C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 183
This log shows that C[1][0] and C[1][1] are computed alternately so that it can be performed in
parallel on a super-scalar computer. One can also verify that
cik =
3�
j=0
aijbjk.
Printing C will also show the same result as for the canonical matrix multiplication.
The implementation above can be simplified. The first functor specialization is only different
to the general functor in the way how the indices are incrememted. We can factor this out with
an additional loop class:
template
struct loop2
{
static const unsigned next index0= Index0, next index1= Index1 + 1;
};
template
struct loop2
{
static const unsigned next index0= Index0 + 1, next index1= 0;
};
Such a general class has a high potential of reuse. With this class we can fuse the funtor
template and the first specialization:
template
struct mult block
{
typedef loop2 l;
typedef mult block next;
template
void operator()(Tmp& tmp, const Matrix& A, const Matrix& B, unsigned i, unsigned j, unsigned k)
{
std::cout ≪ ”tmp.” ≪ tmp.bs ≪ ”+= A[” ≪ i + Index0 ≪ ”][” ≪ j ≪ ”] ∗ B[” ≪ j ≪ ”][” ≪
k + Index1 ≪ ”]\n”;
tmp.value+= A(i + Index0, j) ∗ B(j, k + Index1);
next()(tmp.sub, A, B, i, j, k);
}
};
template
void update(const Tmp& tmp, Matrix& C, unsigned i, unsigned k)
{
std::cout ≪ ”C[” ≪ i + Index0 ≪ ”][” ≪ k + Index1 ≪ ”]= tmp.” ≪ tmp.bs ≪ ”\n”;
C(i + Index0, k + Index1)= tmp.value;
next().update(tmp.sub, C, i, k);
}
The other specialization remains unaltered.
Last but not least we like to see impact of our not-so-simple matrix product. The benchmark
yielded on our test machine: