C++ for Scientists - Technische Universität Dresden

154 CHAPTER 5. META-PROGRAMMING
Discussion 5.1 The drawback is that if the entries are accessed multiple times the sum is
recomputed. On the other hand, most expressions are only used once and this is not a problem.
An example where vector entries are accessed several times is A ∗ (x+y). Here, it is preferable
to compute a true vector first instead of computing the matrix vector product on the expression
template. 12
To evaluate w= x + y we also need an assignment operator for vector sum:
template class vector sum; // forward declaration
template
class vector
{ // ...
vector& operator=(const vector sum& that)
{
check size(size(that));
for (int i= 0; i < my size; ++i)
data[i]= that[i];
return ∗this;
}
};
The assignment runs a loop over w and that. As that is an object of type vector sum the expression
that[i] computes x[i] + y[i]. In contrast to the implementationn in Section 5.3.1 we have now
• Only one loop;
• No temporary vector;
• No additional memory allocation and deallocation; and
• No addional data reads and writes.
In fact, the same operations are performed as in the loop
for (int i= 0; i < size(w); ++i)
w[i] = x[i] + y[i];
The cost to create a vector sum object is negligible. The object will be kept on the stack and does
not require memory allocation. Even that little effort for creating the object will be optimized
away by most compilers with static code analysis.
What happens when we like to add three vectors? The naïve implementation from § 5.3.1
returns a vector and this vector can be added to another vector. Our approach returns a
vector sum and we have no addition for vector sum and vector. Thus we would need another ET
class and an according operation:
template
class vector sum3
{
void check index(int i) const { assert(i >= 0 && i < size(v1)); }
public:
vector sum3(const vector& v1, const vector& v2, const vector& v3) : v1(v1), v2(v2), v3(v3)
{
assert(size(v1) == size(v2)); assert(size(v1) == size(v3));
12 TODO: Shall we provide a solution for this as well? This something that is over-due in MTL4 anyway.