C++ for Scientists - Technische Universität Dresden

5.4. META-TUNING: WRITE YOUR OWN COMPILER OPTIMIZATION 179
of C ++ one can use (or abuse) the compiler to generate the most efficient version without
rewriting the program sources, as one would need in C or Fortran. The power of internal
code generation with the C ++ compiler only makes external code generation as in ATLAS 28
unnecessary. In ATLAS, functions are written in a domain specific language and C programs 29 in
slight variations are generated with a tool and compared regarding performance. The techniques
presented here empower us to generate binaries equivalent to those variations by just using a
C ++ compiler. Thus, we can tune our programs by changing template arguments or constants
(that might be set platform-dependently).
5.4.7 Tuning Nested Loops
⇒ matrix unroll example.cpp
The most used (and abused) example in performance discussions is dense matrix multiplication.
We do not claim to compete with hand-tuned assembler codes but we show the power of metaprogramming
to generate code variations from a single implementation. As starting point we
use a templatized implementation of matrix class from Section 3.7.4.
We begin our implementation with a simple test case:
int main()
{
const unsigned s= 4; // s= 4 for testing and 128 for timing
matrix A(s, s), B(s, s), C(s, s);
}
for (unsigned i= 0; i < s; i++)
for (unsigned j= 0; j < s; j++) {
A(i, j)= 100.0 ∗ i + j;
B(i, j)= 200.0 ∗ i + j;
}
mult(A, B, C);
std::cout ≪ ”C is ” ≪ C ≪ ’\n’;
A matrix multiplication is easily implemented with three nested loops. One of the 6 possible
nestings is a dot-product-like calculation of each entry from C:
cik = Ai · B k
where Ai is the i th row of A and Bk the k th column of B. We use a temporary in the innermost
loop to decrease the cache-invalidation overhead of writing to C’s elements in each operation:
template
void inline mult(const Matrix& A, const Matrix& B, Matrix& C)
{
assert(A.num rows() == B.num rows()); // ...
machines at least for some years since not everybody has GPU card for numerics and not every algorithm is
already successfully ported (e.g. incomplete LU on arbitrary sparse matrices). By the time of this writing their
is not even support for std::complex.
28 http://math-atlas.sourceforge.net/
29 In some cases the C programs contain assembler snippets for a given platform in order to achieve performance
close to peak.