C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 165
{
};
template
void operator()(const Matrix& A, const VecIn& v in, ScalOut& tmp)
{
fsize mat vec mult aux()(A, v in, tmp);
tmp+= A[Rows][Cols] ∗ v in[Cols];
}
To terminate the computation in the column we write a specialization.
template
struct fsize mat vec mult aux
{
template
void operator()(const Matrix& A, const VecIn& v in, ScalOut& tmp)
{
tmp= A[Rows][0] ∗ v in[0];
}
};
In this section we showed different ways to optimize a two-dimensional loop (with fixed sizes).
There are certainely more possibilities: for instance, we could try to implement it in a way that
uses registers but with the same concurrency as in the second-last implementation. Another
form of optimization could be to agglomerate the write-backs so that multiple invalidation
signals are sent at a time and maybe behave less interruptive.
5.4.3 Dynamic Unrolling – Warm up
⇒ vector unroll example.cpp
As important as the fixed-size optimization is, acceleration for dynamically sized containers is
needed even more. We start here with a simple example and some observations. We will reuse
the vector class from Listing 4.1. To show the implementation more clearly, we write the code
without operators and expression templates. Our test case will compute
u = 3v + w
for three short vectors of size 1000. The wall clock time will be measured with boost::timer. 19
The vectors v and w will be initialized and to have the data ready to use (i.e. the vectors are
definitively in cache 20 ) we run few additional operations without timing:
#include
#include
// ...
int main()
{
unsigned s= 1000;
if (argc > 1) s= atoi(argv[1]); // read (potentially) from command line
19 See http://www.boost.org/doc/libs/1_43_0/libs/timer/timer.htm
20 TODO: shouldn’t the initialization make this sure? Do we have a better explanation? Reference to benchmark
literature? Do we really need a bullet proof justification here?