My benchmark results are very strange. On one hand I have the serial function for calculating the quadratic form. On the other hand I wrote two parallel versions. For one thread all functions should need more or less the same running time. But one parallel function just needs half of the time. Is there a "hidden" optimization?
Serial version:
double quadratic_form_serial(const std::vector<double> & A,const std::vector<double> & v, const std::vector<double> & w){
int N= v.size();
volatile double q=0.0;
for(int i=0; i<N; ++i)
for(int j=0; j<N; ++j)
q +=v[i]*A[i*N+j]*w[j];
return q;
}
Parallel version 1:
double quadratic_form_parallel(const std::vector<double> & A,const std::vector<double> & v, const std::vector<double> & w, const int threadnum){
int N= v.size();
omp_set_num_threads(threadnum);
volatile double q[threadnum];
volatile double val = 0.0;
#pragma omp parallel
{
int me = omp_get_thread_num();
q[me] = 0.0;
#pragma omp for collapse(2)
for(int i=0; i<N; ++i)
for(int j=0; j<N; ++j)
q[me]+=v[i]*A[i*N+j]*w[j];
#pragma omp atomic
val+=q[me];
}
return val;
}
Parallel version 2:
double quadratic_form_parallel2(const std::vector<double> & A,const std::vector<double> & v, const std::vector<double> & w, const int threadnum){
int N= v.size();
volatile double result =0.0;
omp_set_num_threads(threadnum);
#pragma omp parallel for reduction(+: result)
for (int i=0; i<N; ++i)
for (int j=0; j<N; ++j)
result += v[i] * A[i*N + j] * w[j];
return result;
}
I run the code for N=10000 and I flushed the cache before I call the function. The function quadratic_form_parallel2 needs with one thread less than the half of the time the two other function needed:
threads serial Parallel1 Parallel2
1 0.0882503 0.0875649 0.0313441
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