C++ for Scientists - Technische Universität Dresden

5.3. EXPRESSION TEMPLATES 155
}
friend int size(const vector sum3& x) { return size(x.v1); }
T operator[](int i) const { check index(i); return v1[i] + v2[i] + v3[i]; }
private:
const vector& v1, v2, v3;
};
template
vector sum3 inline operator+(const vector sum& x, const vector& y)
{
return vector sum3(x.v1, x.v2, y);
}
Furthermore, vector sum must declare our new plus operator as friend to access its private
members and vector needs an assignment for vector sum3. This becomes increasingly annoying.
Also, what happens if we perform the second addition first w= x + (y + z)? Then we
need another plus operator. What if some of the vectors are multiplied by a scalar, e.g.,
w= x + dot(x, y) ∗ y + 4.3 ∗ z, and this scalar product is also implemented by an ET? Our implementation
effort runs into combinatorial explosion and we need a more flexible solution that
we introduce in the next section.
5.3.3 Generic Expression Templates
So far we started from a specific class (vector) and generalized the implementation gradually.
Although this can help us to understand the mechanism, we like to go now to the general version
that takes arbitrary vector types:
template
vector sum inline operator+(const V1& x, const V2& y)
{
return vector sum(x, y);
}
We now need an expression class with arbitrary arguments:
template
class vector sum
{
typedef vector sum self;
void check index(int i) const { assert(i >= 0 && i < size(v1)); }
public:
vector sum(const V1& v1, const V2& v2) : v1(v1), v2(v2)
{
assert(size(v1) == size(v2));
}
???? operator[](int i) const { check index(i); return v1[i] + v2[i]; }
friend int size(const self& x) { return size(x.v1); }
private:
const V1& v1;