xref: /petsc/src/benchmarks/streams/CUDAVersion.cu (revision beceaeb65c30291e7755356830621fe80888c102)

/*
  STREAM benchmark implementation in CUDA.

    COPY:       a(i) = b(i)
    SCALE:      a(i) = q*b(i)
    SUM:        a(i) = b(i) + c(i)
    TRIAD:      a(i) = b(i) + q*c(i)

  It measures the memory system on the device.
  The implementation is in double precision with a single option.

  Code based on the code developed by John D. McCalpin
  http://www.cs.virginia.edu/stream/FTP/Code/stream.c

  Written by: Massimiliano Fatica, NVIDIA Corporation
  Modified by: Douglas Enright (dpephd-nvidia@yahoo.com), 1 December 2010
  Extensive Revisions, 4 December 2010
  Modified for PETSc by: Matthew G. Knepley 14 Aug 2011

  User interface motivated by bandwidthTest NVIDIA SDK example.
*/
static char help[] = "Double-Precision STREAM Benchmark implementation in CUDA\n Performs Copy, Scale, Add, and Triad double-precision kernels\n\n";

#include <petscconf.h>
#include <petscsys.h>
#include <petsctime.h>
#include <petscdevice_cuda.h>

#define N      10000000
#define NTIMES 10

#if !defined(MIN)
  #define MIN(x, y) ((x) < (y) ? (x) : (y))
#endif
#if !defined(MAX)
  #define MAX(x, y) ((x) > (y) ? (x) : (y))
#endif

const float  flt_eps = 1.192092896e-07f;
const double dbl_eps = 2.2204460492503131e-16;

__global__ void set_array(float *a, float value, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    a[idx] = value;
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void set_array_double(double *a, double value, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    a[idx] = value;
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Copy(float *a, float *b, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    b[idx] = a[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Copy_double(double *a, double *b, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    b[idx] = a[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Copy_Optimized(float *a, float *b, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) b[idx] = a[idx];
}

__global__ void STREAM_Copy_Optimized_double(double *a, double *b, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) b[idx] = a[idx];
}

__global__ void STREAM_Scale(float *a, float *b, float scale, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    b[idx] = scale * a[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Scale_double(double *a, double *b, double scale, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    b[idx] = scale * a[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Scale_Optimized(float *a, float *b, float scale, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) b[idx] = scale * a[idx];
}

__global__ void STREAM_Scale_Optimized_double(double *a, double *b, double scale, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) b[idx] = scale * a[idx];
}

__global__ void STREAM_Add(float *a, float *b, float *c, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    c[idx] = a[idx] + b[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Add_double(double *a, double *b, double *c, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    c[idx] = a[idx] + b[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Add_Optimized(float *a, float *b, float *c, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) c[idx] = a[idx] + b[idx];
}

__global__ void STREAM_Add_Optimized_double(double *a, double *b, double *c, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) c[idx] = a[idx] + b[idx];
}

__global__ void STREAM_Triad(float *a, float *b, float *c, float scalar, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    c[idx] = a[idx] + scalar * b[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Triad_double(double *a, double *b, double *c, double scalar, size_t len)
{
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  while (idx < len) {
    c[idx] = a[idx] + scalar * b[idx];
    idx += blockDim.x * gridDim.x;
  }
}

__global__ void STREAM_Triad_Optimized(float *a, float *b, float *c, float scalar, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) c[idx] = a[idx] + scalar * b[idx];
}

__global__ void STREAM_Triad_Optimized_double(double *a, double *b, double *c, double scalar, size_t len)
{
  /*
   * Ensure size of thread index space is as large as or greater than
   * vector index space else return.
   */
  if (blockDim.x * gridDim.x < len) return;
  size_t idx = threadIdx.x + blockIdx.x * blockDim.x;
  if (idx < len) c[idx] = a[idx] + scalar * b[idx];
}

/* Host side verification routines */
bool STREAM_Copy_verify(float *a, float *b, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    float expectedResult     = a[idx];
    float diffResultExpected = (b[idx] - expectedResult);
    float relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.f);
  }

  return bDifferent;
}

bool STREAM_Copy_verify_double(double *a, double *b, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    double expectedResult     = a[idx];
    double diffResultExpected = (b[idx] - expectedResult);
    double relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / dbl_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.);
  }

  return bDifferent;
}

bool STREAM_Scale_verify(float *a, float *b, float scale, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    float expectedResult     = scale * a[idx];
    float diffResultExpected = (b[idx] - expectedResult);
    float relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.f);
  }

  return bDifferent;
}

bool STREAM_Scale_verify_double(double *a, double *b, double scale, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    double expectedResult     = scale * a[idx];
    double diffResultExpected = (b[idx] - expectedResult);
    double relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.);
  }

  return bDifferent;
}

bool STREAM_Add_verify(float *a, float *b, float *c, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    float expectedResult     = a[idx] + b[idx];
    float diffResultExpected = (c[idx] - expectedResult);
    float relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.f);
  }

  return bDifferent;
}

bool STREAM_Add_verify_double(double *a, double *b, double *c, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    double expectedResult     = a[idx] + b[idx];
    double diffResultExpected = (c[idx] - expectedResult);
    double relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 2.);
  }

  return bDifferent;
}

bool STREAM_Triad_verify(float *a, float *b, float *c, float scalar, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    float expectedResult     = a[idx] + scalar * b[idx];
    float diffResultExpected = (c[idx] - expectedResult);
    float relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 3.f);
  }

  return bDifferent;
}

bool STREAM_Triad_verify_double(double *a, double *b, double *c, double scalar, size_t len)
{
  size_t idx;
  bool   bDifferent = false;

  for (idx = 0; idx < len && !bDifferent; idx++) {
    double expectedResult     = a[idx] + scalar * b[idx];
    double diffResultExpected = (c[idx] - expectedResult);
    double relErrorULPS       = (fabsf(diffResultExpected) / fabsf(expectedResult)) / flt_eps;
    /* element-wise relative error determination */
    bDifferent = (relErrorULPS > 3.);
  }

  return bDifferent;
}

/* forward declarations */
PetscErrorCode setupStream(PetscInt device, PetscBool runDouble, PetscBool cpuTiming);
PetscErrorCode runStream(const PetscInt iNumThreadsPerBlock, PetscBool bDontUseGPUTiming);
PetscErrorCode runStreamDouble(const PetscInt iNumThreadsPerBlock, PetscBool bDontUseGPUTiming);
PetscErrorCode printResultsReadable(float times[][NTIMES], size_t);

int main(int argc, char *argv[])
{
  PetscInt        device    = 0;
  PetscBool       runDouble = PETSC_TRUE;
  const PetscBool cpuTiming = PETSC_TRUE; // must be true
  PetscErrorCode  ierr;

  PetscCallCUDA(cudaSetDeviceFlags(cudaDeviceBlockingSync));

  PetscCall(PetscInitialize(&argc, &argv, 0, help));

  PetscOptionsBegin(PETSC_COMM_WORLD, "", "STREAM Benchmark Options", "STREAM");
  PetscCall(PetscOptionsBoundedInt("-device", "Specify the CUDA device to be used", "STREAM", device, &device, NULL, 0));
  PetscCall(PetscOptionsBool("-double", "Also run double precision tests", "STREAM", runDouble, &runDouble, NULL));
  PetscOptionsEnd();

  ierr = setupStream(device, runDouble, cpuTiming);
  if (ierr) PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n[streamBenchmark] - results:\t%s\n\n", (ierr == 0) ? "PASSES" : "FAILED"));
  PetscCall(PetscFinalize());
  return 0;
}

///////////////////////////////////////////////////////////////////////////////
//Run the appropriate tests
///////////////////////////////////////////////////////////////////////////////
PetscErrorCode setupStream(PetscInt deviceNum, PetscBool runDouble, PetscBool cpuTiming)
{
  PetscInt iNumThreadsPerBlock = 128;

  PetscFunctionBegin;
  // Check device
  {
    int deviceCount;

    cudaGetDeviceCount(&deviceCount);
    if (deviceCount == 0) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, "!!!!!No devices found!!!!!\n"));
      return -1000;
    }

    if (deviceNum >= deviceCount || deviceNum < 0) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n!!!!!Invalid GPU number %d given hence default gpu %d will be used !!!!!\n", deviceNum, 0));
      deviceNum = 0;
    }
  }

  cudaSetDevice(deviceNum);
  // PetscCall(PetscPrintf(PETSC_COMM_SELF, "Running on...\n\n"));
  cudaDeviceProp deviceProp;
  if (cudaGetDeviceProperties(&deviceProp, deviceNum) != cudaSuccess) {
    PetscCall(PetscPrintf(PETSC_COMM_SELF, " Unable to determine device %d properties, exiting\n"));
    return -1;
  }

  if (runDouble && deviceProp.major == 1 && deviceProp.minor < 3) {
    PetscCall(PetscPrintf(PETSC_COMM_SELF, " Unable to run double-precision STREAM benchmark on a compute capability GPU less than 1.3\n"));
    return -1;
  }
  if (deviceProp.major == 2 && deviceProp.minor == 1) iNumThreadsPerBlock = 192; /* GF104 architecture / 48 CUDA Cores per MP */
  else iNumThreadsPerBlock = 128;                                                /* GF100 architecture / 32 CUDA Cores per MP */

  if (runDouble) PetscCall(runStreamDouble(iNumThreadsPerBlock, cpuTiming));
  else PetscCall(runStream(iNumThreadsPerBlock, cpuTiming));
  PetscFunctionReturn(PETSC_SUCCESS);
}

///////////////////////////////////////////////////////////////////////////
// runStream
///////////////////////////////////////////////////////////////////////////
PetscErrorCode runStream(const PetscInt iNumThreadsPerBlock, PetscBool bDontUseGPUTiming)
{
  float *d_a, *d_b, *d_c;
  int    k;
  float  times[8][NTIMES];
  float  scalar;

  PetscFunctionBegin;
  /* Allocate memory on device */
  PetscCallCUDA(cudaMalloc((void **)&d_a, sizeof(float) * N));
  PetscCallCUDA(cudaMalloc((void **)&d_b, sizeof(float) * N));
  PetscCallCUDA(cudaMalloc((void **)&d_c, sizeof(float) * N));

  /* Compute execution configuration */

  dim3 dimBlock(iNumThreadsPerBlock); /* (iNumThreadsPerBlock,1,1) */
  dim3 dimGrid(N / dimBlock.x);       /* (N/dimBlock.x,1,1) */
  if (N % dimBlock.x != 0) dimGrid.x += 1;

  /* Initialize memory on the device */
  set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
  set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
  set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

  /* --- MAIN LOOP --- repeat test cases NTIMES times --- */
  PetscLogDouble cpuTimer = 0.0;

  scalar = 3.0f;
  for (k = 0; k < NTIMES; ++k) {
    PetscTimeSubtract(&cpuTimer);
    STREAM_Copy<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[0][k] = cpuTimer * 1.e3; // millisec

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Copy_Optimized<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[1][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Scale<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[2][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Scale_Optimized<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[3][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    // PetscCallCUDA(cudaEventRecord(start, 0));
    STREAM_Add<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    PetscCallCUDA(cudaEventRecord(stop, 0));
    // PetscCallCUDA(cudaEventSynchronize(stop));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[4][k] = cpuTimer * 1.e3;
    else {
      // PetscCallCUDA(cudaEventElapsedTime(&times[4][k], start, stop));
    }

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Add_Optimized<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[5][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Triad<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[6][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Triad_Optimized<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[7][k] = cpuTimer * 1.e3;
  }

  if (1) { /* verify kernels */
    float *h_a, *h_b, *h_c;
    bool   errorSTREAMkernel = true;

    if ((h_a = (float *)calloc(N, sizeof(float))) == (float *)NULL) {
      printf("Unable to allocate array h_a, exiting ...\n");
      exit(1);
    }
    if ((h_b = (float *)calloc(N, sizeof(float))) == (float *)NULL) {
      printf("Unable to allocate array h_b, exiting ...\n");
      exit(1);
    }

    if ((h_c = (float *)calloc(N, sizeof(float))) == (float *)NULL) {
      printf("Unalbe to allocate array h_c, exiting ...\n");
      exit(1);
    }

    /*
   * perform kernel, copy device memory into host memory and verify each
   * device kernel output
   */

    /* Initialize memory on the device */
    set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
    set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
    set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

    STREAM_Copy<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(float) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Copy_verify(h_a, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Copy:\t\tError detected in device STREAM_Copy, exiting\n"));
      exit(-2000);
    }

    /* Initialize memory on the device */
    set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
    set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
    set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

    STREAM_Copy_Optimized<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(float) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Copy_verify(h_a, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Copy_Optimized:\tError detected in device STREAM_Copy_Optimized, exiting\n"));
      exit(-3000);
    }

    /* Initialize memory on the device */
    set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
    set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
    set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

    STREAM_Scale<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(float) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Scale_verify(h_b, h_c, scalar, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Scale:\t\tError detected in device STREAM_Scale, exiting\n"));
      exit(-4000);
    }

    /* Initialize memory on the device */
    set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
    set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
    set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

    STREAM_Add<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(float) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Add_verify(h_a, h_b, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Add:\t\tError detected in device STREAM_Add, exiting\n"));
      exit(-5000);
    }

    /* Initialize memory on the device */
    set_array<<<dimGrid, dimBlock>>>(d_a, 2.f, N);
    set_array<<<dimGrid, dimBlock>>>(d_b, .5f, N);
    set_array<<<dimGrid, dimBlock>>>(d_c, .5f, N);

    STREAM_Triad<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(float) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(float) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Triad_verify(h_b, h_c, h_a, scalar, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Triad:\t\tError detected in device STREAM_Triad, exiting\n"));
      exit(-6000);
    }

    free(h_a);
    free(h_b);
    free(h_c);
  }
  /* continue from here */
  printResultsReadable(times, sizeof(float));

  /* Free memory on device */
  PetscCallCUDA(cudaFree(d_a));
  PetscCallCUDA(cudaFree(d_b));
  PetscCallCUDA(cudaFree(d_c));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode runStreamDouble(const PetscInt iNumThreadsPerBlock, PetscBool bDontUseGPUTiming)
{
  double *d_a, *d_b, *d_c;
  int     k;
  float   times[8][NTIMES];
  double  scalar;

  PetscFunctionBegin;
  /* Allocate memory on device */
  PetscCallCUDA(cudaMalloc((void **)&d_a, sizeof(double) * N));
  PetscCallCUDA(cudaMalloc((void **)&d_b, sizeof(double) * N));
  PetscCallCUDA(cudaMalloc((void **)&d_c, sizeof(double) * N));

  /* Compute execution configuration */

  dim3 dimBlock(iNumThreadsPerBlock); /* (iNumThreadsPerBlock,1,1) */
  dim3 dimGrid(N / dimBlock.x);       /* (N/dimBlock.x,1,1) */
  if (N % dimBlock.x != 0) dimGrid.x += 1;

  /* Initialize memory on the device */
  set_array_double<<<dimGrid, dimBlock>>>(d_a, 2., N);
  set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
  set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

  /* --- MAIN LOOP --- repeat test cases NTIMES times --- */
  PetscLogDouble cpuTimer = 0.0;

  scalar = 3.0;
  for (k = 0; k < NTIMES; ++k) {
    PetscTimeSubtract(&cpuTimer);
    STREAM_Copy_double<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    if (bDontUseGPUTiming) {
      PetscTimeAdd(&cpuTimer);
      times[0][k] = cpuTimer * 1.e3;
    }

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Copy_Optimized_double<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    if (bDontUseGPUTiming) {
      PetscTimeAdd(&cpuTimer);
      times[1][k] = cpuTimer * 1.e3;
    }

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Scale_double<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[2][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Scale_Optimized_double<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[3][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Add_double<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[4][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Add_Optimized_double<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[5][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Triad_double<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[6][k] = cpuTimer * 1.e3;

    cpuTimer = 0.0;
    PetscTimeSubtract(&cpuTimer);
    STREAM_Triad_Optimized_double<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    cudaStreamSynchronize(NULL);
    PetscCallMPI(MPI_Barrier(MPI_COMM_WORLD));
    //get the total elapsed time in ms
    PetscTimeAdd(&cpuTimer);
    if (bDontUseGPUTiming) times[7][k] = cpuTimer * 1.e3;
  }

  if (1) { /* verify kernels */
    double *h_a, *h_b, *h_c;
    bool    errorSTREAMkernel = true;

    if ((h_a = (double *)calloc(N, sizeof(double))) == (double *)NULL) {
      printf("Unable to allocate array h_a, exiting ...\n");
      exit(1);
    }
    if ((h_b = (double *)calloc(N, sizeof(double))) == (double *)NULL) {
      printf("Unable to allocate array h_b, exiting ...\n");
      exit(1);
    }

    if ((h_c = (double *)calloc(N, sizeof(double))) == (double *)NULL) {
      printf("Unalbe to allocate array h_c, exiting ...\n");
      exit(1);
    }

    /*
   * perform kernel, copy device memory into host memory and verify each
   * device kernel output
   */

    /* Initialize memory on the device */
    set_array_double<<<dimGrid, dimBlock>>>(d_a, 2., N);
    set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
    set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

    STREAM_Copy_double<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(double) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Copy_verify_double(h_a, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Copy:\t\tError detected in device STREAM_Copy, exiting\n"));
      exit(-2000);
    }

    /* Initialize memory on the device */
    set_array_double<<<dimGrid, dimBlock>>>(d_a, 2., N);
    set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
    set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

    STREAM_Copy_Optimized_double<<<dimGrid, dimBlock>>>(d_a, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(double) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Copy_verify_double(h_a, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Copy_Optimized:\tError detected in device STREAM_Copy_Optimized, exiting\n"));
      exit(-3000);
    }

    /* Initialize memory on the device */
    set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
    set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

    STREAM_Scale_double<<<dimGrid, dimBlock>>>(d_b, d_c, scalar, N);
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(double) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Scale_verify_double(h_b, h_c, scalar, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Scale:\t\tError detected in device STREAM_Scale, exiting\n"));
      exit(-4000);
    }

    /* Initialize memory on the device */
    set_array_double<<<dimGrid, dimBlock>>>(d_a, 2., N);
    set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
    set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

    STREAM_Add_double<<<dimGrid, dimBlock>>>(d_a, d_b, d_c, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(double) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Add_verify_double(h_a, h_b, h_c, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Add:\t\tError detected in device STREAM_Add, exiting\n"));
      exit(-5000);
    }

    /* Initialize memory on the device */
    set_array_double<<<dimGrid, dimBlock>>>(d_a, 2., N);
    set_array_double<<<dimGrid, dimBlock>>>(d_b, .5, N);
    set_array_double<<<dimGrid, dimBlock>>>(d_c, .5, N);

    STREAM_Triad_double<<<dimGrid, dimBlock>>>(d_b, d_c, d_a, scalar, N);
    PetscCallCUDA(cudaMemcpy(h_a, d_a, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_b, d_b, sizeof(double) * N, cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(h_c, d_c, sizeof(double) * N, cudaMemcpyDeviceToHost));
    errorSTREAMkernel = STREAM_Triad_verify_double(h_b, h_c, h_a, scalar, N);
    if (errorSTREAMkernel) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, " device STREAM_Triad:\t\tError detected in device STREAM_Triad, exiting\n"));
      exit(-6000);
    }

    free(h_a);
    free(h_b);
    free(h_c);
  }
  /* continue from here */
  printResultsReadable(times, sizeof(double));

  /* Free memory on device */
  PetscCallCUDA(cudaFree(d_a));
  PetscCallCUDA(cudaFree(d_b));
  PetscCallCUDA(cudaFree(d_c));
  PetscFunctionReturn(PETSC_SUCCESS);
}

///////////////////////////////////////////////////////////////////////////
//Print Results to Screen and File
///////////////////////////////////////////////////////////////////////////
PetscErrorCode printResultsReadable(float times[][NTIMES], const size_t bsize)
{
  PetscErrorCode ierr;
  PetscInt       j, k;
  float          avgtime[8] = {0., 0., 0., 0., 0., 0., 0., 0.};
  float          maxtime[8] = {0., 0., 0., 0., 0., 0., 0., 0.};
  float          mintime[8] = {1e30, 1e30, 1e30, 1e30, 1e30, 1e30, 1e30, 1e30};
  // char           *label[8]           = {"Copy:      ", "Copy Opt.: ", "Scale:     ", "Scale Opt: ", "Add:       ", "Add Opt:   ", "Triad:     ", "Triad Opt: "};
  const float bytes_per_kernel[8] = {2. * bsize * N, 2. * bsize * N, 2. * bsize * N, 2. * bsize * N, 3. * bsize * N, 3. * bsize * N, 3. * bsize * N, 3. * bsize * N};
  double      rate, irate;
  int         rank, size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(MPI_COMM_WORLD, &rank));
  PetscCallMPI(MPI_Comm_size(MPI_COMM_WORLD, &size));
  /* --- SUMMARY --- */
  for (k = 0; k < NTIMES; ++k) {
    for (j = 0; j < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(avgtime); ++j) {
      avgtime[j] = avgtime[j] + (1.e-03f * times[j][k]); // millisec --> sec
      mintime[j] = MIN(mintime[j], (1.e-03f * times[j][k]));
      maxtime[j] = MAX(maxtime[j], (1.e-03f * times[j][k]));
    }
  }
  for (j = 0; j < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(avgtime); ++j) avgtime[j] = avgtime[j] / (float)(NTIMES - 1);
  j     = 7;
  irate = 1.0E-06 * bytes_per_kernel[j] / mintime[j];
  ierr  = MPI_Reduce(&irate, &rate, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
  if (rank == 0) {
    FILE *fd;
    if (size == 1) {
      printf("%d %11.4f   Rate (MB/s)\n", size, rate);
      fd = fopen("flops", "w");
      fprintf(fd, "%g\n", rate);
      fclose(fd);
    } else {
      double prate;
      fd = fopen("flops", "r");
      fscanf(fd, "%lg", &prate);
      fclose(fd);
      printf("%d %11.4f   Rate (MB/s) %g\n", size, rate, rate / prate);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}