C++ for Scientists - Technische Universität Dresden

178 CHAPTER 5. META-PROGRAMMING
};
}
template
struct one norm ftor
{
template
void operator()(S& s0, S& s1, S& s2, S& s3, S& s4, S& s5, S& s6, S& s7, const V& v, unsigned i) {}
};
The according one norm function based on this functor is straightforward:
template
typename Vector::value type
inline one norm(const Vector& v)
{
using std::abs;
typename Vector::value type s0(0), s1(0), s2(0), s3(0), s4(0), s5(0), s6(0), s7(0);
unsigned s= size(v), sb= s / BSize ∗ BSize;
}
for (unsigned i= 0; i < sb; i+= BSize)
one norm ftor()(s0, s1, s2, s3, s4, s5, s6, s7, v, i);
s0+= s1 + s2 + s3 + s4 + s5 + s6 + s7;
for (unsigned i= sb; i < s; i++)
s0+= abs(v[i]);
return s0;
A slight disadvantage is that all registers must be accumulated after the first iteration no matter
how small BSize is and how short the vector. A great advantage of the rotation is that BSize
is not limited to the number of temporary variables in such accumulations. If BSize is larger
then some or all variables are used multiple times without corrupting the result. The number
of temporaries is nonetheless a limiting factor for the concurrency.
The execution of this implementation durates on the test machine:
Compute time one_norm(v) is 6.77 µs.
Compute time one_norm(v) is 1.13 µs.
Compute time one_norm(v) is 0.71 µs.
Compute time one_norm(v) is 0.75 µs.
Compute time one_norm(v) is 1.07 µs.
This is comparable with the nested class (in this environment).
Résumé on Reduction Tuning
The goal of this section was not to determine the ultimately tuned reduction implementation
for superscalar processors. 27 The main ambition of this section, in fact of the whole book, is to
demonstrate the diversity of implementation opportunities. With the enormous expressiveness
27 In the presence of the new GPU cards with hundreds of cores and millions of threads, the fight for this little
concurrency is not so impressive. Nonetheless, we will still need performance tuning on single-core and “few-core”