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 *    notice, this list of conditions and the following disclaimer in the
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 *  * Neither the name of NVIDIA CORPORATION nor the names of its
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
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/**
 * Matrix multiplication: C = A * B.
 * Host code.
 *
 * This sample implements matrix multiplication which makes use of shared memory
 * to ensure data reuse, the matrix multiplication is done using tiling approach.
 * It has been written for clarity of exposition to illustrate various CUDA programming
 * principles, not with the goal of providing the most performant generic kernel for matrix multiplication.
 * See also:
 * V. Volkov and J. Demmel, "Benchmarking GPUs to tune dense linear algebra,"
 * in Proc. 2008 ACM/IEEE Conf. on Supercomputing (SC '08),
 * Piscataway, NJ: IEEE Press, 2008, pp. Art. 31:1-11.
 */

// System includes
#include <stdio.h>
#include <assert.h>

// CUDA runtime
#include <cuda_runtime.h>

// Helper functions and utilities to work with CUDA
#include <helper_functions.h>
#include <helper_cuda.h>

/**
 * Matrix multiplication (CUDA Kernel) on the device: C = A * B
 * wA is A's width and wB is B's width
 */
template <int BLOCK_SIZE> __global__ void MatrixMulCUDA(float *C, float *A,
    float *B, int wA,
    int wB) {
  // Block index
  int bx = blockIdx.x;
  int by = blockIdx.y;

  // Thread index
  int tx = threadIdx.x;
  int ty = threadIdx.y;

  // Index of the first sub-matrix of A processed by the block
  int aBegin = wA * BLOCK_SIZE * by;

  // Index of the last sub-matrix of A processed by the block
  int aEnd   = aBegin + wA - 1;

  // Step size used to iterate through the sub-matrices of A
  int aStep  = BLOCK_SIZE;

  // Index of the first sub-matrix of B processed by the block
  int bBegin = BLOCK_SIZE * bx;

  // Step size used to iterate through the sub-matrices of B
  int bStep  = BLOCK_SIZE * wB;

  // Csub is used to store the element of the block sub-matrix
  // that is computed by the thread
  float Csub = 0;

  // Loop over all the sub-matrices of A and B
  // required to compute the block sub-matrix
  for (int a = aBegin, b = bBegin;
       a <= aEnd;
       a += aStep, b += bStep) {
    // Declaration of the shared memory array As used to
    // store the sub-matrix of A
    __shared__ float As[BLOCK_SIZE][BLOCK_SIZE];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B
    __shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];

    // Load the matrices from device memory
    // to shared memory; each thread loads
    // one element of each matrix
    As[ty][tx] = A[a + wA * ty + tx];
    Bs[ty][tx] = B[b + wB * ty + tx];

    // Synchronize to make sure the matrices are loaded
    __syncthreads();

    // Multiply the two matrices together;
    // each thread computes one element
    // of the block sub-matrix
#pragma unroll

    for (int k = 0; k < BLOCK_SIZE; ++k) {
      Csub += As[ty][k] * Bs[k][tx];
    }

    // Synchronize to make sure that the preceding
    // computation is done before loading two new
    // sub-matrices of A and B in the next iteration
    __syncthreads();
  }

  // Write the block sub-matrix to device memory;
  // each thread writes one element
  int c = wB * BLOCK_SIZE * by + BLOCK_SIZE * bx;
  C[c + wB * ty + tx] = Csub;
}

void ConstantInit(float *data, int size, float val) {
  for (int i = 0; i < size; ++i) {
    data[i] = val;
  }
}

/**
 * Run a simple test of matrix multiplication using CUDA
 */
int MatrixMultiply(int argc, char **argv,
                   int block_size, const dim3 &dimsA,
                   const dim3 &dimsB) {
  // Allocate host memory for matrices A and B
  unsigned int size_A = dimsA.x * dimsA.y;
  unsigned int mem_size_A = sizeof(float) * size_A;
  float *h_A = reinterpret_cast<float *>(malloc(mem_size_A));
  unsigned int size_B = dimsB.x * dimsB.y;
  unsigned int mem_size_B = sizeof(float) * size_B;
  float *h_B = reinterpret_cast<float *>(malloc(mem_size_B));

  // Initialize host memory
  const float valB = 0.01f;
  ConstantInit(h_A, size_A, 1.0f);
  ConstantInit(h_B, size_B, valB);

  // Allocate device memory
  float *d_A, *d_B, *d_C;

  // Allocate host matrix C
  dim3 dimsC(dimsB.x, dimsA.y, 1);
  unsigned int mem_size_C = dimsC.x * dimsC.y * sizeof(float);
  float *h_C = reinterpret_cast<float *>(malloc(mem_size_C));

  if (h_C == NULL) {
    fprintf(stderr, "Failed to allocate host matrix C!\n");
    exit(EXIT_FAILURE);
  }

  checkCudaErrors(cudaMalloc(reinterpret_cast<void **>(&d_A), mem_size_A));

  checkCudaErrors(cudaMalloc(reinterpret_cast<void **>(&d_B), mem_size_B));

  checkCudaErrors(cudaMalloc(reinterpret_cast<void **>(&d_C), mem_size_C));

  // copy host memory to device
  checkCudaErrors(cudaMemcpy(d_A, h_A, mem_size_A, cudaMemcpyHostToDevice));

  checkCudaErrors(cudaMemcpy(d_B, h_B, mem_size_B, cudaMemcpyHostToDevice));

  // Setup execution parameters
  dim3 threads(block_size, block_size);
  dim3 grid(dimsB.x / threads.x, dimsA.y / threads.y);

  // Create and start timer
  printf("Computing result using CUDA Kernel...\n");

  // Performs warmup operation using matrixMul CUDA kernel
  if (block_size == 16) {
    MatrixMulCUDA<16> <<< grid, threads >>>(d_C, d_A, d_B,
                                            dimsA.x, dimsB.x);
  } else {
    MatrixMulCUDA<32> <<< grid, threads >>>(d_C, d_A, d_B,
                                            dimsA.x, dimsB.x);
  }

  printf("done\n");

  cudaDeviceSynchronize();

  // Allocate CUDA events that we'll use for timing
  cudaEvent_t start;
  checkCudaErrors(cudaEventCreate(&start));

  cudaEvent_t stop;
  checkCudaErrors(cudaEventCreate(&stop));

  // Record the start event
  checkCudaErrors(cudaEventRecord(start, NULL));

  // Execute the kernel
  int nIter = 300;

  for (int j = 0; j < nIter; j++) {
    if (block_size == 16) {
      MatrixMulCUDA<16> <<< grid, threads >>>(d_C, d_A, d_B,
                                              dimsA.x, dimsB.x);
    } else {
      MatrixMulCUDA<32> <<< grid, threads >>>(d_C, d_A, d_B,
                                              dimsA.x, dimsB.x);
    }
  }

  // Record the stop event
  checkCudaErrors(cudaEventRecord(stop, NULL));

  // Wait for the stop event to complete
  checkCudaErrors(cudaEventSynchronize(stop));

  float msecTotal = 0.0f;
  checkCudaErrors(cudaEventElapsedTime(&msecTotal, start, stop));

  // Compute and print the performance
  float msecPerMatrixMul = msecTotal / nIter;
  double flopsPerMatrixMul = 2.0 * static_cast<double>(dimsA.x) *
                             static_cast<double>(dimsA.y) *
                             static_cast<double>(dimsB.x);
  double gigaFlops = (flopsPerMatrixMul * 1.0e-9f) /
                     (msecPerMatrixMul / 1000.0f);
  printf(
    "Performance= %.2f GFlop/s, Time= %.3f msec, Size= %.0f Ops," \
    " WorkgroupSize= %u threads/block\n",
    gigaFlops,
    msecPerMatrixMul,
    flopsPerMatrixMul,
    threads.x * threads.y);

  // Copy result from device to host
  checkCudaErrors(cudaMemcpy(h_C, d_C, mem_size_C, cudaMemcpyDeviceToHost));

  printf("Checking computed result for correctness: ");
  bool correct = true;

  // test relative error by the formula
  //     |<x, y>_cpu - <x,y>_gpu|/<|x|, |y|>  < eps
  double eps = 1.e-6;  // machine zero

  for (int i = 0; i < static_cast<int>(dimsC.x * dimsC.y); i++) {
    double abs_err = fabs(h_C[i] - (dimsA.x * valB));
    double dot_length = dimsA.x;
    double abs_val = fabs(h_C[i]);
    double rel_err = abs_err / abs_val / dot_length;

    if (rel_err > eps) {
      printf("Error! Matrix[%05d]=%.8f, ref=%.8f error term is > %E\n",
             i, h_C[i], dimsA.x * valB, eps);
      correct = false;
    }
  }

  printf("%s\n", correct ? "Result = PASS" : "Result = FAIL");

  // Clean up memory
  free(h_A);
  free(h_B);
  free(h_C);
  checkCudaErrors(cudaFree(d_A));
  checkCudaErrors(cudaFree(d_B));
  checkCudaErrors(cudaFree(d_C));

  printf("\nNOTE: The CUDA Samples are not meant for performance"\
         " measurements. Results may vary when GPU Boost is enabled.\n");

  if (correct) {
    return EXIT_SUCCESS;
  } else {
    return EXIT_FAILURE;
  }
}


/**
 * Program main
 */
int main(int argc, char **argv) {
  printf("[Matrix Multiply Using CUDA] - Starting...\n");

  if (checkCmdLineFlag(argc, (const char **)argv, "help") ||
      checkCmdLineFlag(argc, (const char **)argv, "?")) {
    printf("Usage -device=n (n >= 0 for deviceID)\n");
    printf("      -wA=WidthA -hA=HeightA (Width x Height of Matrix A)\n");
    printf("      -wB=WidthB -hB=HeightB (Width x Height of Matrix B)\n");
    printf("  Note: Outer matrix dimensions of A & B matrices" \
           " must be equal.\n");

    exit(EXIT_SUCCESS);
  }

  // This will pick the best possible CUDA capable device, otherwise
  // override the device ID based on input provided at the command line
  int dev = findCudaDevice(argc, (const char **)argv);

  int block_size = 32;

  dim3 dimsA(5 * 2 * block_size, 5 * 2 * block_size, 1);
  dim3 dimsB(5 * 4 * block_size, 5 * 2 * block_size, 1);

  // width of Matrix A
  if (checkCmdLineFlag(argc, (const char **)argv, "wA")) {
    dimsA.x = getCmdLineArgumentInt(argc, (const char **)argv, "wA");
  }

  // height of Matrix A
  if (checkCmdLineFlag(argc, (const char **)argv, "hA")) {
    dimsA.y = getCmdLineArgumentInt(argc, (const char **)argv, "hA");
  }

  // width of Matrix B
  if (checkCmdLineFlag(argc, (const char **)argv, "wB")) {
    dimsB.x = getCmdLineArgumentInt(argc, (const char **)argv, "wB");
  }

  // height of Matrix B
  if (checkCmdLineFlag(argc, (const char **)argv, "hB")) {
    dimsB.y = getCmdLineArgumentInt(argc, (const char **)argv, "hB");
  }

  if (dimsA.x != dimsB.y) {
    printf("Error: outer matrix dimensions must be equal. (%d != %d)\n",
           dimsA.x, dimsB.y);
    exit(EXIT_FAILURE);
  }

  printf("MatrixA(%d,%d), MatrixB(%d,%d)\n", dimsA.x, dimsA.y,
         dimsB.x, dimsB.y);

  int matrix_result = MatrixMultiply(argc, argv, block_size, dimsA, dimsB);

  exit(matrix_result);
}