Parallelizing the Gaussian Blur Algorithm with OpenMP - openmp

Question

I was trying to parallelize the gaussian blur function using OpenMP,
but I am new at OpenMP, and when I tried to parallelize the two for loops (I don't think there are any variables that need to be private for each thread), it ended up
running even slower than before, and the output was different. So did I do anything wrong? What should I do to make it run faster?
void gaussian_blur(float **src, float **dst, int w, int h, float sigma)
{
int x, y, i;
int ksize = (int)(sigma * 2.f * 4.f + 1) | 1;
int halfk = ksize / 2;
float scale = -0.5f/(sigma*sigma);
float sum = 0.f;
float *kernel, *ringbuf;
int xmax = w - halfk;
int ymax = h - halfk;
// if sigma too small, just copy src to dst
if (ksize <= 1)
{
for (y = 0; y < h; y++)
for (x = 0; x < w; x++)
dst[y][x] = src[y][x];
return;
}
// create Gaussian kernel
kernel = malloc(ksize * sizeof(float));
ringbuf = malloc(ksize * sizeof(float));
#pragma omp parallel for reduction(+ : sum)
for (i = 0; i < ksize; i++)
{
float x = (float)(i - halfk);
float t = expf(scale * x * x);
kernel[i] = t;
sum += t;
}
scale = 1.f / sum;
#pragma omp parallel for
for (i = 0; i < ksize; i++)
kernel[i] *= scale;
// blur each row
#pragma omp parallel for // this is the for loop I parallelized but ended up with wrong output and running slower
for (y = 0; y < h; y++)
{
int x1;
int bufi0 = ksize-1;
float tmp = src[y][0];
for (x1 = 0; x1 < halfk ; x1++) ringbuf[x1] = tmp;
for (; x1 < ksize-1; x1++) ringbuf[x1] = src[y][x1-halfk];
for (x1 = 0; x1 < w; x1++)
{
if(x1 < xmax)
ringbuf[bufi0++] = src[y][x1+halfk];
else
ringbuf[bufi0++] = src[y][w-1];
if (bufi0 == ksize) bufi0 = 0;
dst[y][x1] = convolve(kernel, ringbuf, ksize, bufi0);
}
}
// blur each column
#pragma omp parallel for // this is the for loop I parallelized but ended up with wrong output and running slower
for (x = 0; x < w; x++)
{
int y1;
int bufi0 = ksize-1;
float tmp = dst[0][x];
for (y1 = 0; y1 < halfk ; y1++) ringbuf[y1] = tmp;
for ( ; y1 < ksize-1; y1++) ringbuf[y1] = dst[y1-halfk][x];
for (y1 = 0; y1 < h; y1++)
{
if(y1 < ymax)
ringbuf[bufi0++] = dst[y1+halfk][x];
else
ringbuf[bufi0++] = dst[h-1][x];
if (bufi0 == ksize) bufi0 = 0;
dst[y1][x] = convolve(kernel, ringbuf, ksize, bufi0);
}
}
// clean up
free(kernel);
free(ringbuf);
}

Answer 1

Besides the need to properly identify private and shared data, there are several things that you could do in order to speed up your program.
As a first step you should remove any unnecessary concurrency. For example, how big ksize happens to be on average? If it is less than several hundred elements, it makes absolutely no sense to employ OpenMP for such simple operations as computing the kernel and then normalising it:
#pragma omp parallel for reduction(+ : sum)
for (i = 0; i < ksize; i++)
{
float x = (float)(i - halfk);
float t = expf(scale * x * x);
kernel[i] = t;
sum += t;
}
scale = 1.f / sum;
#pragma omp parallel for
for (i = 0; i < ksize; i++)
kernel[i] *= scale;
On a typical modern CPU it would take more cycles to bootstrap the parallel regions than to compute this on a single core. Also on modern CPUs these loops can be unrolled and vectorised and you can get up to 8x boost on a single core. If the kernel is too small, then besides OpenMP overhead you will also get slowdown from excessive false sharing. You have to make sure that each thread gets an exact multiple of 16 elements (64 bytes of cache line size / sizeof(float)) to work on in order to prevent false sharing.
You also have to make sure that threads do not share cache lines in the column blur section.
// blur each column
#pragma omp parallel for
for (x = 0; x < w; x++)
{
...
for (y1 = 0; y1 < h; y1++)
{
...
dst[y1][x] = convolve(kernel, ringbuf, ksize, bufi0);
}
}
Because of the access pattern here, you have to make sure that each thread gets a chunk of columns that is a multiple of 16 or else there will be a border overlap area of 16*y1 pixels shared by every two consecutive threads where excessive false sharing will occur. If you cannot guarantee that w is divisible by 16, then you can give each thread a starting offset in the y direction, e.g. the innermost loop becomes:
int tid = omp_get_thread_num();
for (y1 = 2*tid; y1 < h; y1++)
{
...
}
for (y1 = 0; y1 < 2*tid; y1++)
{
...
}
The multiplier 2 is arbitrary. The idea is to give the next thread several rows of advance in comparison to the current one so that both threads will not be processing the same line at once at any moment in time. You could also use addition and modulo arithmetic to compute y1, i.e.
for (y2 = 0; y2 < h; y2++)
{
y1 = (y2 + 2*tid) % h;
...
}
but this is generally slower than just separating the loop in two parts.
Also mind your data size. The last level cache (LLC) has very high but still limited bandwidth. If data cannot fit in the private cache of each core then compiler optimisations such as loop vectorisations can put very high pressure on the LLC. Things get more ugly if data doesn't fit in the LLC and therefore the main memory has to be accessed.
If you don't know what false sharing is, there is an article in Dr.Dobb's that kind of explains it here.

Answer 2

I may have fixed your code. You did not post your convolve function so it's difficult to say for sure but I'm not sure it matters. There are at least two bugs. There is a race condition in the ringbuf array. To fix this I extend the array times the number of threads.
ringbuf = (float*)malloc(nthreads*ksize * sizeof(float));
To access the array do something like this
int ithread = omp_get_thread_num();
ringbuf[ksize*ithread + x1]
Edit: I added some code which defines ringbuf inside the parallel block. That way you don't have to access ringbuf based on the thread number.
The second errors is the ibufi0 variable. I defined a new one like this
const int ibufi0_fix = (x1+ksize-1)%ksize;
Below is the code I used to check it. Replace with your convolve function. Note, this may still be quite inefficient. There are probably cache issues such as cache misses and false sharing (particularly when you convolve vertically). Hopefully, though, the image will be correct now.
Edit: here is a paper by Intel that shows how to do this best with AVX. It's optimized to minimize the cache misses. I'm not sure it's optimized for threading though.
http://software.intel.com/en-us/articles/iir-gaussian-blur-filter-implementation-using-intel-advanced-vector-extensions
I'm writing my own function on this (it's actually the reason I started learning OpenMP) which uses SSE/AVX as well. There are a lot of similarities with matrix multiplication and image filtering so I learned how to optimized matrix multiplication first and will do Gaussian Blur shortly...
#include "math.h"
#include "omp.h"
#include "stdio.h"
#include <nmmintrin.h>
float convolve(const float *kernel, const float *ringbuf, const int ksize, const int bufi0) {
float sum = 0.0f;
for(int i=0; i<ksize; i++) {
sum += kernel[i]*ringbuf[i];
}
return sum;
}
void gaussian_blur(float *src, float *dst, int w, int h, float sigma, int nthreads)
{
int x, y, i;
int ksize = (int)(sigma * 2.f * 4.f + 1) | 1;
int halfk = ksize / 2;
printf("ksize %d\n", ksize);
float scale = -0.5f/(sigma*sigma);
float sum = 0.f;
float *kernel, *ringbuf;
int xmax = w - halfk;
int ymax = h - halfk;
// if sigma too small, just copy src to dst
if (ksize <= 1)
{
for (y = 0; y < h; y++)
for (x = 0; x < w; x++)
dst[y*w + x] = src[y*w + x];
return;
}
// create Gaussian kernel
//kernel = malloc(ksize * sizeof(float));
kernel = (float*)_mm_malloc(ksize * sizeof(float),16);
//ringbuf = malloc(ksize * sizeof(float));
ringbuf = (float*)_mm_malloc(nthreads*ksize * sizeof(float),16);
#pragma omp parallel for reduction(+ : sum) if(nthreads>1)
for (i = 0; i < ksize; i++)
{
float x = (float)(i - halfk);
float t = expf(scale * x * x);
kernel[i] = t;
sum += t;
}
scale = 1.f / sum;
#pragma omp parallel for if(nthreads>1)
for (i = 0; i < ksize; i++)
kernel[i] *= scale;
// blur each row
#pragma omp parallel for if(nthreads>1)// this is the for loop I parallelized but ended up with wrong output and running slower
for (y = 0; y < h; y++)
{
int ithread = omp_get_thread_num();
//printf("nthread %d\n", nthread);
int x1;
int bufi0 = ksize-1;
float tmp = src[y*w + 0];
for (x1 = 0; x1 < halfk ; x1++) ringbuf[ksize*ithread + x1] = tmp;
for (; x1 < ksize-1; x1++) ringbuf[ksize*ithread + x1] = src[y*w + x1-halfk];
for (x1 = 0; x1 < w; x1++)
{
const int ibufi0_fix = (x1+ksize-1)%ksize;
if(x1 < xmax)
ringbuf[ksize*ithread + ibufi0_fix] = src[y*w + x1+halfk];
else
ringbuf[ksize*ithread + ibufi0_fix] = src[y*w + w-1];
if (bufi0 == ksize) bufi0 = 0;
dst[y*w + x1] = convolve(kernel, &ringbuf[ksize*ithread], ksize, bufi0);
}
}
// blur each column
#pragma omp parallel for if(nthreads>1)// this is the for loop I parallelized but ended up with wrong output and running slower
for (x = 0; x < w; x++)
{
int ithread = omp_get_thread_num();
int y1;
int bufi0 = ksize-1;
float tmp = dst[0*w + x];
for (y1 = 0; y1 < halfk ; y1++) ringbuf[ksize*ithread + y1] = tmp;
for ( ; y1 < ksize-1; y1++) ringbuf[ksize*ithread + y1] = dst[(y1-halfk)*w + x];
for (y1 = 0; y1 < h; y1++)
{
const int ibufi0_fix = (y1+ksize-1)%ksize;
if(y1 < ymax)
ringbuf[ibufi0_fix] = dst[(y1+halfk)*w + x];
else
ringbuf[ibufi0_fix] = dst[(h-1)*w + x];
if (bufi0 == ksize) bufi0 = 0;
dst[y1*w + x] = convolve(kernel, &ringbuf[ksize*ithread], ksize, bufi0);
}
}
// clean up
_mm_free(kernel);
_mm_free(ringbuf);
}
int compare(float *dst1, float *dst2, const int n) {
int error = 0;
for(int i=0; i<n; i++) {
if(*dst1 != *dst2) error++;
}
return error;
}
int main() {
const int w = 20;
const int h = 20;
float *src = (float*)_mm_malloc(w*h*sizeof(float),16);
float *dst1 = (float*)_mm_malloc(w*h*sizeof(float),16);
float *dst2 = (float*)_mm_malloc(w*h*sizeof(float),16);
for(int i=0; i<w*h; i++) {
src[i] = i;
}
gaussian_blur(src, dst1, w, h, 1.0f, 1);
gaussian_blur(src, dst2, w, h, 1.0f, 4);
int error = compare(dst1, dst2, w*h);
printf("error %d\n", error);
_mm_free(src);
_mm_free(dst1);
_mm_free(dst2);
}
Edit: here is code which defines ringbuf inside the parallel block based on the comment by Hristo. It should be equivalent.
#include "math.h"
#include "omp.h"
#include "stdio.h"
#include <nmmintrin.h>
float convolve(const float *kernel, const float *ringbuf, const int ksize, const int bufi0) {
float sum = 0.0f;
for(int i=0; i<ksize; i++) {
sum += kernel[i]*ringbuf[i];
}
return sum;
}
void gaussian_blur(float *src, float *dst, int w, int h, float sigma, int nthreads)
{
int x, y, i;
int ksize = (int)(sigma * 2.f * 4.f + 1) | 1;
int halfk = ksize / 2;
printf("ksize %d\n", ksize);
float scale = -0.5f/(sigma*sigma);
float sum = 0.f;
float *kernel;
int xmax = w - halfk;
int ymax = h - halfk;
// if sigma too small, just copy src to dst
if (ksize <= 1)
{
for (y = 0; y < h; y++)
for (x = 0; x < w; x++)
dst[y*w + x] = src[y*w + x];
return;
}
// create Gaussian kernel
//kernel = malloc(ksize * sizeof(float));
kernel = (float*)_mm_malloc(ksize * sizeof(float),16);
#pragma omp parallel for reduction(+ : sum) if(nthreads>1)
for (i = 0; i < ksize; i++)
{
float x = (float)(i - halfk);
float t = expf(scale * x * x);
kernel[i] = t;
sum += t;
}
scale = 1.f / sum;
#pragma omp parallel for if(nthreads>1)
for (i = 0; i < ksize; i++)
kernel[i] *= scale;
// blur each row
//#pragma omp parallel for if(nthreads>1)// this is the for loop I parallelized but ended up with wrong output and running slower
#pragma omp parallel if(nthreads>1)
{
float *ringbuf = (float*)_mm_malloc(ksize * sizeof(float),16);
#pragma omp for// this is the for loop I parallelized but ended up with wrong output and running slower
for (y = 0; y < h; y++)
{
//printf("nthread %d\n", nthread);
int x1;
int bufi0 = ksize-1;
float tmp = src[y*w + 0];
for (x1 = 0; x1 < halfk ; x1++) ringbuf[x1] = tmp;
for (; x1 < ksize-1; x1++) ringbuf[x1] = src[y*w + x1-halfk];
for (x1 = 0; x1 < w; x1++)
{
const int ibufi0_fix = (x1+ksize-1)%ksize;
if(x1 < xmax)
ringbuf[ibufi0_fix] = src[y*w + x1+halfk];
else
ringbuf[ibufi0_fix] = src[y*w + w-1];
if (bufi0 == ksize) bufi0 = 0;
dst[y*w + x1] = convolve(kernel, ringbuf, ksize, bufi0);
}
}
_mm_free(ringbuf);
}
// blur each column
#pragma omp parralel if(ntheads>1)
{
float *ringbuf = (float*)_mm_malloc(ksize * sizeof(float),16);
#pragma omp for// this is the for loop I parallelized but ended up with wrong output and running slower
for (x = 0; x < w; x++)
{
int y1;
int bufi0 = ksize-1;
float tmp = dst[0*w + x];
for (y1 = 0; y1 < halfk ; y1++) ringbuf[y1] = tmp;
for ( ; y1 < ksize-1; y1++) ringbuf[y1] = dst[(y1-halfk)*w + x];
for (y1 = 0; y1 < h; y1++)
{
const int ibufi0_fix = (y1+ksize-1)%ksize;
if(y1 < ymax)
ringbuf[ibufi0_fix] = dst[(y1+halfk)*w + x];
else
ringbuf[ibufi0_fix] = dst[(h-1)*w + x];
if (bufi0 == ksize) bufi0 = 0;
dst[y1*w + x] = convolve(kernel, ringbuf, ksize, bufi0);
}
}
_mm_free(ringbuf);
}
// clean up
_mm_free(kernel);
}
int compare(float *dst1, float *dst2, const int n) {
int error = 0;
for(int i=0; i<n; i++) {
if(*dst1 != *dst2) error++;
}
return error;
}
int main() {
const int w = 20;
const int h = 20;
float *src = (float*)_mm_malloc(w*h*sizeof(float),16);
float *dst1 = (float*)_mm_malloc(w*h*sizeof(float),16);
float *dst2 = (float*)_mm_malloc(w*h*sizeof(float),16);
for(int i=0; i<w*h; i++) {
src[i] = i;
}
gaussian_blur(src, dst1, w, h, 1.0f, 1);
gaussian_blur(src, dst2, w, h, 1.0f, 4);
int error = compare(dst1, dst2, w*h);
printf("error %d\n", error);
_mm_free(src);
_mm_free(dst1);
_mm_free(dst2);
}