C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 173
The functor is also implemented in the same manner as before:
template
struct one norm ftor
{
template
void operator()(S& sum, const V& v, unsigned i)
{
using std::abs;
sum+= abs(v[i+Offset]);
one norm ftor()(sum, v, i);
}
};
template
struct one norm ftor
{
template
void operator()(S& sum, const V& v, unsigned i) {}
};
The measured run-time behavior behavior is:
Compute time one_norm(v) is 7.42 µs.
Compute time one_norm(v) is 3.64 µs.
Compute time one_norm(v) is 1.9 µs.
Compute time one_norm(v) is 1.25 µs.
Compute time one_norm(v) is 1.03 µs.
This is already a good improvement but maybe we can do better. 23
Reducing on an Array
⇒ reduction unroll array example.cpp
When we look at the previous computation, we see that a different entry of v is used in each
iteration. But every computation accesses the same temporary variable sum and this limits
concurrency. To provide more concurrency, we can use multiple temporaries 24 in an array for
instance. The modified function reads then:
template
typename Vector::value type
inline one norm(const Vector& v)
{
using std::abs;
typename Vector::value type sum[BSize];
for (unsigned i= 0; i < BSize; i++)
sum[i]= 0;
23 TODO: Test it with gcc 3.4 and MSVC. Speed up in table
24 Strictly speaking, this is not true for every possible scalar type we can think of. The addition of the sum type
must be a commutative monoid because we change the evaluation order. This holds of course for all intrinsic
numeric types and certainly for almost all user-defined arithmetic types. But one is free to define an addition
that is not commutative or not monoidal. In this case our transformation would be wrong. To deal with such
exceptions we need semantic concepts which hopefully become part of C ++ in the next years.