Hi everyone

I have recently been going over the matrix matrix multiplication code from PGI but I have some trouble understanding how the kernel works.

The values for matrix dimensions as follows: N = 512, M = 512, L =1024

```
! start the module containing the matrix multiply kernel
module mmul_mod
use cudafor
contains
! mmul_kernel computes A*B into C where A is NxM, B is MxL, C is then NxL
attributes(global) subroutine mmul_kernel( A, B, C, N, M, L )
real,device :: A(N,M), B(M,L), C(N,L)
integer, value :: N, M, L
integer :: i, j, kb, k, tx, ty
! submatrices are declared to be in CUDA shared memory
real, shared :: Asub(16,16), Bsub(16,16)
! the value of C(i,j) being computed, a temporary scalar
real :: Cij
! Start execution, first get my thread indices
tx = threadidx%x
ty = threadidx%y
! This thread computes C(i,j) = sum(A(i,:) * B(:,j))
i = (blockidx%x-1) * 16 + tx
j = (blockidx%y-1) * 16 + ty
Cij = 0.0
! Do the k loop in chunks of 16, the block size
do kb = 1, M, 16
! Fill the submatrices; each of 16x16 threads in the thread block
! loads one element of Asub and Bsub
Asub(tx,ty) = A(i,kb+ty-1)
Bsub(tx,ty) = B(kb+tx-1,j)
! Wait until all elements are filled
call syncthreads()
! Multiply the two submatrices; ! Each of the 16x16 threads accumulates the
! dot product for its element of C(i,j)
do k = 1,16
Cij = Cij + Asub(tx,k) * Bsub(k,ty)
enddo
! Synchronize to make sure all threads are done reading the submatrices before
! overwriting them in the next iteration of the kb loop
call syncthreads()
enddo
! Each of the 16x16 threads stores its element to the global C array
C(i,j) = Cij
end subroutine mmul_kernel
```

Although I have gone over the article that goes over the code I am not sure how the two 16x16 submatrices Asub and Bsub aid in the dot product of the row of A and the column of B. Also, I would like to understand more of how they came up with the equations for i and j from the thread index and the block index. I am sorry if this is too much of an easy question >_>

Sincerely,

-Chris