C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 169
};
}
my axpy ftor()(u, v, w, i);
The only difference to fixed-size unrolling is that the indices are relative to an argument —
here i. The operator() is first called with Offset equal to 0, then with 1, 2, . . . Since each call is
inlined the functor call results in one monolithic block of operations without loop control and
function call. Thus, the call of my axpy ftor()(u, v, w, i) performs the same operations as
one iteration of the first loop in Listing 5.4.
Of course this compilation would end in an infinite loop if we forget to specialize it for Max:
template
struct my axpy ftor
{
template
void operator()(U& u, const V& v, const W& w, unsigned i) {}
};
Performing the considered vector operation with different unrollings yields
Compute time unrolled loop is 1.44 µs.
Compute time unrolled loop is 1.15 µs.
Compute time unrolled loop is 1.15 µs.
Compute time unrolled loop is 1.14 µs.
Now we can call this operation for any block size we like. On the other hand, it is rather
cumbersome to implement the according functions and functors for each vector expression.
Therefore, we combine this technique now with expression templates.
5.4.5 Tuning an Expression Template
⇒ vector unroll example2.cpp
Let us recall Section 5.3.3. So far, we developed a vector class with expression templates for
vector sums. In the same manner we can implement the product of a scalar and a vector but
we leave this as exercise and consider expressions with addition only, for example:
u = v + v + w
Now we frame this vector operation with a repeting loop and the time measure:
boost::timer t;
for (unsigned j= 0; j < rep; j++)
u= v + v + w;
std::cout ≪ ”Compute time is ” ≪ 1000000.0 ∗ t.elapsed() / double(rep) ≪ ” µs.\n”;
This results in:
Compute time is 1.72 µs.
To incorporate meta-tuning into expression templates we only need to modify the actual assignment
because only here a loop is performed. All the other operations (well so far we have