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    //
    // cudapic.cu
    // Neil Gershenfeld 7/14/20
    // calculation of pi by a CUDA sum with CPU reduction
    // pi = 3.14159265358979323846 
    //
    #include <iostream>
    #include <chrono>
    #include <cstdint>
    uint64_t blocks = 1024;
    uint64_t threads = 1024;
    uint64_t nloop = 1000000;
    uint64_t npts = blocks*threads;
    __global__ void init(double *arr,uint64_t nloop) {
       uint64_t i = blockIdx.x*blockDim.x+threadIdx.x;
       uint64_t start = nloop*i+1;
       uint64_t end = nloop*(i+1)+1;
       arr[i] = 0;
       for (uint64_t j = start; j < end; ++j)
          arr[i] += 0.5/((j-0.75)*(j-0.25));
       }
    int main(void) {
       double *arr,*darr;
       arr = new double[npts];
       cudaMalloc(&darr,npts*sizeof(double));
       auto tstart = std::chrono::high_resolution_clock::now();        
       init<<<blocks,threads>>>(darr,nloop);
       cudaDeviceSynchronize();
       cudaMemcpy(arr,darr,npts*sizeof(double),cudaMemcpyDeviceToHost);
    
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       double pi = 0;
    
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       for (int i = 0; i < npts; ++i)
          pi += arr[i];
       auto tend = std::chrono::high_resolution_clock::now();        
    	auto dt = std::chrono::duration_cast<std::chrono::microseconds>(tend-tstart).count();
       auto mflops = npts*nloop*5.0/dt;
       printf("npts = %ld, nloop = %ld, pi = %lf\n",npts,nloop,pi);
       printf("time = %f, estimated MFlops = %f\n",1e-6*dt,mflops);
       cudaFree(darr);
       return 0;
       }