C++ for Scientists - Technische Universität Dresden

156 CHAPTER 5. META-PROGRAMMING
};
const V2& v2;
This is rather straightforward. The only issue is what type to return in operator[]? For this
we must define value type in each class — more flexible would be an external type trait. In
vector sum we take the value type of the first argument which can itself be taken from another
class.
template
class vector sum
{
// ...
typedef typename V1::value type value type;
};
value type operator[](int i) const { check index(i); return v1[i] + v2[i]; }
To assign such an expression to a vector we can also generalize the assign operator:
template
class vector
{
public:
typedef T value type;
};
template
vector& operator=(const Src& that)
{
check size(size(that));
for (int i= 0; i < my size; ++i)
data[i]= that[i];
return ∗this;
}
This assigment can also handle vector as argument and we can omit the standard assignment
operator.
Advantages of expression templates: Although the availability of operator overloading
in C ++ resulted in notationally nicer code, the scientific community refused to give up programming
in Fortran or to implement the loops directly in C/C ++. The reason was that the
traditional operator implementations were too expensive. Due to the overhead of the creation
of temporary variables and the copying of vector and matrix objects, C ++ could not compete
with the performance of programs written in Fortran. This problem has now been resolved
by the introduction of generics and expression templates. Now it is possible to write efficient
scientific programs in a notationally convenient manner.
5.4 Meta-Tuning: Write Your Own Compiler Optimization
Compiler technology is progressing and provides us an increasing number of optimization techniques.
Ideally, everyone writes his software in the way it is the easiest for him and the compiler