parallelizing matrix multiplication through threading and SIMD - c

Question

I am trying to speed up matrix multiplication on multicore architecture. For this end, I try to use threads and SIMD at the same time. But my results are not good. I test speed up over sequential matrix multiplication:
void sequentialMatMul(void* params)
{
cout << "SequentialMatMul started.";
int i, j, k;
for (i = 0; i < N; i++)
{
for (k = 0; k < N; k++)
{
for (j = 0; j < N; j++)
{
X[i][j] += A[i][k] * B[k][j];
}
}
}
cout << "\nSequentialMatMul finished.";
}
I tried to add threading and SIMD to matrix multiplication as follows:
void threadedSIMDMatMul(void* params)
{
bounds *args = (bounds*)params;
int lowerBound = args->lowerBound;
int upperBound = args->upperBound;
int idx = args->idx;
int i, j, k;
for (i = lowerBound; i <upperBound; i++)
{
for (k = 0; k < N; k++)
{
for (j = 0; j < N; j+=4)
{
mmx1 = _mm_loadu_ps(&X[i][j]);
mmx2 = _mm_load_ps1(&A[i][k]);
mmx3 = _mm_loadu_ps(&B[k][j]);
mmx4 = _mm_mul_ps(mmx2, mmx3);
mmx0 = _mm_add_ps(mmx1, mmx4);
_mm_storeu_ps(&X[i][j], mmx0);
}
}
}
_endthread();
}
And the following section is used for calculating lowerbound and upperbound of each thread:
bounds arg[CORES];
for (int part = 0; part < CORES; part++)
{
arg[part].idx = part;
arg[part].lowerBound = (N / CORES)*part;
arg[part].upperBound = (N / CORES)*(part + 1);
}
And finally threaded SIMD version is called like this:
HANDLE handle[CORES];
for (int part = 0; part < CORES; part++)
{
handle[part] = (HANDLE)_beginthread(threadedSIMDMatMul, 0, (void*)&arg[part]);
}
for (int part = 0; part < CORES; part++)
{
WaitForSingleObject(handle[part], INFINITE);
}
The result is as follows:
Test 1:
// arrays are defined as follow
float A[N][N];
float B[N][N];
float X[N][N];
N=2048
Core=1//just one thread
Sequential time: 11129ms
Threaded SIMD matmul time: 14650ms
Speed up=0.75x
Test 2:
//defined arrays as follow
float **A = (float**)_aligned_malloc(N* sizeof(float), 16);
float **B = (float**)_aligned_malloc(N* sizeof(float), 16);
float **X = (float**)_aligned_malloc(N* sizeof(float), 16);
for (int k = 0; k < N; k++)
{
A[k] = (float*)malloc(cols * sizeof(float));
B[k] = (float*)malloc(cols * sizeof(float));
X[k] = (float*)malloc(cols * sizeof(float));
}
N=2048
Core=1//just one thread
Sequential time: 15907ms
Threaded SIMD matmul time: 18578ms
Speed up=0.85x
Test 3:
//defined arrays as follow
float A[N][N];
float B[N][N];
float X[N][N];
N=2048
Core=2
Sequential time: 10855ms
Threaded SIMD matmul time: 27967ms
Speed up=0.38x
Test 4:
//defined arrays as follow
float **A = (float**)_aligned_malloc(N* sizeof(float), 16);
float **B = (float**)_aligned_malloc(N* sizeof(float), 16);
float **X = (float**)_aligned_malloc(N* sizeof(float), 16);
for (int k = 0; k < N; k++)
{
A[k] = (float*)malloc(cols * sizeof(float));
B[k] = (float*)malloc(cols * sizeof(float));
X[k] = (float*)malloc(cols * sizeof(float));
}
N=2048
Core=2
Sequential time: 16579ms
Threaded SIMD matmul time: 30160ms
Speed up=0.51x
My question: why I don’t get speed up?

Answer 1

Here are the times I get building on your algorithm on my four core i7 IVB processor.
sequential: 3.42 s
4 threads: 0.97 s
4 threads + SSE: 0.86 s
Here are the times on a 2 core P9600 #2.53 GHz which is similar to the OP's E2200 #2.2 GHz
sequential: time 6.52 s
2 threads: time 3.66 s
2 threads + SSE: 3.75 s
I used OpenMP because it makes this easy. Each thread in OpenMP runs over effectively
lowerBound = N*part/CORES;
upperBound = N*(part + 1)/CORES;
(note that that is slightly different than your definition. Your definition can give the wrong result due to rounding for some values of N since you divide by CORES first.)
As to the SIMD version. It's not much faster probably due it being memory bandwidth bound . It's probably not really faster because GCC already vectroizes the loop.
The most optimal solution is much more complicated. You need to use loop tiling and reorder the elements within tiles to get the optimal performance. I don't have time to do that today.
Here is the code I used:
//c99 -O3 -fopenmp -Wall foo.c
#include <stdio.h>
#include <string.h>
#include <x86intrin.h>
#include <omp.h>
void gemm(float * restrict a, float * restrict b, float * restrict c, int n) {
for(int i=0; i<n; i++) {
for(int k=0; k<n; k++) {
for(int j=0; j<n; j++) {
c[i*n+j] += a[i*n+k]*b[k*n+j];
}
}
}
}
void gemm_tlp(float * restrict a, float * restrict b, float * restrict c, int n) {
#pragma omp parallel for
for(int i=0; i<n; i++) {
for(int k=0; k<n; k++) {
for(int j=0; j<n; j++) {
c[i*n+j] += a[i*n+k]*b[k*n+j];
}
}
}
}
void gemm_tlp_simd(float * restrict a, float * restrict b, float * restrict c, int n) {
#pragma omp parallel for
for(int i=0; i<n; i++) {
for(int k=0; k<n; k++) {
__m128 a4 = _mm_set1_ps(a[i*n+k]);
for(int j=0; j<n; j+=4) {
__m128 c4 = _mm_load_ps(&c[i*n+j]);
__m128 b4 = _mm_load_ps(&b[k*n+j]);
c4 = _mm_add_ps(_mm_mul_ps(a4,b4),c4);
_mm_store_ps(&c[i*n+j], c4);
}
}
}
}
int main(void) {
int n = 2048;
float *a = _mm_malloc(n*n * sizeof *a, 64);
float *b = _mm_malloc(n*n * sizeof *b, 64);
float *c1 = _mm_malloc(n*n * sizeof *c1, 64);
float *c2 = _mm_malloc(n*n * sizeof *c2, 64);
float *c3 = _mm_malloc(n*n * sizeof *c2, 64);
for(int i=0; i<n*n; i++) a[i] = 1.0*i;
for(int i=0; i<n*n; i++) b[i] = 1.0*i;
memset(c1, 0, n*n * sizeof *c1);
memset(c2, 0, n*n * sizeof *c2);
memset(c3, 0, n*n * sizeof *c3);
double dtime;
dtime = -omp_get_wtime();
gemm(a,b,c1,n);
dtime += omp_get_wtime();
printf("time %f\n", dtime);
dtime = -omp_get_wtime();
gemm_tlp(a,b,c2,n);
dtime += omp_get_wtime();
printf("time %f\n", dtime);
dtime = -omp_get_wtime();
gemm_tlp_simd(a,b,c3,n);
dtime += omp_get_wtime();
printf("time %f\n", dtime);
printf("error %d\n", memcmp(c1,c2, n*n*sizeof *c1));
printf("error %d\n", memcmp(c1,c3, n*n*sizeof *c1));
}

Answer 2

It looks to me that the threads are sharing __m128 mmx* variables, you probably defined them global/static. You must be getting wrong results in your X array too. Define __m128 mmx* variables inside threadedSIMDMatMul function scope and it will run much faster.
void threadedSIMDMatMul(void* params)
{
__m128 mmx0, mmx1, mmx2, mmx3, mmx4;
// rest of the code here
}