C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 157
transforms the operations to a form that is best for execution time. We would only need a new
compiler and our programs become faster. 13 But live — especially as advanced C ++ programmer
— is no walk in the park. Of course, the compiler helps us a lot to speed up our programs.
But there are limitations, many optimizations need knowledge of the semantic behavior and can
therefore only be applied on types and operations where the semantic is known at the time the
compiler is written, see also discussion in [?]. Research is going on, to overcome this limitations
by providing concept-based optimization [?]. Unfortunately, this will take time until it becomes
mainstream, especially now that concepts are taken out of the C ++0x standard. An alternative
is source-to-source code transformation with external tools like ROSE [?].
Even for types and operations that the compiler can handle, it has its limitations. Most compilers
(gcc, . . . 14 ) only deal with the inner loop in nested ones (see solution in Section 5.4.2)
and does not dare to introduce extra temporaries (see solution in Section ??). Some compilers
are particularly tuned for benchmarks. 15 For instance, they have pattern matching to recognize
a 3-nested loop that computes a dense matrix product and transform those in BLAS-like code
with 7 or 9 platform-dependent loops. 16 All this said, writing high-performance software is no
walk in the park. That does not mean that such software must be unreadable and unmaintainable
hackery. The route of success is again to provide appropriate abstractions. Those can be
empowered with compile-time optimizations so that the applications are still writen in natural
mathematical notation whereas the generated binaries can still explore all known techniques
for fast execution.
5.4.1 Classical Fixed-Size Unrolling
The easiest form of compile-time optimization can be realized for fixed-size data types, in
particular vectors as in Section 4.7. Simular to the default assignment, we can write a generic
vector assignment:
template
class fsize vector
{
public:
const static int my size= Size;
};
template
self& operator=(const self& that)
{
for (int i= 0; i < my size; ++i)
data[i]= that[i];
}
13
In some sense, this is the programming equivalent of communism: everybody contributes as much as he
pleases and like he pleases and in the end, the right thing will happen anyway thanks to a self-improving society.
Likewise, some people write software in a very naïve fashion and blame the compiler not transforming their
programs into high-performance code.
14
TODO: we should run some benchmarks on MSVC and icc.
15
TODO: search for paper on kcc.
16
One could sometimes get the impression that the HPC community beliefs that multiplying dense matrices
at near-peak performance solves all performance issues of the world or at least demonstrates that everything can
be computed at near-peak performance if only one tries hard enough. Fortunately, more and more people in the
supercomputer centers realize that their machines are not only running BLAS3 and LAPACK operations and
that real-world applications are more often than not limited by memory bandwidth and latency.