C++ for Scientists - Technische Universität Dresden

164 CHAPTER 5. META-PROGRAMMING
Using Registers
Another feature of modern processors one should keep in mind: cache coherency. Processors
are nowadays designed to share memory while pertaining consistency in their caches. As a
result, every time we write into data structure in memory like our vector w a cache invalidation
signal is sent on the bus. Even if no other processor is present. Unfortunately, this slows down
computation perceivably (from our experience).
Fortunately, this can be avoided in many cases in a rather simple way by introducing a temporary
in a function that resides in register(s) if the type allows. We can rely on the compiler to
decide reasonably the location of temporaries.
This implementation requires two classes: one for the outer and one for the inner loop. Let us
start with the outer loop:
1 template
2 struct fsize mat vec mult reg
3 {
4 template
5 void operator()(const Matrix& A, const VecIn& v in, VecOut& v out)
6 {
7 fsize mat vec mult reg()(A, v in, v out);
8
9 typename VecOut::value type tmp;
10 fsize mat vec mult aux()(A, v in, tmp);
11 v out[Rows]= tmp;
12 }
13 };
We assume that fsize mat vec mult aux is defined or declared before this class. The first statement
in line 7 calls the computations on the preceeding rows. A temporary is defined in line 9 with
the hope that it will be located in a register. Then we call the computation within this row. The
temporary is passed as reference to an inline function so that the summation will be performed
in a register. In line 10 we write the result back to v out. This still causes the invalidation signal
on the bus but only once for each entry.
The functor must be specialized for row 0 to avoid infinite loops:
template
struct fsize mat vec mult reg
{
template
void operator()(const Matrix& A, const VecIn& v in, VecOut& v out)
{
typename VecOut::value type tmp;
fsize mat vec mult aux()(A, v in, tmp);
v out[0]= tmp;
}
};
Within each row we iterate over the columns and increment the temporary (in the register
hopefully):
template
struct fsize mat vec mult aux