Question

I would like to read (BS_X+1)*(BS_Y+1) global memory locations by BS_x*BS_Y threads moving the contents to shared memory and I have developed the following code.

int i       = threadIdx.x;
int j       = threadIdx.y;
int idx     = blockIdx.x*BLOCK_SIZE_X + threadIdx.x;
int idy     = blockIdx.y*BLOCK_SIZE_Y + threadIdx.y;

int index1  = j*BLOCK_SIZE_Y+i;

int i1      = (index1)%(BLOCK_SIZE_X+1);
int j1      = (index1)/(BLOCK_SIZE_Y+1);

int i2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)%(BLOCK_SIZE_X+1);
int j2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)/(BLOCK_SIZE_Y+1);

__shared__ double Ezx_h_shared_ext[BLOCK_SIZE_X+1][BLOCK_SIZE_Y+1];     

Ezx_h_shared_ext[i1][j1]=Ezx_h[(blockIdx.y*BLOCK_SIZE_Y+j1)*xdim+(blockIdx.x*BLOCK_SIZE_X+i1)];

if ((i2<(BLOCK_SIZE_X+1))&&(j2<(BLOCK_SIZE_Y+1))) 
    Ezx_h_shared_ext[i2][j2]=Ezx_h[(blockIdx.y*BLOCK_SIZE_Y+j2)*xdim+(blockIdx.x*BLOCK_SIZE_X+i2)];

In my understanding, coalescing is the parallel equivalent of consecutive memory reads of sequential processing. How can I detect now if the global memory accesses are coalesced? I remark that there is an index jump from (i1,j1) to (i2,j2).
Thanks in advance.

Answer 1

I’ve evaluated the memory accesses of your code with a hand-written coalescing analyzer. The evaluation shows the code less exploits the coalescing. Here is the coalescing analyzer that you may find useful:

#include <stdio.h>
#include <malloc.h>

typedef struct dim3_t{
    int x;
    int y;
} dim3;


// KERNEL LAUNCH PARAMETERS
#define GRIDDIMX 4
#define GRIDDIMY 4
#define BLOCKDIMX 16
#define BLOCKDIMY 16


// ARCHITECTURE DEPENDENT
// number of threads aggregated for coalescing
#define COALESCINGWIDTH 32
// number of bytes in one coalesced transaction
#define CACHEBLOCKSIZE 128
#define CACHE_BLOCK_ADDR(addr,size)  (addr*size)&(~(CACHEBLOCKSIZE-1))


int main(){
    // fixed dim3 variables
    // grid and block size
    dim3 blockDim,gridDim;
    blockDim.x=BLOCKDIMX;
    blockDim.y=BLOCKDIMY;
    gridDim.x=GRIDDIMX;
    gridDim.y=GRIDDIMY;

    // counters
    int unq_accesses=0;
    int *unq_addr=(int*)malloc(sizeof(int)*COALESCINGWIDTH);
    int total_unq_accesses=0;

    // iter over total number of threads
    // and count the number of memory requests (the coalesced requests)
    int I, II, III;
    for(I=0; I<GRIDDIMX*GRIDDIMY; I++){
        dim3 blockIdx;
        blockIdx.x = I%GRIDDIMX;
        blockIdx.y = I/GRIDDIMX;
        for(II=0; II<BLOCKDIMX*BLOCKDIMY; II++){
            if(II%COALESCINGWIDTH==0){
                // new coalescing bunch
                total_unq_accesses+=unq_accesses;
                unq_accesses=0;
            }
            dim3 threadIdx;
            threadIdx.x=II%BLOCKDIMX;
            threadIdx.y=II/BLOCKDIMX;

            ////////////////////////////////////////////////////////
            // Change this section to evaluate different accesses //
            ////////////////////////////////////////////////////////
            // do your indexing here
            #define BLOCK_SIZE_X BLOCKDIMX
            #define BLOCK_SIZE_Y BLOCKDIMY
            #define xdim 32
            int i       = threadIdx.x;
            int j       = threadIdx.y;
            int idx     = blockIdx.x*BLOCK_SIZE_X + threadIdx.x;
            int idy     = blockIdx.y*BLOCK_SIZE_Y + threadIdx.y;

            int index1  = j*BLOCK_SIZE_Y+i;

            int i1      = (index1)%(BLOCK_SIZE_X+1);
            int j1      = (index1)/(BLOCK_SIZE_Y+1);

            int i2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)%(BLOCK_SIZE_X+1);
            int j2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)/(BLOCK_SIZE_Y+1);
            // calculate the accessed location and offset here
            // change the line "Ezx_h[(blockIdx.y*BLOCK_SIZE_Y+j1)*xdim+(blockIdx.x*BLOCK_SIZE_X+i1)];" to
            int addr = (blockIdx.y*BLOCK_SIZE_Y+j1)*xdim+(blockIdx.x*BLOCK_SIZE_X+i1);
            int size = sizeof(double);
            //////////////////////////
            // End of modifications //
            //////////////////////////

            printf("tid (%d,%d) from blockid (%d,%d) accessing to block %d\n",threadIdx.x,threadIdx.y,blockIdx.x,blockIdx.y,CACHE_BLOCK_ADDR(addr,size));
            // check whether it can be merged with existing requests or not
            short merged=0;
            for(III=0; III<unq_accesses; III++){
                if(CACHE_BLOCK_ADDR(addr,size)==CACHE_BLOCK_ADDR(unq_addr[III],size)){
                    merged=1;
                    break;
                }
            }
            if(!merged){
                // new cache block accessed over this coalescing width
                unq_addr[unq_accesses]=CACHE_BLOCK_ADDR(addr,size);
                unq_accesses++;
            }
        }
    }
    printf("%d threads make %d memory transactions\n",GRIDDIMX*GRIDDIMY*BLOCKDIMX*BLOCKDIMY, total_unq_accesses);
}

The code will run for every thread of the grid and calculates the number of merged requests, metric of memory access coalescing.

To use the analyzer, paste the index calculation portion of your code in the specified region and decompose the memory accesses (array) into ‘address’ and ‘size’. I’ve already done this for your code where the indexings are:

int i       = threadIdx.x;
int j       = threadIdx.y;
int idx     = blockIdx.x*BLOCK_SIZE_X + threadIdx.x;
int idy     = blockIdx.y*BLOCK_SIZE_Y + threadIdx.y;

int index1  = j*BLOCK_SIZE_Y+i;

int i1      = (index1)%(BLOCK_SIZE_X+1);
int j1      = (index1)/(BLOCK_SIZE_Y+1);

int i2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)%(BLOCK_SIZE_X+1);
int j2      = (BLOCK_SIZE_X*BLOCK_SIZE_Y+index1)/(BLOCK_SIZE_Y+1);

and the memory access is:

Ezx_h_shared_ext[i1][j1]=Ezx_h[(blockIdx.y*BLOCK_SIZE_Y+j1)*xdim+(blockIdx.x*BLOCK_SIZE_X+i1)];

The analyzer reports 4096 threads access to 4064 cache blocks. Run the code for your actual grid and block size and analyze the coalescing behavior.