[CppAD] Performance of CppAD and OpenMP

[schattenpflanze at arcor.de]

Hello,

I have another question concerning the performance of CppAD when OpenMP 
is enabled. It seems that CppAD scales very badly when the number of 
threads and cores exceeds a certain number. I have tried to construct a 
minimal example reproducing the issue. Running the simple (and 
absolutely pointless) example code listed below on a machine with 32 
native cores (no hyperthreading, single workstation) yields the 
following results:
1 thread:  8.6 seconds
4 threads: 2.8 s
8 threads: 2.2 s
10 threads: 2.4 s
12 threads: 4 s
14 threads: 3.8 s
16 threads: 4.2 s
24 threads: 8.1 s (!)
28 threads: 9.5 s (!)

I am, of course, aware that additional threads cause additional 
overhead, and that the performance does not necessarily increase with 
the number of threads. However, this significant _decrease_ seems 
strange. In particular, if I remove the line
CppAD::Independent(x)
from the code, I obtain:
4 threads: 0.38 s
8 threads: 0.20 s
16 threads: 0.14 s
24 threads: 0.12 s,
which is the kind of scaling that I would have expected.

Memory consumption seems to be low. I have tried various scheduling and 
variable sharing policies, but the problem persists. I also attach the 
interesting results of the CppAD openmp test script. What is the reason 
for this behaviour and how can I counter it?

Thank you and best regards,
Peter


Test code:
----------------------------------------------------
int n_par = 45;
CppAD::vector<AD<double> > x(n_par);
for (int i=0; i<n_par; ++i) {
   x[i] = i;
}	

#pragma omp parallel for \
	firstprivate(x) \
	schedule(dynamic,1) \
	num_threads(global_paras->n_threads)
for (int i=0; i<1000; ++i) {		
   CppAD::Independent(x);
   CppAD::vector<AD<double> > y(1);

   y[0] = 0.0;
   for (int i=0; i<1000; ++i) {
     for (int j=0; j<(int)x.size(); ++j) {
       y[0] += CppAD::pow(x[j] - y[0], 0.1);
     }
   }
}
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