C++ for Scientists - Technische Universität Dresden

152 CHAPTER 5. META-PROGRAMMING
• 3n assignments;
• 5n reads;
• 3n writes;
• 2 memory allocations; and
• 2 memory deallocations.
As comparison, if we could write a single loop or an inline function:
template
void inline add3(const vector& x, const vector& y, const vector& z, vector& sum)
{
x.check size(size(y));
x.check size(size(z));
x.check size(size(sum));
for (int i= 0; i < size(x); ++i)
sum[i] = x[i] + y[i] + z[i];
}
This function performs:
• 2n additions;
• n assignments;
• 3n reads;
• n writes;
The call of this function:
add3(x, y, z, w);
is of course less elegant than the operator notation. Often, one need another look at the
documentation wether the first or the last argument contains the result. With operators this is
evident.
In high-performance software, programmers tend to implement a hard-coded version of every
important operation instead of freely compose them from smaller expressions. The reason is
obvious, our operator implementation performed additionally:
• 2n assignments;
• 2n reads;
• 2n writes;
• 2 memory allocations; and
• 2 memory deallocations.
The good news is we have not performed additional arithmetic. The bad news is that the
operations above are more expensive. On modern computers, it takes much more time to
read data from or write to the memory than executing fixed or floating point operations. 11
Unfortunately, vectors in scientific applications tend to be rather long, often larger than the
11 TODO: Maybe quantifying for some machine.