C++ for Scientists - Technische Universität Dresden

5.3. EXPRESSION TEMPLATES 153
caches of the platform and the vectors must really be transfer to and from main memory. In
case of shorter vectors, the data might reside in L1 or L2 cache and the data transfer is less
critical. But in this case, the allocation and deallocation becomes a serious slow down factor.
The purpose of expression templates is to keep the original operator notation without introducing
the overhead induced by temporaries.
5.3.2 An Expression Template Class
The solution is to introduce a special class that keeps references to the vectors and allows us
to perform all computations later in one sweep. The addition does not return now a vector but
an object with the references:
template
class vector sum
{
public:
vector sum(const vector& v1, const vector& v2) : v1(v1), v2(v2) {}
private:
const vector& v1, v2;
};
template
vector sum inline operator+(const vector& x, const vector& y)
{
return vector sum(x, y);
}
Now we can already write x + y but not w= x + y yet. It is not only that the assignment is not
defined, we have not yet provided vector sum with enough functionality to perform something
useful in the assignment. Thus, we first extend vector sum so that it looks like a vector itself:
template
class vector sum
{
void check index(int i) const { assert(i >= 0 && i < size(v1)); }
public:
vector sum(const vector& v1, const vector& v2) : v1(v1), v2(v2)
{
assert(size(v1) == size(v2));
}
friend int size(const vector sum& x) { return size(x.v1); }
T operator[](int i) const { check index(i); return v1[i] + v2[i]; }
private:
const vector& v1, v2;
};
For the sake of defensive programming, we added a test that the two vectors have the same
size and can be consistently added. Then we consider the size of the first vector as the size of
our vector sum. The most important function is the bracket operator: when the i th entry we
compute the sum of the operands i th entries.