Elements of Design for Containers and Solutions in the LinBox Library

We describe in this paper new design techniques used in the \cpp exact linear algebra library \linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified structure for containers, based on our \emph{founding scope allocation} model. We explain design choices and their impact on coding: unification of our matrix classes, clearer model for matrices and submatrices, \etc Then we present a variation of the \emph{strategy} design pattern that is comprised of a controller--plugin system: the controller (solution) chooses among plug-ins (algorithms) that always call back the controllers for subtasks. We give examples using the solution \mul. Finally we present a benchmark architecture that serves two purposes: Providing the user with easier ways to produce graphs; Creating a framework for automatically tuning the library and supporting regression testing.Comment: 8 pages, 4th International Congress on Mathematical Software, Seoul : Korea, Republic Of (2014

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The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than a classic strategy. Moreover, we leverage a high performance communication scheme for fully exploiting network bandwidth via pipeline broadcast. Overall, the integrated approach achieves substantial energy savings (up to 51.4%) and performance gain (28.6% on average) compared to ScaLAPACK pdgemm() on a cluster with an Ethernet switch, and outperforms ScaLAPACK and DPLASMA pdgemm() respectively by 33.3% and 32.7% on average on a cluster with an Infiniband switch

Cache-aware Performance Modeling and Prediction for Dense Linear Algebra

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