within a block */
   index = blockDim.x / 2;
   while (index) {
      __syncthreads();
      if (me < index) {
	 sums_per_block[me] += sums_per_block[me + index];
      }
      index /= 2;
   }
   if (me == 0) {
      sums[blockIdx.x] = sums_per_block[0];
   }
}

template<typename TX, typename TY, typename T>
__global__ void dot(std::size_t n,
      const TX* x, std::ptrdiff_t incX,
      TY* y, std::ptrdiff_t incY, T* sums) {
   std::size_t index = threadIdx.x + blockIdx.x * blockDim.x;

   T res;
   if (index < n) {
      res = x[index * incX] * y[index * incY];
   } else {
      res = 0;
   }

   __shared__ double sums_per_block[THREADS_PER_BLOCK];
   std::size_t me = threadIdx.x;
   sums_per_block[me] = res;

   /* aggregate sum within a block */
   std::size_t active = blockDim.x / 2;
   while (active > 0) {
      __syncthreads();
      if (me < active) {
	 sums_per_block[me] += sums_per_block[me + active];
      }
      active /= 2;
   }
   if (me == 0) {
      sums[blockIdx.x] = sums_per_block[0];
   }
}

int main() {
   using T = double;
   hpc::matvec::DenseVector<T> a(N);
   hpc::matvec::DenseVector<T> b(a.length());
   for (std::size_t i = 0; i < a.length(); ++i) {
      a(i) = i; b(i) = i * i;
   }

   /* transfer vectors to GPU memory */
   hpc::cuda::DeviceDenseVector<T> dev_a(a.length());
   hpc::cuda::DeviceDenseVector<T> dev_b(b.length());
   copy(a, dev_a); copy(b, dev_b);

   auto dev_sums = new hpc::cuda::DeviceDenseVector<T>(NUM_BLOCKS);

   /* execute kernel function on GPU */
   dot<<<NUM_BLOCKS, THREADS_PER_BLOCK>>>(dev_a.length(), dev_a.data(),
      dev_a.inc(), dev_b.data(), dev_b.inc(), dev_sums->data());
   std::size_t len = NUM_BLOCKS;
   while (len > 1) {
      std::size_t num_blocks = (len + THREADS_PER_BLOCK - 1) /
	 THREADS_PER_BLOCK;
      auto dev_sums2 = new hpc::cuda::DeviceDenseVector<T>(num_blocks);
      asum<<<num_blocks, THREADS_PER_BLOCK>>>(len,
	 dev_sums->data(), dev_sums2->data());
      delete dev_sums; dev_sums = dev_sums2;
      len = num_blocks;
   }

   /* transfer result vector from GPU to host memory */
   hpc::matvec::DenseVector<T> result(1);
   copy(*dev_sums, result); delete dev_sums;

   /* print difference to local result */
   auto local_sum = dot(a.length(), a.data(), a.inc(), b.data(), b.inc());
   fmt::printf("diff: %12.4lg\n", std::abs(result(0) - local_sum));
}