How to find if I have a memory leak - c++

I wrote a number crunching algorithm. The idea is that:
A small main programs needs very few memory (starts at 2 MB)
Then, in a loop, it calls a function that needs quite some memory (around 100 MB) which should be released when the function end. In order to understand what's going on, the function is now always called with the same parameters.
It seems that the program slowly eats memory so I suspect a memory leak. I have tried Address Sanitizer from Clang and Pointer Checker from Intel but they don't find anything.
Now, I am looking at the memory consumption in my Activity Monitor (I am running OSX, but I get the same memory usage from the Unix command "top") and just before the big function is called, the program takes 2 MB. When running the function, the program takes 120 MB. What is strange is that when the program ends up the big function and comes back inside the loop, it now takes 37 MB! Then, when it goes back into the big function, it takes 130 MB. Again, coming back in the loop, it takes 36 MB, then in the big function it takes 140 MB...
So it is slowly drifting away, but not with a regular pattern. How should I trust the memory usage in "top"?
Can memory fragmentation increase the memory usage without memory leak?
I let the program run overnight, and here is the data I get:
In the first loop, the program takes 150 MB
2 hours later, after 68 loops, the program takes 220 MB
After one night and 394 loops, the program takes 480 MB
So it seems that the function that allocates and deallocates memory (about 120 MB) seems to "leak" 1 MB each time it is called.

First, make sure that over a long period of time (for example if one iteration takes a minute, run a couple hours) the growth continues. If the growths asyptotes then there's no problem. Next I would try valgrind. Then if that doesn't help, you'll have to binary search your code: Comment out bits until the growth stops. I would start by totally removing use of the MKL library (leave stubs if you want to) and see what happens. Next, change your vector to std::vector just to see if that helps it. After that you'll have to use your judgment.

I think that I have found the culprit: the MKL (the latest version as of today). I use Pardiso, and the following example leaks very slowly: about 0.1 MB every 13 seconds which leads to 280 MB overnight. These are the numbers I get from my simulation.
If you want to give it a try, you can compile it with:
icpc -std=c++11 pardiso-leak.cpp -o main -lmkl_intel_lp64 -lmkl_core -lmkl_intel_thread -liomp5 -ldl -lpthread -lm
Thanks everyone for your help. I have reported the bug to Intel.
#include <iostream>
#include <vector>
#include "mkl_pardiso.h"
#include "mkl_types.h"
int main (int argc, char const *argv[])
{
const auto n = std::size_t{1000};
auto m = MKL_INT{n * n};
auto values = std::vector<double>();
auto column = std::vector<MKL_INT>();
auto row = std::vector<MKL_INT>();
row.push_back(1);
for(std::size_t j = 0; j < n; ++j) {
column.push_back(j + 1);
values.push_back(1.0);
column.push_back(j + n + 1);
values.push_back(0.1);
row.push_back(column.size() + 1);
}
for(std::size_t i = 1; i < n - 1; ++i) {
for(std::size_t j = 0; j < n; ++j) {
column.push_back(n * i + j - n + 1);
values.push_back(0.1);
column.push_back(n * i + j + 1);
values.push_back(1.0);
column.push_back(n * i + j + n + 1);
values.push_back(0.1);
row.push_back(column.size() + 1);
}
}
for(std::size_t j = 0; j < n; ++j) {
column.push_back((n - 1) * n + j - n + 1);
values.push_back(0.1);
column.push_back((n - 1) * n + j + 1);
values.push_back(1.0);
row.push_back(column.size() + 1);
}
auto y = std::vector<double>(m, 1.0);
auto x = std::vector<double>(m, 0.0);
auto pardiso_nrhs = MKL_INT{1};
auto pardiso_max_fact = MKL_INT{1};
auto pardiso_mnum = MKL_INT{1};
auto pardiso_mtype = MKL_INT{11};
auto pardiso_msglvl = MKL_INT{0};
MKL_INT pardiso_iparm[64];
for (int i = 0; i < 64; ++i) {
pardiso_iparm[i] = 0;
}
pardiso_iparm[0] = 1;
pardiso_iparm[1] = 2;
pardiso_iparm[3] = 0;
pardiso_iparm[4] = 0;
pardiso_iparm[5] = 0;
pardiso_iparm[7] = 0;
pardiso_iparm[8] = 0;
pardiso_iparm[9] = 13;
pardiso_iparm[10] = 1;
pardiso_iparm[11] = 0;
pardiso_iparm[12] = 1;
pardiso_iparm[17] = -1;
pardiso_iparm[18] = 0;
pardiso_iparm[20] = 0;
pardiso_iparm[23] = 1;
pardiso_iparm[24] = 0;
pardiso_iparm[26] = 0;
pardiso_iparm[27] = 0;
pardiso_iparm[30] = 0;
pardiso_iparm[31] = 0;
pardiso_iparm[32] = 0;
pardiso_iparm[33] = 0;
pardiso_iparm[34] = 0;
pardiso_iparm[59] = 0;
pardiso_iparm[60] = 0;
pardiso_iparm[61] = 0;
pardiso_iparm[62] = 0;
pardiso_iparm[63] = 0;
void* pardiso_pt[64];
for (int i = 0; i < 64; ++i) {
pardiso_pt[i] = nullptr;
}
auto error = MKL_INT{0};
auto phase = MKL_INT{11};
MKL_INT i_dummy;
double d_dummy;
PARDISO(pardiso_pt, &pardiso_max_fact, &pardiso_mnum, &pardiso_mtype,
&phase, &m, values.data(), row.data(), column.data(), &i_dummy,
&pardiso_nrhs, pardiso_iparm, &pardiso_msglvl, &d_dummy,
&d_dummy, &error);
phase = 22;
PARDISO(pardiso_pt, &pardiso_max_fact, &pardiso_mnum, &pardiso_mtype,
&phase, &m, values.data(), row.data(), column.data(), &i_dummy,
&pardiso_nrhs, pardiso_iparm, &pardiso_msglvl, &d_dummy,
&d_dummy, &error);
phase = 33;
for(size_t i = 0; i < 10000; ++i) {
std::cout << "i = " << i << std::endl;
PARDISO(pardiso_pt, &pardiso_max_fact, &pardiso_mnum, &pardiso_mtype,
&phase, &m, values.data(), row.data(), column.data(), &i_dummy,
&pardiso_nrhs, pardiso_iparm, &pardiso_msglvl, y.data(),
x.data(), &error);
}
phase = -1;
PARDISO(pardiso_pt, &pardiso_max_fact, &pardiso_mnum, &pardiso_mtype,
&phase, &m, values.data(), row.data(), column.data(), &i_dummy,
&pardiso_nrhs, pardiso_iparm, &pardiso_msglvl, &d_dummy,
&d_dummy, &error);
return 0;
}

Related

Loops optimization

I have a loop and inside a have a inner loop. How can I optimise it please in order to optimise execution time like avoiding accessing to memory many times to the same thing and avoid the maximum possible the addition and multiplication.
int n,m,x1,y1,x2,y2,cnst;
int N = 9600;
int M = 1800;
int temp11,temp12,temp13,temp14;
int temp21,temp22,temp23,temp24;
int *arr1 = new int [32000]; // suppose it's already filled
int *arr2 = new int [32000];// suppose it's already filled
int sumFirst = 0;
int maxFirst = 0;
int indexFirst = 0;
int sumSecond = 0;
int maxSecond = 0;
int indexSecond = 0;
int jump = 2400;
for( n = 0; n < N; n++)
{
temp14 = 0;
temp24 = 0;
for( m = 0; m < M; m++)
{
x1 = m + cnst;
y1 = m + n + cnst;
temp11 = arr1[x1];
temp12 = arr2[y1];
temp13 = temp11 * temp12;
temp14+= temp13;
x2 = m + cnst + jump;
y2 = m + n + cnst + jump;
temp21 = arr1[x2];
temp22 = arr2[y2];
temp23 = temp21 * temp22;
temp24+= temp23;
}
sumFirst += temp14;
if (temp14 > maxFirst)
{
maxFirst = temp14;
indexFirst = m;
}
sumSecond += temp24;
if (temp24 > maxSecond)
{
maxSecond = temp24;
indexSecond = n;
}
}
// At the end we use sum , index and max for first and second;
You are multiplying array elements and accumulating the result.
This can be optimized by:
SIMD (doing multiple operations at a single CPU step)
Parallel execution (using multiple physical/logical CPUs at once)
Look for CPU-specific SIMD way of doing this. Like _mm_mul_epi32 from SSE4.1 can possibly be used on x86-64. Before trying to write your own SIMD version with compiler intrinsics, make sure the compiler doesn't do it already for you.
As for parallel execution, look into omp, or using C++17 parallel accumulate.

Multiple threads taking more time than single process [duplicate]

This question already has answers here:
C: using clock() to measure time in multi-threaded programs
(2 answers)
Closed 2 years ago.
I am implementing pattern matching algorithm, by moving template gradient info over entire target's gradient image , that too at each rotation (-60 to 60). I have already saved the template info for each rotation ,i.e. 121 templates are already preprocessed and saved.
But the issue is, this is consuming lot of time (approx 110ms), so decided to split the matching at set of rotations (-60 to -30 , -30 to 0, 0 to 30 and 30 to 60) into 4 threads, but threading is taking more time that single process (approx 115ms to 120ms).
Snippet of code is...
#define MAXTARGETNUM 64
MatchResultA totalResultsTemp[MAXTARGETNUM];
void CShapeMatch::match(ShapeInfo *ShapeInfoVec, search_region SearchRegion, float MinScore, float Greediness, int width,int height, int16_t *pBufGradX ,int16_t *pBufGradY,float *pBufMag, bool corr)
{
MatchResultA resultsPerDeg[MAXTARGETNUM];
....
....
int startX = SearchRegion.StartX;
int startY = SearchRegion.StartY;
int endX = SearchRegion.EndX;
int endY = SearchRegion.EndY;
float AngleStep = SearchRegion.AngleStep;
float AngleStart = SearchRegion.AngleStart;
float AngleStop = SearchRegion.AngleStop;
int startIndex = (int)(ShapeInfoVec[0].AngleNum/2) + ShapeInfoVec[0].AngleNum%2+(int)AngleStart/AngleStep;
int stopIndex = (int)(ShapeInfoVec[0].AngleNum/2) + ShapeInfoVec[0].AngleNum%2+(int)AngleStop/AngleStep;
for (int k = startIndex; k < stopIndex ; k++){
....
for(int j = startY; j < endY; j++){
for(int i = startX; i < endX; i++){
for(int m = 0; m < ShapeInfoVec[k].NoOfCordinates; m++)
{
curX = i + (ShapeInfoVec[k].Coordinates + m)->x; // template X coordinate
curY = j + (ShapeInfoVec[k].Coordinates + m)->y ; // template Y coordinate
iTx = *(ShapeInfoVec[k].EdgeDerivativeX + m); // template X derivative
iTy = *(ShapeInfoVec[k].EdgeDerivativeY + m); // template Y derivative
iTm = *(ShapeInfoVec[k].EdgeMagnitude + m); // template gradients magnitude
if(curX < 0 ||curY < 0||curX > width-1 ||curY > height-1)
continue;
offSet = curY*width + curX;
iSx = *(pBufGradX + offSet); // get corresponding X derivative from source image
iSy = *(pBufGradY + offSet); // get corresponding Y derivative from source image
iSm = *(pBufMag + offSet);
if (PartialScore > MinScore)
{
float Angle = ShapeInfoVec[k].Angel;
bool hasFlag = false;
for(int n = 0; n < resultsNumPerDegree; n++)
{
if(abs(resultsPerDeg[n].CenterLocX - i) < 5 && abs(resultsPerDeg[n].CenterLocY - j) < 5)
{
hasFlag = true;
if(resultsPerDeg[n].ResultScore < PartialScore)
{
resultsPerDeg[n].Angel = Angle;
resultsPerDeg[n].CenterLocX = i;
resultsPerDeg[n].CenterLocY = j;
resultsPerDeg[n].ResultScore = PartialScore;
break;
}
}
}
if(!hasFlag)
{
resultsPerDeg[resultsNumPerDegree].Angel = Angle;
resultsPerDeg[resultsNumPerDegree].CenterLocX = i;
resultsPerDeg[resultsNumPerDegree].CenterLocY = j;
resultsPerDeg[resultsNumPerDegree].ResultScore = PartialScore;
resultsNumPerDegree ++;
}
minScoreTemp = minScoreTemp < PartialScore ? PartialScore : minScoreTemp;
}
}
}
for(int i = 0; i < resultsNumPerDegree; i++)
{
mtx.lock();
totalResultsTemp[totalResultsNum] = resultsPerDeg[i];
totalResultsNum++;
mtx.unlock();
}
n++;
}
void CallerFunction(){
int16_t *pBufGradX = (int16_t *) malloc(bufferSize * sizeof(int16_t));
int16_t *pBufGradY = (int16_t *) malloc(bufferSize * sizeof(int16_t));
float *pBufMag = (float *) malloc(bufferSize * sizeof(float));
clock_t start = clock();
float temp_stop = SearchRegion->AngleStop;
SearchRegion->AngleStop = -30;
thread t1(&CShapeMatch::match, this, ShapeInfoVec, *SearchRegion, MinScore, Greediness, width, height, pBufGradX ,pBufGradY,pBufMag, corr);
SearchRegion->AngleStart = -30;
SearchRegion->AngleStop=0;
thread t2(&CShapeMatch::match, this, ShapeInfoVec, *SearchRegion, MinScore, Greediness, width, height, pBufGradX ,pBufGradY,pBufMag, corr);
SearchRegion->AngleStart = 0;
SearchRegion->AngleStop=30;
thread t3(&CShapeMatch::match, this, ShapeInfoVec, *SearchRegion, MinScore, Greediness,width, height, pBufGradX ,pBufGradY,pBufMag, corr);
SearchRegion->AngleStart = 30;
SearchRegion->AngleStop=temp_stop;
thread t4(&CShapeMatch::match, this, ShapeInfoVec, *SearchRegion, MinScore, Greediness,width, height, pBufGradX ,pBufGradY,pBufMag, corr);
t1.join();
t2.join();
t3.join();
t4.join();
clock_t end = clock();
cout << 1000*(double)(end-start)/CLOCKS_PER_SEC << endl;
}
As we can see there are plenty of heap access but they just are read-only. Only totalResultTemp and totalResultNum are shared global resource on which write are performed.
My PC configuration is,
i5-7200U CPU # 2.50GHz 4 cores
4 Gig RAM
Ubuntu 18
for(int i = 0; i < resultsNumPerDegree; i++)
{
mtx.lock();
totalResultsTemp[totalResultsNum] = resultsPerDeg[i];
totalResultsNum++;
mtx.unlock();
}
You writing into static array, and mutexes are really time consuming. Instead of creating locks try to use std::atomic_int, or in my opinion even better, just pass to function exact place where to store result, so problem with sync is not your problem anymore
POSIX Threads in c/c++ are not concurrent since the time assigned by the operative system to each parent process must be split into the number of threads it has. Thus, your algorithm is executing only core. To leverage multicore technology, you must use OpenMP. This interface library let you split your algorithm in different physic cores. This is a good OpenMP tutorial

I would like to improve the performance of this code using AVX

I profiled my code and the most expensive part of the code is the loop included in the post. I want to improve the performance of this loop using AVX. I have tried manually unrolling the loop and, while that does improve performance, the improvements are not satisfactory.
int N = 100000000;
int8_t* data = new int8_t[N];
for(int i = 0; i< N; i++) { data[i] = 1 ;}
std::array<float, 10> f = {1,2,3,4,5,6,7,8,9,10};
std::vector<float> output(N, 0);
int k = 0;
for (int i = k; i < N; i = i + 2) {
for (int j = 0; j < 10; j++, k = j + 1) {
output[i] += f[j] * data[i - k];
output[i + 1] += f[j] * data[i - k + 1];
}
}
Could I have some guidance on how to approach this.
I would assume that data is a large input array of signed bytes, and f is a small array of floats of length 10, and output is the large output array of floats. Your code goes out of bounds for the first 10 iterations by i, so I will start i from 10 instead. Here is a clean version of the original code:
int s = 10;
for (int i = s; i < N; i += 2) {
for (int j = 0; j < 10; j++) {
output[i] += f[j] * data[i-j-1];
output[i+1] += f[j] * data[i-j];
}
}
As it turns out, processing two iterations by i does not change anything, so we simplify it further to:
for (int i = s; i < N; i++)
for (int j = 0; j < 10; j++)
output[i] += f[j] * data[i-j-1];
This version of code (along with declarations of input/output data) should have been present in the question itself, without others having to clean/simplify the mess.
Now it is obvious that this code applies one-dimensional convolution filter, which is a very common thing in signal processing. For instance, it can by computed in Python using numpy.convolve function. The kernel has very small length 10, so Fast Fourier Transform won't provide any benefits compared to bruteforce approach. Given that the problem is well-known, you can read a lot of articles on vectorizing small-kernel convolution. I will follow the article by hgomersall.
First, let's get rid of reverse indexing. Obviously, we can reverse the kernel before running the main algorithm. After that, we have to compute the so-called cross-correlation instead of convolution. In simple words, we move the kernel array along the input array, and compute the dot product between them for every possible offset.
std::reverse(f.data(), f.data() + 10);
for (int i = s; i < N; i++) {
int b = i-10;
float res = 0.0;
for (int j = 0; j < 10; j++)
res += f[j] * data[b+j];
output[i] = res;
}
In order to vectorize it, let's compute 8 consecutive dot products at once. Recall that we can pack eight 32-bit float numbers into one 256-bit AVX register. We will vectorize the outer loop by i, which means that:
The loop by i will be advanced by 8 every iteration.
Every value inside the outer loop turns into a 8-element pack, such that k-th element of the pack holds this value for (i+k)-th iteration of the outer loop from the scalar version.
Here is the resulting code:
//reverse the kernel
__m256 revKernel[10];
for (size_t i = 0; i < 10; i++)
revKernel[i] = _mm256_set1_ps(f[9-i]); //every component will have same value
//note: you have to compute the last 16 values separately!
for (size_t i = s; i + 16 <= N; i += 8) {
int b = i-10;
__m256 res = _mm256_setzero_ps();
for (size_t j = 0; j < 10; j++) {
//load: data[b+j], data[b+j+1], data[b+j+2], ..., data[b+j+15]
__m128i bytes = _mm_loadu_si128((__m128i*)&data[b+j]);
//convert first 8 bytes of loaded 16-byte pack into 8 floats
__m256 floats = _mm256_cvtepi32_ps(_mm256_cvtepi8_epi32(bytes));
//compute res = res + floats * revKernel[j] elementwise
res = _mm256_fmadd_ps(revKernel[j], floats, res);
}
//store 8 values packed in res into: output[i], output[i+1], ..., output[i+7]
_mm256_storeu_ps(&output[i], res);
}
For 100 millions of elements, this code takes about 120 ms on my machine, while the original scalar implementation took 850 ms. Beware: I have Ryzen 1600 CPU, so results on Intel CPUs may be somewhat different.
Now if you really want to unroll something, the inner loop by 10 kernel elements is the perfect place. Here is how it is done:
__m256 revKernel[10];
for (size_t i = 0; i < 10; i++)
revKernel[i] = _mm256_set1_ps(f[9-i]);
for (size_t i = s; i + 16 <= N; i += 8) {
size_t b = i-10;
__m256 res = _mm256_setzero_ps();
#define DOIT(j) {\
__m128i bytes = _mm_loadu_si128((__m128i*)&data[b+j]); \
__m256 floats = _mm256_cvtepi32_ps(_mm256_cvtepi8_epi32(bytes)); \
res = _mm256_fmadd_ps(revKernel[j], floats, res); \
}
DOIT(0);
DOIT(1);
DOIT(2);
DOIT(3);
DOIT(4);
DOIT(5);
DOIT(6);
DOIT(7);
DOIT(8);
DOIT(9);
_mm256_storeu_ps(&output[i], res);
}
It takes 110 ms on my machine (slightly better that the first vectorized version).
The simple copy of all elements (with conversion from bytes to floats) takes 40 ms for me, which means that this code is not memory-bound yet, and there is still some room for improvement left.

C++ use SSE instructions for comparing huge vectors of ints

I have a huge vector<vector<int>> (18M x 128). Frequently I want to take 2 rows of this vector and compare them by this function:
int getDiff(int indx1, int indx2) {
int result = 0;
int pplus, pminus, tmp;
for (int k = 0; k < 128; k += 2) {
pplus = nodeL[indx2][k] - nodeL[indx1][k];
pminus = nodeL[indx1][k + 1] - nodeL[indx2][k + 1];
tmp = max(pplus, pminus);
if (tmp > result) {
result = tmp;
}
}
return result;
}
As you see, the function, loops through the two row vectors does some subtraction and at the end returns a maximum. This function will be used a million times, so I was wondering if it can be accelerated through SSE instructions. I use Ubuntu 12.04 and gcc.
Of course it is microoptimization but it would helpful if you could provide some help, since I know nothing about SSE. Thanks in advance
Benchmark:
int nofTestCases = 10000000;
vector<int> nodeIds(nofTestCases);
vector<int> goalNodeIds(nofTestCases);
vector<int> results(nofTestCases);
for (int l = 0; l < nofTestCases; l++) {
nodeIds[l] = randomNodeID(18000000);
goalNodeIds[l] = randomNodeID(18000000);
}
double time, result;
time = timestamp();
for (int l = 0; l < nofTestCases; l++) {
results[l] = getDiff2(nodeIds[l], goalNodeIds[l]);
}
result = timestamp() - time;
cout << result / nofTestCases << "s" << endl;
time = timestamp();
for (int l = 0; l < nofTestCases; l++) {
results[l] = getDiff(nodeIds[l], goalNodeIds[l]);
}
result = timestamp() - time;
cout << result / nofTestCases << "s" << endl;
where
int randomNodeID(int n) {
return (int) (rand() / (double) (RAND_MAX + 1.0) * n);
}
/** Returns a timestamp ('now') in seconds (incl. a fractional part). */
inline double timestamp() {
struct timeval tp;
gettimeofday(&tp, NULL);
return double(tp.tv_sec) + tp.tv_usec / 1000000.;
}
FWIW I put together a pure SSE version (SSE4.1) which seems to run around 20% faster than the original scalar code on a Core i7:
#include <smmintrin.h>
int getDiff_SSE(int indx1, int indx2)
{
int result[4] __attribute__ ((aligned(16))) = { 0 };
const int * const p1 = &nodeL[indx1][0];
const int * const p2 = &nodeL[indx2][0];
const __m128i vke = _mm_set_epi32(0, -1, 0, -1);
const __m128i vko = _mm_set_epi32(-1, 0, -1, 0);
__m128i vresult = _mm_set1_epi32(0);
for (int k = 0; k < 128; k += 4)
{
__m128i v1, v2, vmax;
v1 = _mm_loadu_si128((__m128i *)&p1[k]);
v2 = _mm_loadu_si128((__m128i *)&p2[k]);
v1 = _mm_xor_si128(v1, vke);
v2 = _mm_xor_si128(v2, vko);
v1 = _mm_sub_epi32(v1, vke);
v2 = _mm_sub_epi32(v2, vko);
vmax = _mm_add_epi32(v1, v2);
vresult = _mm_max_epi32(vresult, vmax);
}
_mm_store_si128((__m128i *)result, vresult);
return max(max(max(result[0], result[1]), result[2]), result[3]);
}
You probably can get the compiler to use SSE for this. Will it make the code quicker? Probably not. The reason being is that there is a lot of memory access compared to computation. The CPU is much faster than the memory and a trivial implementation of the above will already have the CPU stalling when it's waiting for data to arrive over the system bus. Making the CPU faster will just increase the amount of waiting it does.
The declaration of nodeL can have an effect on the performance so it's important to choose an efficient container for your data.
There is a threshold where optimising does have a benfit, and that's when you're doing more computation between memory reads - i.e. the time between memory reads is much greater. The point at which this occurs depends a lot on your hardware.
It can be helpful, however, to optimise the code if you've got non-memory constrained tasks that can run in prarallel so that the CPU is kept busy whilst waiting for the data.
This will be faster. Double dereference of vector of vectors is expensive. Caching one of the dereferences will help. I know it's not answering the posted question but I think it will be a more helpful answer.
int getDiff(int indx1, int indx2) {
int result = 0;
int pplus, pminus, tmp;
const vector<int>& nodetemp1 = nodeL[indx1];
const vector<int>& nodetemp2 = nodeL[indx2];
for (int k = 0; k < 128; k += 2) {
pplus = nodetemp2[k] - nodetemp1[k];
pminus = nodetemp1[k + 1] - nodetemp2[k + 1];
tmp = max(pplus, pminus);
if (tmp > result) {
result = tmp;
}
}
return result;
}
A couple of things to look at. One is the amount of data you are passing around. That will cause a bigger issue than the trivial calculation.
I've tried to rewrite it using SSE instructions (AVX) using library here
The original code on my system ran in 11.5s
With Neil Kirk's optimisation, it went down to 10.5s
EDIT: Tested the code with a debugger rather than in my head!
int getDiff(std::vector<std::vector<int>>& nodeL,int row1, int row2) {
Vec4i result(0);
const std::vector<int>& nodetemp1 = nodeL[row1];
const std::vector<int>& nodetemp2 = nodeL[row2];
Vec8i mask(-1,0,-1,0,-1,0,-1,0);
for (int k = 0; k < 128; k += 8) {
Vec8i nodeA(nodetemp1[k],nodetemp1[k+1],nodetemp1[k+2],nodetemp1[k+3],nodetemp1[k+4],nodetemp1[k+5],nodetemp1[k+6],nodetemp1[k+7]);
Vec8i nodeB(nodetemp2[k],nodetemp2[k+1],nodetemp2[k+2],nodetemp2[k+3],nodetemp2[k+4],nodetemp2[k+5],nodetemp2[k+6],nodetemp2[k+7]);
Vec8i tmp = select(mask,nodeB-nodeA,nodeA-nodeB);
Vec4i tmp_a(tmp[0],tmp[2],tmp[4],tmp[6]);
Vec4i tmp_b(tmp[1],tmp[3],tmp[5],tmp[7]);
Vec4i max_tmp = max(tmp_a,tmp_b);
result = select(max_tmp > result,max_tmp,result);
}
return horizontal_add(result);
}
The lack of branching speeds it up to 9.5s but still data is the biggest impact.
If you want to speed it up more, try to change the data structure to a single array/vector rather than a 2D one (a.l.a. std::vector) as that will reduce cache pressure.
EDIT
I thought of something - you could add a custom allocator to ensure you allocate the 2*18M vectors in a contiguous block of memory which allows you to keep the data structure and still go through it quickly. But you'd need to profile it to be sure
EDIT 2: Tested the code with a debugger rather than in my head!
Sorry Alex, this should be better. Not sure it will be faster than what the compiler can do. I still maintain that it's memory access that's the issue, so I would still try the single array approach. Give this a go though.

How to speed up my sparse matrix solver?

I'm writing a sparse matrix solver using the Gauss-Seidel method. By profiling, I've determined that about half of my program's time is spent inside the solver. The performance-critical part is as follows:
size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
for (size_t y = 1; y < d_ny - 1; ++y) {
for (size_t x = 1; x < d_nx - 1; ++x) {
d_x[ic] = d_b[ic]
- d_w[ic] * d_x[iw] - d_e[ic] * d_x[ie]
- d_s[ic] * d_x[is] - d_n[ic] * d_x[in];
++ic; ++iw; ++ie; ++is; ++in;
}
ic += 2; iw += 2; ie += 2; is += 2; in += 2;
}
All arrays involved are of float type. Actually, they are not arrays but objects with an overloaded [] operator, which (I think) should be optimized away, but is defined as follows:
inline float &operator[](size_t i) { return d_cells[i]; }
inline float const &operator[](size_t i) const { return d_cells[i]; }
For d_nx = d_ny = 128, this can be run about 3500 times per second on an Intel i7 920. This means that the inner loop body runs 3500 * 128 * 128 = 57 million times per second. Since only some simple arithmetic is involved, that strikes me as a low number for a 2.66 GHz processor.
Maybe it's not limited by CPU power, but by memory bandwidth? Well, one 128 * 128 float array eats 65 kB, so all 6 arrays should easily fit into the CPU's L3 cache (which is 8 MB). Assuming that nothing is cached in registers, I count 15 memory accesses in the inner loop body. On a 64-bits system this is 120 bytes per iteration, so 57 million * 120 bytes = 6.8 GB/s. The L3 cache runs at 2.66 GHz, so it's the same order of magnitude. My guess is that memory is indeed the bottleneck.
To speed this up, I've attempted the following:
Compile with g++ -O3. (Well, I'd been doing this from the beginning.)
Parallelizing over 4 cores using OpenMP pragmas. I have to change to the Jacobi algorithm to avoid reads from and writes to the same array. This requires that I do twice as many iterations, leading to a net result of about the same speed.
Fiddling with implementation details of the loop body, such as using pointers instead of indices. No effect.
What's the best approach to speed this guy up? Would it help to rewrite the inner body in assembly (I'd have to learn that first)? Should I run this on the GPU instead (which I know how to do, but it's such a hassle)? Any other bright ideas?
(N.B. I do take "no" for an answer, as in: "it can't be done significantly faster, because...")
Update: as requested, here's a full program:
#include <iostream>
#include <cstdlib>
#include <cstring>
using namespace std;
size_t d_nx = 128, d_ny = 128;
float *d_x, *d_b, *d_w, *d_e, *d_s, *d_n;
void step() {
size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
for (size_t y = 1; y < d_ny - 1; ++y) {
for (size_t x = 1; x < d_nx - 1; ++x) {
d_x[ic] = d_b[ic]
- d_w[ic] * d_x[iw] - d_e[ic] * d_x[ie]
- d_s[ic] * d_x[is] - d_n[ic] * d_x[in];
++ic; ++iw; ++ie; ++is; ++in;
}
ic += 2; iw += 2; ie += 2; is += 2; in += 2;
}
}
void solve(size_t iters) {
for (size_t i = 0; i < iters; ++i) {
step();
}
}
void clear(float *a) {
memset(a, 0, d_nx * d_ny * sizeof(float));
}
int main(int argc, char **argv) {
size_t n = d_nx * d_ny;
d_x = new float[n]; clear(d_x);
d_b = new float[n]; clear(d_b);
d_w = new float[n]; clear(d_w);
d_e = new float[n]; clear(d_e);
d_s = new float[n]; clear(d_s);
d_n = new float[n]; clear(d_n);
solve(atoi(argv[1]));
cout << d_x[0] << endl; // prevent the thing from being optimized away
}
I compile and run it as follows:
$ g++ -o gstest -O3 gstest.cpp
$ time ./gstest 8000
0
real 0m1.052s
user 0m1.050s
sys 0m0.010s
(It does 8000 instead of 3500 iterations per second because my "real" program does a lot of other stuff too. But it's representative.)
Update 2: I've been told that unititialized values may not be representative because NaN and Inf values may slow things down. Now clearing the memory in the example code. It makes no difference for me in execution speed, though.
Couple of ideas:
Use SIMD. You could load 4 floats at a time from each array into a SIMD register (e.g. SSE on Intel, VMX on PowerPC). The disadvantage of this is that some of the d_x values will be "stale" so your convergence rate will suffer (but not as bad as a jacobi iteration); it's hard to say whether the speedup offsets it.
Use SOR. It's simple, doesn't add much computation, and can improve your convergence rate quite well, even for a relatively conservative relaxation value (say 1.5).
Use conjugate gradient. If this is for the projection step of a fluid simulation (i.e. enforcing non-compressability), you should be able to apply CG and get a much better convergence rate. A good preconditioner helps even more.
Use a specialized solver. If the linear system arises from the Poisson equation, you can do even better than conjugate gradient using an FFT-based methods.
If you can explain more about what the system you're trying to solve looks like, I can probably give some more advice on #3 and #4.
I think I've managed to optimize it, here's a code, create a new project in VC++, add this code and simply compile under "Release".
#include <iostream>
#include <cstdlib>
#include <cstring>
#define _WIN32_WINNT 0x0400
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <conio.h>
using namespace std;
size_t d_nx = 128, d_ny = 128;
float *d_x, *d_b, *d_w, *d_e, *d_s, *d_n;
void step_original() {
size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
for (size_t y = 1; y < d_ny - 1; ++y) {
for (size_t x = 1; x < d_nx - 1; ++x) {
d_x[ic] = d_b[ic]
- d_w[ic] * d_x[iw] - d_e[ic] * d_x[ie]
- d_s[ic] * d_x[is] - d_n[ic] * d_x[in];
++ic; ++iw; ++ie; ++is; ++in;
}
ic += 2; iw += 2; ie += 2; is += 2; in += 2;
}
}
void step_new() {
//size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
float
*d_b_ic,
*d_w_ic,
*d_e_ic,
*d_x_ic,
*d_x_iw,
*d_x_ie,
*d_x_is,
*d_x_in,
*d_n_ic,
*d_s_ic;
d_b_ic = d_b;
d_w_ic = d_w;
d_e_ic = d_e;
d_x_ic = d_x;
d_x_iw = d_x;
d_x_ie = d_x;
d_x_is = d_x;
d_x_in = d_x;
d_n_ic = d_n;
d_s_ic = d_s;
for (size_t y = 1; y < d_ny - 1; ++y)
{
for (size_t x = 1; x < d_nx - 1; ++x)
{
/*d_x[ic] = d_b[ic]
- d_w[ic] * d_x[iw] - d_e[ic] * d_x[ie]
- d_s[ic] * d_x[is] - d_n[ic] * d_x[in];*/
*d_x_ic = *d_b_ic
- *d_w_ic * *d_x_iw - *d_e_ic * *d_x_ie
- *d_s_ic * *d_x_is - *d_n_ic * *d_x_in;
//++ic; ++iw; ++ie; ++is; ++in;
d_b_ic++;
d_w_ic++;
d_e_ic++;
d_x_ic++;
d_x_iw++;
d_x_ie++;
d_x_is++;
d_x_in++;
d_n_ic++;
d_s_ic++;
}
//ic += 2; iw += 2; ie += 2; is += 2; in += 2;
d_b_ic += 2;
d_w_ic += 2;
d_e_ic += 2;
d_x_ic += 2;
d_x_iw += 2;
d_x_ie += 2;
d_x_is += 2;
d_x_in += 2;
d_n_ic += 2;
d_s_ic += 2;
}
}
void solve_original(size_t iters) {
for (size_t i = 0; i < iters; ++i) {
step_original();
}
}
void solve_new(size_t iters) {
for (size_t i = 0; i < iters; ++i) {
step_new();
}
}
void clear(float *a) {
memset(a, 0, d_nx * d_ny * sizeof(float));
}
int main(int argc, char **argv) {
size_t n = d_nx * d_ny;
d_x = new float[n]; clear(d_x);
d_b = new float[n]; clear(d_b);
d_w = new float[n]; clear(d_w);
d_e = new float[n]; clear(d_e);
d_s = new float[n]; clear(d_s);
d_n = new float[n]; clear(d_n);
if(argc < 3)
printf("app.exe (x)iters (o/n)algo\n");
bool bOriginalStep = (argv[2][0] == 'o');
size_t iters = atoi(argv[1]);
/*printf("Press any key to start!");
_getch();
printf(" Running speed test..\n");*/
__int64 freq, start, end, diff;
if(!::QueryPerformanceFrequency((LARGE_INTEGER*)&freq))
throw "Not supported!";
freq /= 1000000; // microseconds!
{
::QueryPerformanceCounter((LARGE_INTEGER*)&start);
if(bOriginalStep)
solve_original(iters);
else
solve_new(iters);
::QueryPerformanceCounter((LARGE_INTEGER*)&end);
diff = (end - start) / freq;
}
printf("Speed (%s)\t\t: %u\n", (bOriginalStep ? "original" : "new"), diff);
//_getch();
//cout << d_x[0] << endl; // prevent the thing from being optimized away
}
Run it like this:
app.exe 10000 o
app.exe 10000 n
"o" means old code, yours.
"n" is mine, the new one.
My results:
Speed (original):
1515028
1523171
1495988
Speed (new):
966012
984110
1006045
Improvement of about 30%.
The logic behind:
You've been using index counters to access/manipulate.
I use pointers.
While running, breakpoint at a certain calculation code line in VC++'s debugger, and press F8. You'll get the disassembler window.
The you'll see the produced opcodes (assembly code).
Anyway, look:
int *x = ...;
x[3] = 123;
This tells the PC to put the pointer x at a register (say EAX).
The add it (3 * sizeof(int)).
Only then, set the value to 123.
The pointers approach is much better as you can understand, because we cut the adding process, actually we handle it ourselves, thus able to optimize as needed.
I hope this helps.
Sidenote to stackoverflow.com's staff:
Great website, I hope I've heard of it long ago!
For one thing, there seems to be a pipelining issue here. The loop reads from the value in d_x that has just been written to, but apparently it has to wait for that write to complete. Just rearranging the order of the computation, doing something useful while it's waiting, makes it almost twice as fast:
d_x[ic] = d_b[ic]
- d_e[ic] * d_x[ie]
- d_s[ic] * d_x[is] - d_n[ic] * d_x[in]
- d_w[ic] * d_x[iw] /* d_x[iw] has just been written to, process this last */;
It was Eamon Nerbonne who figured this out. Many upvotes to him! I would never have guessed.
Poni's answer looks like the right one to me.
I just want to point out that in this type of problem, you often gain benefits from memory locality. Right now, the b,w,e,s,n arrays are all at separate locations in memory. If you could not fit the problem in L3 cache (mostly in L2), then this would be bad, and a solution of this sort would be helpful:
size_t d_nx = 128, d_ny = 128;
float *d_x;
struct D { float b,w,e,s,n; };
D *d;
void step() {
size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
for (size_t y = 1; y < d_ny - 1; ++y) {
for (size_t x = 1; x < d_nx - 1; ++x) {
d_x[ic] = d[ic].b
- d[ic].w * d_x[iw] - d[ic].e * d_x[ie]
- d[ic].s * d_x[is] - d[ic].n * d_x[in];
++ic; ++iw; ++ie; ++is; ++in;
}
ic += 2; iw += 2; ie += 2; is += 2; in += 2;
}
}
void solve(size_t iters) { for (size_t i = 0; i < iters; ++i) step(); }
void clear(float *a) { memset(a, 0, d_nx * d_ny * sizeof(float)); }
int main(int argc, char **argv) {
size_t n = d_nx * d_ny;
d_x = new float[n]; clear(d_x);
d = new D[n]; memset(d,0,n * sizeof(D));
solve(atoi(argv[1]));
cout << d_x[0] << endl; // prevent the thing from being optimized away
}
For example, this solution at 1280x1280 is a little less than 2x faster than Poni's solution (13s vs 23s in my test--your original implementation is then 22s), while at 128x128 it's 30% slower (7s vs. 10s--your original is 10s).
(Iterations were scaled up to 80000 for the base case, and 800 for the 100x larger case of 1280x1280.)
I think you're right about memory being a bottleneck. It's a pretty simple loop with just some simple arithmetic per iteration. the ic, iw, ie, is, and in indices seem to be on opposite sides of the matrix so i'm guessing that there's a bunch of cache misses there.
I'm no expert on the subject, but I've seen that there are several academic papers on improving the cache usage of the Gauss-Seidel method.
Another possible optimization is the use of the red-black variant, where points are updated in two sweeps in a chessboard-like pattern. In this way, all updates in a sweep are independent and can be parallelized.
I suggest putting in some prefetch statements and also researching "data oriented design":
void step_original() {
size_t ic = d_ny + 1, iw = d_ny, ie = d_ny + 2, is = 1, in = 2 * d_ny + 1;
float dw_ic, dx_ic, db_ic, de_ic, dn_ic, ds_ic;
float dx_iw, dx_is, dx_ie, dx_in, de_ic, db_ic;
for (size_t y = 1; y < d_ny - 1; ++y) {
for (size_t x = 1; x < d_nx - 1; ++x) {
// Perform the prefetch
// Sorting these statements by array may increase speed;
// although sorting by index name may increase speed too.
db_ic = d_b[ic];
dw_ic = d_w[ic];
dx_iw = d_x[iw];
de_ic = d_e[ic];
dx_ie = d_x[ie];
ds_ic = d_s[ic];
dx_is = d_x[is];
dn_ic = d_n[ic];
dx_in = d_x[in];
// Calculate
d_x[ic] = db_ic
- dw_ic * dx_iw - de_ic * dx_ie
- ds_ic * dx_is - dn_ic * dx_in;
++ic; ++iw; ++ie; ++is; ++in;
}
ic += 2; iw += 2; ie += 2; is += 2; in += 2;
}
}
This differs from your second method since the values are copied to local temporary variables before the calculation is performed.