C++ for Scientists - Technische Universität Dresden

150 CHAPTER 5. META-PROGRAMMING
5.3 Expression Templates
Scientific software has usually strong performance requirements — especially those problems
we tackle with C ++. Many large-scale simulations of physical, chemical, or biological processes
run for weeks or months and everybody is glad if at least a part of this very long execution
times can be safed. Such safings are often at the price of readable and maintainable program
sources. In Section 5.3.1 we will show a simple implementation of an operator and discuss why
this is not efficient and in the remainder of Section 5.3 we will demonstrate how to improve to
improve the performance without sacrificing the natural notation.
5.3.1 Simple Operator Implementation
Assume we have an application with vector addition. We want for instance write an expression
of the following form for vectors w, x, y and z:
w = x + y + z;
Say, we have a vector class as in Section 4.3:
template
class vector
{
public:
explicit vector(int size) : my size(size), data(new T[my size]) {}
vector() : my size(0), data(0) {}
};
friend int size(const vector& x) { return x.my size; }
const T& operator[](int i) const { check index(i); return data[i]; }
T& operator[](int i) { check index(i); return data[i]; }
// ...
We can of course provide an operator for adding such vectors:
template
vector inline operator+(const vector& x, const vector& y)
{
x.check size(size(y));
vector sum(size(x));
for (int i= 0; i < size(x); ++i)
sum[i] = x[i] + y[i];
return sum;
}
A short test program checks that everything works:
int main()
{
vector x(4), y(4), z(4), w(4);
x[0]= x[1]= 1.0; x[2]= 2.0; x[3] = −3.0;
y[0]= y[1]= 1.7; y[2]= 4.0; y[3] = −6.0;
z[0]= z[1]= 4.1; z[2]= 2.6; z[3] = 11.0;