Countless applications cast their computational core in terms of dense linear
algebra operations. These operations can usually be implemented by combining
the routines offered by standard linear algebra libraries such as BLAS and
LAPACK, and typically each operation can be obtained in many alternative ways.
Interestingly, identifying the fastest implementation -- without executing it
-- is a challenging task even for experts. An equally challenging task is that
of tuning each routine to performance-optimal configurations. Indeed, the
problem is so difficult that even the default values provided by the libraries
are often considerably suboptimal; as a solution, normally one has to resort to
executing and timing the routines, driven by some form of parameter search. In
this paper, we discuss a methodology to solve both problems: identifying the
best performing algorithm within a family of alternatives, and tuning
algorithmic parameters for maximum performance; in both cases, we do not
execute the algorithms themselves. Instead, our methodology relies on timing
and modeling the computational kernels underlying the algorithms, and on a
technique for tracking the contents of the CPU cache. In general, our
performance predictions allow us to tune dense linear algebra algorithms within
few percents from the best attainable results, thus allowing computational
scientists and code developers alike to efficiently optimize their linear
algebra routines and codes.Comment: Submitted to PMBS1
