GPU编程--Shared Memory（4）

GPU的内存按照所属对象大致分为三类：线程独有的、block共享的、全局共享的。细分的话，包含global, local, shared, constant, and texture memoey, 我们重点关注以下两类内存

• Global memory

Global memory resides in device memory and device memory is accessed via 32-, 64-, or 128-bytes memory transactions

• Shared memory

Because it is on-chip, shared memory has much higher bandwidth and much lower latency than local or global memory

简单理解就是，Shared memory更快。以下是内存按照所属对象分类示意图

有了对Global memory、Shared memory的印象之后，我们通过矩阵相乘的例子要谈谈这两种内存的运用，并对比他们的优劣（老规矩，先代码，后解释）

// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.width + col)
typedef struct {
　　int width;
　　int height;
　　float* elements;
} Matrix;
// Thread block size
#define BLOCK_SIZE 16
// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);
// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix B, Matrix C)
{
　　// Load A and B to device memory
　　Matrix d_A;
　　d_A.width = A.width; d_A.height = A.height;
　　size_t size = A.width * A.height * sizeof(float);
　　cudaMalloc(&d_A.elements, size);
　　cudaMemcpy(d_A.elements, A.elements, size,
　　cudaMemcpyHostToDevice);
　　Matrix d_B;
　　d_B.width = B.width; d_B.height = B.height;
　　size = B.width * B.height * sizeof(float);
　　cudaMalloc(&d_B.elements, size);
　　cudaMemcpy(d_B.elements, B.elements, size,
　　cudaMemcpyHostToDevice);
　　// Allocate C in device memory
　　Matrix d_C;
　　d_C.width = C.width; d_C.height = C.height;
　　size = C.width * C.height * sizeof(float);
　　cudaMalloc(&d_C.elements, size);
　　// Invoke kernel
　　dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
　　dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
　　MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);
　　// Read C from device memory
　　cudaMemcpy(C.elements, Cd.elements, size,
　　cudaMemcpyDeviceToHost);
　　// Free device memory
　　cudaFree(d_A.elements);
　　cudaFree(d_B.elements);
　　cudaFree(d_C.elements);
}
// Matrix multiplication kernel called by MatMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
　　// Each thread computes one element of C
　　// by accumulating results into Cvalue
　　float Cvalue = 0;
　　int row = blockIdx.y * blockDim.y + threadIdx.y;
　　int col = blockIdx.x * blockDim.x + threadIdx.x;
　　for (int e = 0; e < A.width; ++e)
　　　　Cvalue += A.elements[row * A.width + e]
　　　　　　* B.elements[e * B.width + col];
　　C.elements[row * C.width + col] = Cvalue;
}

计算原理如下

 host端代码很常规，我们重点关注__global__标记的这个device端代码，她完成的功能很简单就是去A矩阵的一行、B矩阵的一列。行列对应元素相乘累加，也就是向量的点击运算。当运算结束的时候矩阵C=AB。这是很常规的一种思路。

那么，如何用Shared memory完成上述功能呢？这样的好处又是什么呢？（老规矩，先代码，后解释）

// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.stride + col)
typedef struct {
　　int width;
　　int height;
　　int stride;
　　float* elements;
} Matrix;
// Get a matrix element
__device__ float GetElement(const Matrix A, int row, int col)
{
　　return A.elements[row * A.stride + col];
}
// Set a matrix element
__device__ void SetElement(Matrix A, int row, int col,
　　float value)
{
　　A.elements[row * A.stride + col] = value;
}
// Get the BLOCK_SIZExBLOCK_SIZE sub-matrix Asub of A that is
// located col sub-matrices to the right and row sub-matrices down
// from the upper-left corner of A
__device__ Matrix GetSubMatrix(Matrix A, int row, int col)
{
　　Matrix Asub;
　　Asub.width = BLOCK_SIZE;
　　Asub.height = BLOCK_SIZE;
　　Asub.stride = A.stride;
　　Asub.elements = &A.elements[A.stride * BLOCK_SIZE * row
　　　　+ BLOCK_SIZE * col];
　　return Asub;
}
// Thread block size
#define BLOCK_SIZE 16
// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);
// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix B, Matrix C)
{
　　// Load A and B to device memory
　　Matrix d_A;
　　d_A.width = d_A.stride = A.width; d_A.height = A.height;
　　size_t size = A.width * A.height * sizeof(float);
　　cudaMalloc(&d_A.elements, size);
　　cudaMemcpy(d_A.elements, A.elements, size,
　　cudaMemcpyHostToDevice);
　　Matrix d_B;
　　d_B.width = d_B.stride = B.width; d_B.height = B.height;
　　size = B.width * B.height * sizeof(float);
　　cudaMalloc(&d_B.elements, size);
　　cudaMemcpy(d_B.elements, B.elements, size,
　　cudaMemcpyHostToDevice);
　　// Allocate C in device memory
　　Matrix d_C;
　　d_C.width = d_C.stride = C.width; d_C.height = C.height;
　　size = C.width * C.height * sizeof(float);
　　cudaMalloc(&d_C.elements, size);
　　// Invoke kernel
　　dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
　　dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
　　MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);
　　// Read C from device memory
　　cudaMemcpy(C.elements, d_C.elements, size,
　　cudaMemcpyDeviceToHost);
　　// Free device memory
　　cudaFree(d_A.elements);
　　cudaFree(d_B.elements);
　　cudaFree(d_C.elements);
}
// Matrix multiplication kernel called by MatMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
　　// Block row and column
　　int blockRow = blockIdx.y;
　　int blockCol = blockIdx.x;
　　// Each thread block computes one sub-matrix Csub of C
　　Matrix Csub = GetSubMatrix(C, blockRow, blockCol);
　　// Each thread computes one element of Csub
　　// by accumulating results into Cvalue
　　float Cvalue = 0;
　　// Thread row and column within Csub
　　int row = threadIdx.y;
　　int col = threadIdx.x;
　　// Loop over all the sub-matrices of A and B that are
　　// required to compute Csub
　　// Multiply each pair of sub-matrices together
　　// and accumulate the results
　　for (int m = 0; m < (A.width / BLOCK_SIZE); ++m) {
　　// Get sub-matrix Asub of A
　　　　Matrix Asub = GetSubMatrix(A, blockRow, m);
　　// Get sub-matrix Bsub of B
　　Matrix Bsub = GetSubMatrix(B, m, blockCol);
　　// Shared memory used to store Asub and Bsub respectively
　　__shared__ float As[BLOCK_SIZE][BLOCK_SIZE];
　　__shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];
　　// Load Asub and Bsub from device memory to shared memory
　　// Each thread loads one element of each sub-matrix
　　As[row][col] = GetElement(Asub, row, col);
　　Bs[row][col] = GetElement(Bsub, row, col);
　　// Synchronize to make sure the sub-matrices are loaded
　　// before starting the computation
　　__syncthreads();

　　// Multiply Asub and Bsub together
　　for (int e = 0; e < BLOCK_SIZE; ++e)
　　　　Cvalue += As[row][e] * Bs[e][col];
　　// 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 Csub to device memory
　　// Each thread writes one element
　　SetElement(Csub, row, col, Cvalue);
}

计算原理如下

__device__标记的函数只能由__device__、__global__标记的函数调用。GetElement函数就是得到矩阵A（row，col）这一坐标上的值，SetElement函数就是将矩阵A（row，col）的值设置为value。GetSubMatrix函数就是得到矩阵A的子矩阵，用matlab的语法表示就是Asub=A[row：row+BLOCK_SIZE,col：col+BLOCK_SIZE]。

host端代码还是很常规的，下面重点分析__global__标记的函数。这个函数是以block为单位组织的，她首先获取矩阵C的一个子矩阵Csub，然后用该block内的线程ID索引Csub矩阵的所有元素。每一次for循环，获取A的子矩阵Asub、B的子矩阵Bsub（请参考上述示意图）。然后将Asub、Bsub的有global memory搬迁到shared memory。__syncthreads()的作用是，等所有的线程都将数据搬迁完了，再向下执行。之后的一个for循环完成的功能是Asub、Bsub对应元素向量点击运算。沿A的宽度方向、B的高度方向迭代，即可完成Csub内所有点的向量点击运算。

总结：引入shared memory的好处可以概括为“不要把时间浪费在路上，尤其是路途遥远的路上”。将Global memory的数据搬迁到thread比较费时。