globalToShmemAsyncCopy.cu

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/**
 * Matrix multiplication: C = A * B.
 *
 * This sample demonstrates implements matrix multiplication which makes use of shared memory
 * to ensure data reuse, the matrix multiplication is done using tiling approach.
 * With compute capability 8.0 or higher the CUDA kernels involved uses asynchronously copy data
 * from global to shared memory; a.k.a., async-copy.
 * This sample 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.
 */

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

// CUDA runtime
#include <cuda_runtime.h>
#include <cuda/pipeline>

#if __CUDA_ARCH__ >= 700
#include <cuda/barrier>
#endif
#include  <cooperative_groups.h>

namespace cg = cooperative_groups;

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

enum kernels
{
    AsyncCopyMultiStageLargeChunk  = 0,
    AsyncCopyLargeChunk            = 1,
    AsyncCopyLargeChunkAWBarrier   = 2,
    AsyncCopyMultiStageSharedState = 3,
    AsyncCopyMultiStage            = 4,
    AsyncCopySingleStage           = 5,
    Naive                          = 6,
    NaiveLargeChunk                = 7
};

const char* kernelNames[] = {"AsyncCopyMultiStageLargeChunk", "AsyncCopyLargeChunk", 
                            "AsyncCopyLargeChunkAWBarrier", "AsyncCopyMultiStageSharedState",
                            "AsyncCopyMultiStage", "AsyncCopySingleStage", "Naive", "NaiveLargeChunk"};

constexpr int blockSize = 16;

// Multi Stage memcpy_async pipeline with large chunk copy
template <int BLOCK_SIZE> __global__ void MatrixMulAsyncCopyMultiStageLargeChunk(float* __restrict__ C, 
                                                        const float* __restrict__ A,
                                                        const float* __restrict__ B, int wA,
                                                        int wB) {
    // Requires BLOCK_SIZE % 4 == 0 

    // Multi-stage pipeline version
    constexpr size_t maxPipelineStages = 4;

    // Declaration of the shared memory array As used to
    // store the sub-matrix of A for each stage
    __shared__ alignas(alignof(float4)) float As[maxPipelineStages][BLOCK_SIZE][BLOCK_SIZE];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B for each stage
    __shared__ alignas(alignof(float4)) float Bs[maxPipelineStages][BLOCK_SIZE][BLOCK_SIZE];

    float Csub = 0.0;

    // Index of the first sub-matrix of A processed by the block
    const int aBegin = wA * (BLOCK_SIZE) * blockIdx.y;

    // Index of the last sub-matrix of A processed by the block
    const 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
    const int bBegin = BLOCK_SIZE * blockIdx.x;

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

    const int t4x = threadIdx.x * 4;
    const auto shape4 = cuda::aligned_size_t<alignof(float4)>(sizeof(float4));

    cuda::pipeline<cuda::thread_scope_thread> pipe = cuda::make_pipeline();

    // Loop over all the sub-matrices of A and B
    // required to compute the block sub-matrix
    for (int a = aBegin, b = bBegin, i = 0, aStage = aBegin, bStage = bBegin, iStage = 0; a <= aEnd; a += aStep, b += bStep, ++i ) {
        // Load the matrices from device memory to shared memory; each thread loads
        // one element of each matrix
        for ( ; aStage <= a + aStep * maxPipelineStages ; aStage += aStep, bStage += bStep, ++iStage )
        {
            pipe.producer_acquire();
            if ( aStage <= aEnd && t4x < BLOCK_SIZE )
            {
                // Rotating buffer
                const int j = iStage % maxPipelineStages;
                cuda::memcpy_async(&As[j][threadIdx.y][t4x], &A[aStage + wA * threadIdx.y + t4x], shape4, pipe);
                cuda::memcpy_async(&Bs[j][threadIdx.y][t4x], &B[aStage + wA * threadIdx.y + t4x], shape4, pipe);
            }
            pipe.producer_commit();
        }

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

        // Rotating buffer
        const int j = i % maxPipelineStages;

        // 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[j][threadIdx.y][k] * Bs[j][k][threadIdx.x];
        }
        pipe.consumer_release();

        // Don't have to synchronize because maxPipelineStages is greater than one
        // therefore next iteration is loading to a different buffer.
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    int c = wB * BLOCK_SIZE * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}


// Single Stage memcpy_async pipeline with Large copy chunk (float4)
template <int BLOCK_SIZE> __global__ void MatrixMulAsyncCopyLargeChunk(float* __restrict__ C, 
                                                        const float* __restrict__ A,
                                                        const float* __restrict__ B, int wA,
                                                        int wB) {
    // Requires BLOCK_SIZE % 4 == 0 

    // Declaration of the shared memory array As used to
    // store the sub-matrix of A
    __shared__ alignas(alignof(float4)) float As[BLOCK_SIZE][BLOCK_SIZE];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B
    __shared__ alignas(alignof(float4)) float Bs[BLOCK_SIZE][BLOCK_SIZE];

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

    // 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 * blockIdx.x;

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

    // Single-stage pipeline version
    float Csub = 0.0;

    const int t4x = threadIdx.x * 4;
    const auto shape4 = cuda::aligned_size_t<alignof(float4)>(sizeof(float4));
    cuda::pipeline<cuda::thread_scope_thread> pipe = cuda::make_pipeline();

    // 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) {
        // Load the matrices from device memory to shared memory; 
        // a subset of threads loads a contiguous chunk of elements.

        // Previously, per-thread:
        // As[ty][tx] = A[a + wA * ty + tx];
        // Bs[ty][tx] = B[b + wB * ty + tx];

        // Now, one fourth of the threads load four elements of each matrix
        if ( t4x < BLOCK_SIZE ) {

            pipe.producer_acquire();

            cuda::memcpy_async(&As[threadIdx.y][t4x], &A[a + wA * threadIdx.y + t4x], shape4, pipe);
            cuda::memcpy_async(&Bs[threadIdx.y][t4x], &B[a + wA * threadIdx.y + t4x], shape4, pipe);

            pipe.producer_commit();
            pipe.consumer_wait();
        }

        // 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[threadIdx.y][k] * Bs[k][threadIdx.x];
        }

        pipe.consumer_release();

        // Synchronize to make sure that the preceding
        // computation is done before overwriting the
        // shared memory sub-matrix buffers As and Bs in the next iteration.
        __syncthreads();
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    int c = wB * BLOCK_SIZE * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}

// Single Stage memcpy_async pipeline with Large copy chunk (float4) using arrive-wait barrier
template <int BLOCK_SIZE> __global__ void MatrixMulAsyncCopyLargeChunkAWBarrier(float* __restrict__ C, 
                                                        const float* __restrict__ A,
                                                        const float* __restrict__ B, int wA,
                                                        int wB) {
#if __CUDA_ARCH__ >= 700
#pragma diag_suppress static_var_with_dynamic_init
    // Requires BLOCK_SIZE % 4 == 0 

    __shared__ cuda::barrier<cuda::thread_scope_block> bar;

    // Declaration of the shared memory array As used to
    // store the sub-matrix of A
    __shared__  alignas(alignof(float4)) float As[BLOCK_SIZE][BLOCK_SIZE];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B
    __shared__ alignas(alignof(float4)) float Bs[BLOCK_SIZE][BLOCK_SIZE];

    if (threadIdx.x == 0) {
        init(&bar, blockDim.x*blockDim.y);
    }
    __syncthreads();

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

    // 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 * blockIdx.x;

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

    float Csub = 0.0;

    const int t4x = threadIdx.x * 4;

    // 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) {
        // Load the matrices from device memory to shared memory; 
        // a subset of threads loads a contiguous chunk of elements.

        // Now, one fourth of the threads load four elements of each matrix
        if ( t4x < BLOCK_SIZE ) {
            float4 * const A4s = reinterpret_cast<float4*>(& As[threadIdx.y][t4x]);
            float4 * const B4s = reinterpret_cast<float4*>(& Bs[threadIdx.y][t4x]);
            const float4 * const A4  = reinterpret_cast<const float4*>(& A[a + wA * threadIdx.y + t4x]);
            const float4 * const B4  = reinterpret_cast<const float4*>(& B[a + wA * threadIdx.y + t4x]);

            cuda::memcpy_async(A4s, A4, sizeof(float4), bar);
            cuda::memcpy_async(B4s, B4, sizeof(float4), bar);
         }

        // Synchronize to make sure the matrices are loaded
        bar.arrive_and_wait();

        // 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[threadIdx.y][k] * Bs[k][threadIdx.x];
        }

        // Synchronize to make sure that the preceding
        // computation is done before overwriting the
        // shared memory sub-matrix buffers As and Bs in the next iteration.
        bar.arrive_and_wait();
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    int c = wB * BLOCK_SIZE * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
#endif
}

// Single Stage memcpy_async pipeline with float copy
template <int BLOCK_SIZE> __global__ void MatrixMulAsyncCopySingleStage(float *C, const float *A,
                                                        const float *B, int wA,
                                                        int wB) {

    // 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];

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

    // 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 * blockIdx.x;

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

    // Single-stage pipeline version
    float Csub = 0.0;

    cuda::pipeline<cuda::thread_scope_thread> pipe = cuda::make_pipeline();
    const auto shape1 = cuda::aligned_size_t<alignof(float)>(sizeof(float));


    // 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) {
        // Load the matrices from device memory to shared memory; each thread loads
        // one element of each matrix
        {
            pipe.producer_acquire();

            cuda::memcpy_async(&As[threadIdx.y][threadIdx.x], &A[a + wA * threadIdx.y + threadIdx.x], shape1, pipe);
            cuda::memcpy_async(&Bs[threadIdx.y][threadIdx.x], &B[b + wB * threadIdx.y + threadIdx.x], shape1, pipe);

            pipe.producer_commit();
        }

        pipe.consumer_wait();
        // 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[threadIdx.y][k] * Bs[k][threadIdx.x];
        }

        // Synchronize to make sure that the preceding
        // computation is done before overwriting the
        // shared memory sub-matrix buffers As and Bs in the next iteration.
        __syncthreads();
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    int c = wB * BLOCK_SIZE * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}

// Multi Stage memcpy_async thread_scope_thread pipeline with single-element async-copy
template <int BLOCK_SIZE> __global__ void MatrixMulAsyncCopyMultiStage(float* __restrict__ C, 
                                                        const float* __restrict__ A,
                                                        const float* __restrict__ B, int wA,
                                                        int wB) {
    // Multi-stage pipeline version
    constexpr size_t maxPipelineStages = 4;

    // Declaration of the shared memory array As used to
    // store the sub-matrix of A for each stage
    __shared__ float As[maxPipelineStages][BLOCK_SIZE][BLOCK_SIZE];

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

    float Csub = 0.0;

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

    // Index of the last sub-matrix of A processed by the block
    const 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
    const int bBegin = BLOCK_SIZE * blockIdx.x;

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

    cuda::pipeline<cuda::thread_scope_thread> pipe = cuda::make_pipeline();
    const auto shape1 = cuda::aligned_size_t<alignof(float)>(sizeof(float));

    // Loop over all the sub-matrices of A and B
    // required to compute the block sub-matrix
    for (int a = aBegin, b = bBegin, i = 0, aStage = aBegin, bStage = bBegin, iStage = 0; a <= aEnd; a += aStep, b += bStep, ++i ) {
        // Load the matrices from device memory to shared memory; each thread loads
        // one element of each matrix

        for ( ; aStage <= a + aStep * maxPipelineStages ; aStage += aStep, bStage += bStep, ++iStage )
        {
            if ( aStage <= aEnd )
            {
                // Rotating buffer
                const int j = iStage % maxPipelineStages;

                pipe.producer_acquire();

                cuda::memcpy_async(&As[j][threadIdx.y][threadIdx.x], &A[aStage + wA * threadIdx.y + threadIdx.x], shape1, pipe);
                cuda::memcpy_async(&Bs[j][threadIdx.y][threadIdx.x], &B[bStage + wB * threadIdx.y + threadIdx.x], shape1, pipe);

                pipe.producer_commit();
            }
        }
        pipe.consumer_wait();

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

        const int j = i % maxPipelineStages;

        // Multiply the two matrices together;
        // each thread computes one element
        // of the block sub-matrix
        for (int k = 0; k < BLOCK_SIZE; ++k) {
            Csub += As[j][threadIdx.y][k] * Bs[j][k][threadIdx.x];
        }

        pipe.consumer_release();
        // Don't have to synchronize because maxPipelineStages is greater than one
        // therefore next iteration is loading to a different buffer.
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    int c = wB * BLOCK_SIZE * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}

// Multi Stage shared state memcpy_async pipeline thread_scope_block
// with parititioned producer & consumer, here we've 1 warp as producer
// group which issues memcpy_async operations and rest all warps are part of
// consumer group which perform gemm computation on the loaded matrices by producer.
template <int BLOCK_SIZE_X> __global__ void MatrixMulAsyncCopyMultiStageSharedState(float* __restrict__ C, 
                                                        const float* __restrict__ A,
                                                        const float* __restrict__ B, int wA,
                                                        int wB) {
    // Multi-stage pipeline version
    constexpr size_t maxPipelineStages = 4;

    // Declaration of the shared memory array As used to
    // store the sub-matrix of A for each stage
    __shared__ float As[maxPipelineStages][BLOCK_SIZE_X][BLOCK_SIZE_X];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B for each stage
    __shared__ float Bs[maxPipelineStages][BLOCK_SIZE_X][BLOCK_SIZE_X];

    float Csub = 0.0;

    // Index of the first sub-matrix of A processed by the block
    const int aBegin = wA * BLOCK_SIZE_X * blockIdx.y;

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

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

    // Index of the first sub-matrix of B processed by the block
    const int bBegin = BLOCK_SIZE_X * blockIdx.x;

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

    auto cta = cg::this_thread_block();

    const auto shape1 = cuda::aligned_size_t<alignof(float)>(sizeof(float));
    __shared__ cuda::pipeline_shared_state<cuda::thread_scope_block, maxPipelineStages> shared_state;
    constexpr int consumer_row_count =  BLOCK_SIZE_X;

    const auto thread_role = (cta.thread_index().y < consumer_row_count)
                                ? cuda::pipeline_role::consumer
                                : cuda::pipeline_role::producer;
    auto pipe = cuda::make_pipeline(cta, &shared_state, thread_role);

    // Loop over all the sub-matrices of A and B
    // required to compute the block sub-matrix
    for (int a = aBegin, b = bBegin, i = 0, aStage = aBegin, bStage = bBegin, iStage = 0;
                                                a <= aEnd; a += aStep, b += bStep, ++i) {
        if (threadIdx.y >= consumer_row_count) {
            // this is a whole producer warp because threadIdx.y >= 16 where 16 == consumer_row_count,
            // which loads the matrices from device memory to shared memory; 
            for (; aStage <= a + aStep * maxPipelineStages; aStage += aStep, bStage += bStep, ++iStage) {
                if (aStage <= aEnd) {
                    // Rotating buffer
                    const int j = iStage % maxPipelineStages;
                    const int strideRows = (blockDim.y - consumer_row_count);
                    pipe.producer_acquire();
                    for (int rowId = threadIdx.y - consumer_row_count; rowId < BLOCK_SIZE_X; rowId += strideRows) {
                        cuda::memcpy_async(&As[j][rowId][threadIdx.x], 
                                            &A[aStage + wA * rowId + threadIdx.x], shape1, pipe);
                        cuda::memcpy_async(&Bs[j][rowId][threadIdx.x],
                                            &B[bStage + wB * rowId + threadIdx.x], shape1, pipe);
                    }
                    pipe.producer_commit();
                }
            }
        }
        else {
            // this is a whole set of consumer group because threadIdx.y < consumer_row_count where consumer_row_count == 16,
            // which computes gemm operation on matrices loaded in shared memory by producer warp. 
            const int j = i % maxPipelineStages;
            // Synchronize consumer group to make sure the matrices are loaded by producer group.
            pipe.consumer_wait();
            // Multiply the two matrices together;
            // each thread computes one element
            // of the block sub-matrix
            #pragma unroll
            for (int k = 0; k < BLOCK_SIZE_X; ++k) {
                Csub += As[j][threadIdx.y][k] * Bs[j][k][threadIdx.x];
            }
            pipe.consumer_release();
        }
    }

    // Write the block sub-matrix to device memory;
    // each thread writes four element
    if (threadIdx.y < consumer_row_count)
    {
        const int c = wB * BLOCK_SIZE_X * blockIdx.y + BLOCK_SIZE_X * blockIdx.x;
        C[c + wB * threadIdx.y + threadIdx.x] = Csub;
    }
}

/**
 * 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 MatrixMulNaive(float *C, float *A,
                                                        float *B, int wA,
                                                        int wB) {
    // 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];

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

    // 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 * blockIdx.x;

    // 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) {

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

        // 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[threadIdx.y][k] * Bs[k][threadIdx.x];
        }

        // 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 * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}

template <int BLOCK_SIZE> __global__ void MatrixMulNaiveLargeChunk(float *C, float *A,
                                                        float *B, int wA,
                                                        int wB) {
    // Declaration of the shared memory array As used to
    // store the sub-matrix of A
    __shared__ alignas(alignof(float4)) float As[BLOCK_SIZE][BLOCK_SIZE];

    // Declaration of the shared memory array Bs used to
    // store the sub-matrix of B
    __shared__ alignas(alignof(float4)) float Bs[BLOCK_SIZE][BLOCK_SIZE];

    int t4x = threadIdx.x * 4 ;

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

    // 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 * blockIdx.x;

    // 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) {

        // Load the matrices from device memory
        // to shared memory; 

        // One fourth of the threads load four elements of each matrix
        if ( t4x < BLOCK_SIZE ) {
            float4 * const A4s = reinterpret_cast<float4*>(& As[threadIdx.y][t4x]);
            float4 * const B4s = reinterpret_cast<float4*>(& Bs[threadIdx.y][t4x]);
            const float4 * const A4 = reinterpret_cast<float4*>(& A[a + wA * threadIdx.y + t4x]);
            const float4 * const B4 = reinterpret_cast<float4*>(& B[a + wA * threadIdx.y + t4x]);
            *A4s = *A4 ;
            *B4s = *B4 ;
        }

        // 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[threadIdx.y][k] * Bs[k][threadIdx.x];
        }

        // 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 * blockIdx.y + BLOCK_SIZE * blockIdx.x;
    C[c + wB * threadIdx.y + threadIdx.x] = Csub;
}


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

/**
 * Run matrix multiplication using CUDA
 */
int MatrixMultiply(int argc, char **argv,
                   const dim3 &dimsA,
                   const dim3 &dimsB,
                   kernels kernel_number) {
    // 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;
    checkCudaErrors(cudaMallocHost(&h_A, mem_size_A));
    unsigned int size_B = dimsB.x * dimsB.y;
    unsigned int mem_size_B = sizeof(float) * size_B;
    float* h_B;
    checkCudaErrors(cudaMallocHost(&h_B, mem_size_B));
    cudaStream_t stream;

    // Initialize host memory
    const float valB = 2.10f;
    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;
    checkCudaErrors(cudaMallocHost(&h_C, 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));
    // Allocate CUDA events that we'll use for timing
    cudaEvent_t start, stop;
    checkCudaErrors(cudaEventCreate(&start));
    checkCudaErrors(cudaEventCreate(&stop));

    checkCudaErrors(cudaStreamCreateWithFlags(&stream, cudaStreamNonBlocking));

    // copy host memory to device
    checkCudaErrors(cudaMemcpyAsync(d_A, h_A, mem_size_A, cudaMemcpyHostToDevice, stream));
    checkCudaErrors(cudaMemcpyAsync(d_B, h_B, mem_size_B, cudaMemcpyHostToDevice, stream));
    checkCudaErrors(cudaMemsetAsync(d_C, 0, mem_size_C, stream));

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

    // Here the block size is 16x18, where first 16 rows are consumer thread group
    // and last 2 rows (1 warp) is producer thread group
    dim3 threadsSharedStateKernel(blockSize, blockSize + 2, 1);
    dim3 gridSharedStateKernel(dimsB.x / threadsSharedStateKernel.x, dimsA.y / threadsSharedStateKernel.x);

    printf("Running kernel = %d - %s\n", kernel_number, kernelNames[kernel_number]);
    // Create and start timer
    printf("Computing result using CUDA Kernel...\n");

    // Performs warmup operation using matrixMul CUDA kernel
    switch (kernel_number)
    {
        case AsyncCopyMultiStageLargeChunk :
        default:
            MatrixMulAsyncCopyMultiStageLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case AsyncCopyLargeChunk :
            MatrixMulAsyncCopyLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case AsyncCopyLargeChunkAWBarrier :
            MatrixMulAsyncCopyLargeChunkAWBarrier<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case AsyncCopyMultiStageSharedState :
            MatrixMulAsyncCopyMultiStageSharedState<blockSize><<<gridSharedStateKernel, threadsSharedStateKernel, 0, stream>>>
                                                                                        (d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case AsyncCopyMultiStage :
            MatrixMulAsyncCopyMultiStage<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case AsyncCopySingleStage :
            MatrixMulAsyncCopySingleStage<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case Naive :
            MatrixMulNaive<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
        case NaiveLargeChunk:
            MatrixMulNaiveLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
            break;
    }

    printf("done\n");
    checkCudaErrors(cudaStreamSynchronize(stream));


    // Execute the kernel
    int nIter = 100;

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

    for (int j = 0; j < nIter; j++) {
        switch (kernel_number)
        {
            case AsyncCopyMultiStageLargeChunk :
            default:
                MatrixMulAsyncCopyMultiStageLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case AsyncCopyLargeChunk :
                MatrixMulAsyncCopyLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case AsyncCopyLargeChunkAWBarrier :
                MatrixMulAsyncCopyLargeChunkAWBarrier<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case AsyncCopyMultiStageSharedState :
                MatrixMulAsyncCopyMultiStageSharedState<blockSize><<<gridSharedStateKernel, threadsSharedStateKernel, 0, stream>>>
                                                                                                (d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case AsyncCopyMultiStage :
                MatrixMulAsyncCopyMultiStage<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case AsyncCopySingleStage :
                MatrixMulAsyncCopySingleStage<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case Naive :
                MatrixMulNaive<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
            case NaiveLargeChunk:
                MatrixMulNaiveLargeChunk<blockSize><<<grid, threads, 0, stream>>>(d_C, d_A, d_B, dimsA.x, dimsB.x);
                break;
        }
    }

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

    // 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(cudaMemcpyAsync(h_C, d_C, mem_size_C, cudaMemcpyDeviceToHost, stream));
    checkCudaErrors(cudaStreamSynchronize(stream));

    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
    checkCudaErrors(cudaFreeHost(h_A));
    checkCudaErrors(cudaFreeHost(h_B));
    checkCudaErrors(cudaFreeHost(h_C));
    checkCudaErrors(cudaFree(d_A));
    checkCudaErrors(cudaFree(d_B));
    checkCudaErrors(cudaFree(d_C));
    checkCudaErrors(cudaEventDestroy(start));
    checkCudaErrors(cudaEventDestroy(stop));
    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;
    }
}


int main(int argc, char **argv) {
    printf("[globalToShmemAsyncCopy] - 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("      -kernel=kernel_number (0 - AsyncCopyMultiStageLargeChunk; 1 - AsyncCopyLargeChunk)\n");
        printf("                            (2 - AsyncCopyLargeChunkAWBarrier; 3 - AsyncCopyMultiStageSharedState)\n");
        printf("                            (4 - AsyncCopyMultiStage; 5 - AsyncCopySingleStage; 6 - Naive without memcpy_async)\n");
        printf("                            (7 - NaiveLargeChunk without memcpy_async)\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 matrixBlock = 32;
    dim3 dimsA(10 * 4 * matrixBlock, 10 * 4 * matrixBlock, 1);
    dim3 dimsB(10 * 4 * matrixBlock, 10 * 4 * matrixBlock, 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);
    }

    kernels selected_kernel = AsyncCopyMultiStageLargeChunk;

    // kernel to run - default (AsyncCopyMultiStageLargeChunk == 0)
    if (checkCmdLineFlag(argc, (const char **)argv, "kernel")) {
        int kernel_number = getCmdLineArgumentInt(argc, (const char **)argv, "kernel");
        if (kernel_number < 8)
        {
            selected_kernel = (kernels)kernel_number;
        }
        else
        {
            printf("Error: kernel number should be between 0 to 6, you have entered %d\n", kernel_number);
            exit(EXIT_FAILURE);
        }
    }

    int major = 0;
    checkCudaErrors(cudaDeviceGetAttribute(&major, cudaDevAttrComputeCapabilityMajor, dev));
    if (major < 7)
    {
        printf("globalToShmemAsyncCopy requires SM 7.0 or higher.  Exiting...\n");
        exit(EXIT_WAIVED);
    }

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

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

    exit(matrix_result);
}