C++ for Scientists - Technische Universität Dresden

172 CHAPTER 5. META-PROGRAMMING
for (unsigned i= 0; i < sb; i+= BSize)
assign()(ref, that, i);
for (unsigned i= sb; i < s; i++)
ref[i]= that[i];
return ref;
}
private:
V& ref;
};
Evaluting the considered vector expressions for some block sizes yields:
Compute time unroll(u)= v + v + w is 1.72 µs.
Compute time unroll(u)= v + v + w is 1.52 µs.
Compute time unroll(u)= v + v + w is 1.36 µs.
Compute time unroll(u)= v + v + w is 1.37 µs.
Compute time unroll(u)= v + v + w is 1.4 µs.
This few benchmarks are consistent with the previous results, i.e. unroll is equal to the
canocical implementation and unroll is as fast as the hard-wired unrolling.
5.4.6 Tuning Reduction Operations
Reducing on a Single Variable
⇒ reduction unroll example.cpp
In the preceding vector operations, the i th entry of each vector was handled independently of
any other entry. For reduction operations, they are related by one or more temporary variables.
And this temporary variable(s) can become a serious bottle neck.
First, we test if a reduction operation, say the discrete L1 norm (also known as Manhattan
norm) can be accelerated by the techniques from Section 5.4.4. We implement the one norm
function in terms of a functor for the iteration block:
template
typename Vector::value type
inline one norm(const Vector& v)
{
using std::abs;
typename Vector::value type sum(0);
unsigned s= size(v), sb= s / BSize ∗ BSize;
}
for (unsigned i= 0; i < sb; i+= BSize)
one norm ftor()(sum, v, i);
for (unsigned i= sb; i < s; i++)
sum+= abs(v[i]);
return sum;