I'm trying to write a code for matrix multiplication. As far as I understand OMP and pararel programming this code may suffer from race condition.
#pragma omp parallel
#pragma omp for
for (int k = 0; k < size; k++){
for (int i = 0; i < size; i++) {
for (int j = 0; j < size; j++) {
c[i][j] += a[i][k] * b[k][j];
}}}
Do I get rid of it if I put #pragma omp atomic before writing to c matrix or by adding private(i) to 2nd #pragma? Also is it possible to make this code false-sharing free? If yes, how ?
A race condition occurs when 2 or more threads access the same memory location and at least one of them is writing it. Line c[i][j] +=... can cause data race in your code. The solution is to reorder your nested loops (use the order of i,j,k) and you may introduce a temporary variable to calculate the dot product:
#pragma omp parallel for
for (int i = 0; i < size; i++) {
for (int j = 0; j < size; j++) {
double tmp=0; // change its type as needed
for (int k = 0; k < size; k++){
tmp += a[i][k] * b[k][j];
}
c[i][j] = tmp; //note that += was used in your original code
}
}
Note that your code will be faster if you calculate the transpose of matrix b. For more details read this.
UPDATE:
If you need to maintain the order of loops, there are 2 possibilities (but these solutions may be slower than the serial code):
Use atomic operation (i.e #pragma omp atomic). In this case false sharing also can be a problem.
If your stack is large enough to store the matrix for all threads, a better alternative is to use reduction: #pragma omp parallel for reduction(+:c[:size][:size]) (Another alternative is to do the reduction manually. In this case you can allocate the matrices used for reduction on the heap.)
Related
As a first step into OpenMP I set myself a challenge to parallelize some matrix decomposition algorithm. I picked Crout with pivoting, source can be found here:
http://www.mymathlib.com/c_source/matrices/linearsystems/crout_pivot.c
At the bottom of that decomposition function there's an outer for loop that walks over i and p_row at the same time. Of course OpenMP is as confused as I am when looking at this and refuses to do anything with it.
After wrapping my mind around it I think I got it untangled into readable form:
p_row = p_k + n;
for (i = k+1; i < n; i++) {
for (j = k+1; j < n; j++) *(p_row + j) -= *(p_row + k) * *(p_k + j);
p_row += n;
}
At this point serial run still comes up with the same result as the original code.
Then I add some pragmas, like this:
p_row = p_k + n;
#pragma omp parallel for private (i,j) shared (n,k,p_row,p_k)
for (i = k+1; i < n; i++) {
for (j = k+1; j < n; j++) *(p_row + j) -= *(p_row + k) * *(p_k + j);
#pragma omp critical
p_row += n;
#pragma omp flush(p_row)
}
Yet the results are essentially random.
What am I missing?
I haven't tested your adaptation of original code, but your program has several problems.
#pragma omp parallel for private (i,j) shared (n,k,p_row,p_k)
Default behavior is to have vars declared outside of scope shared, so the shared declaration is useless.
But these var should not be shared and rendered private.
n is unchanged during iterations, so better have a local copy
ditto for k and p_k
p_row is modified, but you really want several copies of p_row. This what will insure a proper parallel processing, so that each thread processes different rows. The problem is to compute p_row value in the different threads.
In the outer loop, iteration 0 will use p_row, second iteration p_row+n, iteration l p_row+l*n. Your iterations will be spread over several threads. Assume each thread processes m iterations. Thread 0 will process i=k+1 to i=m+(k+1) and p_row to p_row+m*n, thread 1 i=m+1+(k+1) to i=2m+(k+1) and p_row+n*(m+1) to p_row+2*m*n, etc. Hence you can compute the value that should have p_row at the start of the loop with the value of i.
Here is a possible implementation
p_row = p_k + n;
#pragma omp parallel for private(i,j) firstprivate(n, k, p_row, p_k)
// first private insures initial values are kept
{
for (i = k+1, p_row=p_row+(i-(k+1))*n; i < n; i++, p_row += n) {
for (j = k+1; j < n; j++)
*(p_row + j) -= *(p_row + k) * *(p_k + j);
}
p_row incrementation is in the for loop. This should continue to work in a sequential environment.
Critical is useless (and was buggy in your previous code). Flush is implicit at the end of a parallel section (and the pragma is just "omp flush").
I have such a uninformative nested loops (just as test of performance):
const int N = 300;
for (int num = 0; num < 10000; num++) {
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
The elapsed time was
about 6 s
I tried to parallelize different loops with OpenMP. But I am very confused with the results I got.
In the first step I used "parallel for" pragma only for the first (outermost) loop:
#pragma omp parallel for schedule(static) reduction(+:sum1,sum2)
for (int num = 0; num < 10000; num++) {
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
The elapsed time was (2 cores)
3.81
Then I tried to parallelize two inner loops with "collapse" clause (2 cores):
for (int num = 0; num < 10000; num++) {
#pragma omp parallel for collapse(2) schedule(static) reduction(+:sum1, sum2)
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
The elapsed time was
3.76
This is faster then in previous case. And I do not understand the reason of this.
If I use fusing of these inner loops (which is meant to be better in the sense of performance) like this
#pragma omp parallel for schedule(static) reduction(+:sum1,sum2)
for (int n = 0; n < N * N; n++) {
int i = n / N; int j = n % N;
the elapsed time is
5.53
This confuses me so much. The performance is worse in this case, though usually people advise to fuse loops for better performance.
Okay, now let's try to parallelize only middle loop like this (2 cores):
for (int num = 0; num < 10000; num++) {
#pragma omp parallel for schedule(static) reduction(+:sum1,sum2)
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
Again, the performance becomes better:
3.703
And the final step - parallelization of the innermost loop only (assuming that this will be the fastest case according to the previous results) (2 cores):
for (int num = 0; num < 10000; num++) {
for (int i=0; i<N; i++) {
#pragma omp parallel for schedule(static) reduction(+:sum1,sum2)
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
But (surprise!) the elapsed time is
about 11 s
This is much slower than in previous cases. I cannot catch the reason of all of this.
By the way, I was looking for similar questions, and I found advice of adding
#pragma omp parallel
before the first loop (for example, in this and that questions). But why is it right procedure? If we place
#pragma omp parallel#
before for-loop it means that each thread executes for-loop completely, which is incorrect (excess work). Indeed, I tried to insert
#pragma omp parallel
before the outermost loop with different locations of
#pragma omp parallel for
as I am describing here, and the performance was worse in call cases (moreover, in the latest case when parallelizing the innermost loop only, answer was also incorrect (namely, "sum2" was different - as there was a race condition).
I would like to know the reasons of such a performance (probably the reason is that time of data exchange is greater than time of actual computation on each thread, but this is in the latest case) and what solution is the most correct one.
EDIT: I've disabled compiler's optimization (by $-O0$ option) and results still the same (except that time elapsed in the latest example (when parallelizing the innermost loop) reduced from 11 s to 8 s).
Compiler options:
g++ -std=gnu++0x -fopenmp -O0 test.cpp
Definition of variables:
unsigned int seed;
const int N = 300;
int main()
{
double arr[N][N];
double brr[N][N];
for (int i=0; i < N; i++) {
for (int j = 0; j < N; j++) {
arr[i][j] = i * j;
brr[i][j] = i + j;
}
}
double start = omp_get_wtime();
double crr[N][N];
double sum1 = 0;
double sum2 = 0;
And the final step - parallelization of the innermost loop only (assuming that this will be the fastest case according to the previous results) (2 cores)
But (surprise!) the elapsed time is:
about 11 s
It is not a surprise at all. Parallel blocks perform implicit barriers and can even join and create threads (some libraries may use thread pools to reduce the cost of thread creation).
In the end, opening parallel regions is expensive. You should do it as few times as possible. The threads will run the outer loops in parallel, at the same time, but will divide the iteration space once they reach the omp for block, so the result should still be correct (you should make your program check this if you are unsure).
For testing performance, you should always run your experiments turning compiler optimizations, as they have a heavy impact on the behavior of the application (you should not make assumptions about performance on unoptimized programs because their problems may be already addressed during optimization).
When making a single parallel block that contains all the loops, the execution time is halved in my setup (started with 9.536s using 2 threads, and reduced to 4.757s).
The omp for block still applies implicit barriers, which is not needed in your example. Adding the nowait clause to the example reduces the execution time by another half: 2.120s.
From this point, you can now try to explore the other options.
Parallelizing middle loop reduces execution time to only 0.732s due to much better usage of the memory hierarchy and vectorization. L1 miss ratio reduced from ~29% to ~0.3%.
Using collapse with the two innermost loops made no big deal using two threads (strong scaling should be checked).
Using other directives such as omp simd does not improve performance in this case, as the compiler is sure enough that it can vectorize the innermost loop safely.
#pragma omp parallel reduction(+:sum1,sum2)
for (int num = 0; num < 10000; num++) {
#pragma omp for schedule(static) nowait
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
arr[i][j] = brr[i][j];
crr[i][j] = arr[i][j] - brr[i][j];
sum1 += crr[i][j];
sum2 += arr[i][j];
}
}
}
Note: L1 miss ratio computed using perf:
$ perf stat -e cache-references,cache-misses -r 3 ./test
Since variables in parallel programming are shared among threads (cores), you should consider how the processor cache-memory take in action. at this point your code might executed with a false-sharing which could hurt your processor performance.
At your 1st parallel code, you call #pragma omp for right at the first for, it means each thread has its own i and j. Compare with 2nd and 3rd (only differentiated by collapse) parallel code that parallelized the 2nd of for, it means each of i has its own j. These two code better because each thread/core more often hits the cache-line of j. The 4th code is completely disaster for caches processor because nothing to be shared there.
I recommends you to measure your code with Intel's PCM or PAPI in order to get a proper analyst.
Regards.
I found Intel's performance suggestion on Xeon Phi on Collapse clause in OpenMP.
#pragma omp parallel for collapse(2)
for (i = 0; i < imax; i++) {
for (j = 0; j < jmax; j++) a[ j + jmax*i] = 1.;
}
Modified example for better performance:
#pragma omp parallel for collapse(2)
for (i = 0; i < imax; i++) {
for (j = 0; j < jmax; j++) a[ k++] = 1.;
}
I test both case in Fortran with similar code on regular CPU using GFortran 4.8, they both get correct result. Test using similar Fortran Code with later code does not pass for GFortran5.2.0 and Intel 14.0
But as far as I understand, the loop body for OpenMP should avoid "loop sequence dependent" variable, for this case is k, so why in the later case it can get correct result and even better performance?
Here's the equivalent code for the two approaches when using collapse clause. You could see the second one is better.
for(int k=0; k<imax*jmax; k++) {
int i = k / jmax;
int j = k % jmax;
a[j + jmax*i]=1.;
}
for(int k=0; k<imax*jmax; k++) {
a[k]=1.;
}
Consider the following code segment
sum = 0;
for (i=0; i<n; i++)
sum = myfunc(a[i])+ sum;
Write the corresponding parallel code segment using OPENMP.
I did this way,
sum = 0;
#pragma omp parallel for
for (i=0; i<n; i++)
sum = myfunc(a[i])+ sum;
I'm a newcomer in parallel computing. Do you think is it correct?
Thank you very much for your help!
The sum variable will become a point of contention because every iteration touches it. Since you are doing a reduction, you should use the reduction clause to let OpenMP know that you want that variable accumulated across all threads:
sum = 0;
#pragma omp parallel for reduction(+ : sum)
for (i=0; i<n; i++)
sum = myfunc(a[i])+ sum;
Quite similar to that question
Sorting an array in openmp
which has several hundred views but no correct answer. Therefore I give it another try asking here again.
I am aware of the overhead and uselessness of this regarding speedup or performance. It simply is a small example to get into openMP. The fact that is is insertSort is given by my courseinstructor.
Here is my code:
std::vector<int> insertionSort(std::vector<int> a) {
int i, j, k;
#pragma omp parallel for private(i,j,k)
for(i = 0; i < a.size(); i++) {
#pragma omp critical
k = a[i];
for (j = i; j > 0 && a[j-1] > k; j--)
#pragma omp critical
{
a[j] = a[j-1];
a[j] = k;
}
}
return a;
}
I understand that the critical aspect is the race-condition between threads accessing (reading and writing) elements of a - that is, why I put a critical section arround all of them. That does not seem to be sufficient. What am I missing here. Without the pragmas, the sorting is correct.