How does the operation like "some_fragment.x[index]" work in wmma api?

I have to use the wmma api to do some matrix multiplication, and I want to access every single element in the fragment to do some operation, maybe simple as multiply a variable or something more complex.

Below is the example. At the beginning, I think that I should let thread access different index according to the threadIdx, like thread 0 operate x[0] to x[7], thread 1 operate x[8] to x[15], but is doesn’t work.

After some tries, I find out that it seems every single have different acces to the fragment, like for thread 0, x[0] maps to the first element in the fragment, x[1] maps to the second, x[2] maps to 8th, x[3] maps to 9th… So, how does it maps? I don’t find any instructions in any docs(or maybe I missed)

#include <cuda_runtime.h>
#include <mma.h>
#include <iostream>
using namespace nvcuda;

__global__ void wmma_ker(half *a, half *b, float *c) {
   wmma::fragment<wmma::matrix_a, 16, 16, 16, half, wmma::row_major> a_frag;
   wmma::fragment<wmma::matrix_b, 16, 16, 16, half, wmma::col_major> b_frag;
   wmma::fragment<wmma::accumulator, 16, 16, 16, float> c_frag;
   wmma::fill_fragment(c_frag, 0.0f);
   wmma::load_matrix_sync(a_frag, a, 16);
   wmma::load_matrix_sync(b_frag, b, 16);
   wmma::mma_sync(c_frag, a_frag, b_frag, c_frag);
   // here is the operation
   for (int i = 0; i < 16; i++){
        c_frag.x[i] = c_frag.x[i] * threadIdx.x;
   wmma::store_matrix_sync(c, c_frag, 16, wmma::mem_row_major);

void print_data(half *data){
    for (int i = 0; i < 16; i++){
        for (int j = 0; j < 16; j++){
            std::cout << __half2float(data[16*i+j]) << ",";
        std::cout << std::endl;
    std::cout << std::endl << std::endl;

int main(){
    half* data_a_host = (half*)malloc(sizeof(half) * 16 * 16);
    half* data_b_host = (half*)malloc(sizeof(half) * 16 * 16);
    float* data_c_host = (float*)malloc(sizeof(float) * 16 * 16);
    for (int i = 0; i < 256; i++){
        data_a_host[i] = half(i);
        data_b_host[i] = half(i);
    half* data_a, *data_b;
    float* data_c;
    cudaMalloc(&data_a, sizeof(half) * 16 * 16);
    cudaMalloc(&data_b, sizeof(half) * 16 * 16);
    cudaMalloc(&data_c, sizeof(float) * 16 * 16);
    cudaMemcpy(data_a, data_a_host, sizeof(half) * 256, cudaMemcpyHostToDevice);
    cudaMemcpy(data_b, data_b_host, sizeof(half) * 256, cudaMemcpyHostToDevice);
    wmma_ker<<<1, 32>>>(data_a, data_b, data_c);
    cudaMemcpy(data_c_host, data_c, sizeof(float) * 256, cudaMemcpyDeviceToHost);
    for (int i = 0; i < 16; i++){
        for (int j = 0; j < 16; j++){
            std::cout << data_c_host[16*i+j] << ",";
        std::cout << std::endl;
    return 0;

The mapping is intentionally not given, not specified, and should not be relied upon, if discovered experimentally.

The only usage for individual access to fragment elements is when the operation to be done is uniform across all threads in the warp and all fragment elements. From the documentation:

Because the map of matrix elements into each thread’s fragment is unspecified

In the special case where all threads in the warp will apply an element-wise operation uniformly to all fragment elements, direct element access can be implemented using the following fragment class members.

For people who are looking for direct control of the matrix-multiply operands, I usually offer the suggestion to use PTX mma instructions, instead. Here is an example.

Thanks for your reply. Actually, I only need to do matrix multiplication and element-wise multiplication, so I think wmma is enough for me. Thanks to your reply, now I know how to deal with element-wise multiplication.

But I still have another question. If I want to copy one fragment to another fragment, like copy C to D. Comparing to store the C to shared memory and then load to D, will operations like this be faster?

for(int i = 0; i < C.num_elements; i++) D.x[i] = C.x[i];

I have no idea. If it were me, and I were using wmma operations, I would use the load and store functionality to copy one fragment to another.

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