# Local memory in matrix multiplication

Hi there,

I was playing around with the memory model theses days until I saw an example
how to use local memory in matrix multiplication.

I got two kernels as follow:

``````
// A[M][N] * B[N][P] = C[M][P]
kernel void mult_mem_global
(
const int Mdim,
const int Ndim,
const int Pdim,
global int *A,
global int *B,
global int *C
)
{
int k, j, tmp;
int i = get_global_id(0);

if (i > Mdim) return;

for (j = 0; j < Pdim; j++) {
tmp = 0;
for (k = 0; k < Ndim; k++)
tmp += A[i*Mdim + k] * B[k*Ndim + j];
C[i*Mdim + j] = tmp;
}
}

kernel void mult_mem_private_local
(
const int Mdim,
const int Ndim,
const int Pdim,
global int *A,
global int *B,
global int *C,
local int *local_B_column
)
{
int k, j, tmp;
int i = get_global_id(0);
int iloc = get_local_id(0);
int nloc = get_local_size(0);
int private_A_line;

if (i > Mdim) return;

/* private memory */
for (k = 0; k < Ndim; k++)
private_A_line[k] = A[i*Mdim + k];

local int local_B_column;

for(j = 0; j < Pdim; j++) {
for(k = iloc; k < Ndim; k += nloc) {
local_B_column[k] = B[k*Ndim + j];
}

barrier(CLK_LOCAL_MEM_FENCE);

for (k = tmp = 0; k < Ndim; k++)
tmp += private_A_line[k] * local_B_column[k];
C[i*Mdim + j] = tmp;
}
}

``````

The first kernel is a simple matrix multiplication and the second one
does the multiplication using local and private memory. The problem
is that the results are different.

I tried multiplying two 500x500 matrixes and using a local work size
of 250, so I have two work groups, as each work item computes one
row of the result. However, when comparing the results they are wrong
and if I use 50 as my local work size, the results are equal.

I tested it in two NVidia’s Geforce 650M and 210. Does anybody know
what I’m missing?

You need another barrier(CLK_LOCAL_MEM_FENCE) just before C[i*Mdim + j] = tmp.

Thanks, it really worked, but I didn’t get way the previous kernel didn’t work =/
I though the barrier was only necessary in that line to synchronize the work-items.
The C[i*Mdim + j] = tmp is writing to global memory, so I thought it was not needed
to put a barrier after that. Why is this happened?

You can easily visualize it if you mentally unroll the main loop:

``````
for(k = iloc; k < Ndim; k += nloc)
local_B_column[k] = B[k*Ndim + j];

barrier(CLK_LOCAL_MEM_FENCE);

for (k = tmp = 0; k < Ndim; k++)
tmp += private_A_line[k] * local_B_column[k];

C[i*Mdim + j] = tmp;

for(k = iloc; k < Ndim; k += nloc)
local_B_column[k] = B[k*Ndim + j];

barrier(CLK_LOCAL_MEM_FENCE);
...

``````

You can see that a barrier is needed near “C[i*Mdim + j] = tmp” because the content of local_B_column[] being read just before can be overwritten by the following write to local_B_column[].

Yeah, you’re right. Unrolling the loop makes it clear.
Thanks again for your help =D