BLIS is a new software framework for instantiating high-performance BLAS-like dense linear algebra libraries. We demonstrate how BLIS acts as a productivity multiplier by using it to implement the level-3 BLAS on a variety of current architectures. The systems for which we demonstrate the framework include state-of-the-art general-purpose, low-power, and many-core architectures. We show, with very little effort, how the BLIS framework yields sequential and parallel implementations that are competitive with the performance of ATLAS, OpenBLAS (an effort to maintain and extend the GotoBLAS), and commercial vendor implementations such as AMD’s ACML, IBM’s ESSL, and Intel’s MKL libraries. Although most of this article focuses on single-core implementation, we also provide compelling results that suggest the framework’s leverage extends to the multithreaded domain.

How do experts navigate the huge space of implementations for a given specification to find an efficient choice with minimal searching? Answer: They use "heuristics" -- rules of thumb that are more street wisdom than scientific fact. We provide a scientific justification for Dense Linear Algebra (DLA) heuristics by showing that only a few decisions (out of many possible) are critical to performance; once these decisions are made, the die is cast and only relatively minor performance improvements are possible. The (implementation x performance) space of DLA is stair-stepped. Each stair is a set of implementations with very similar performance and (surprisingly) share key design decision(s). High-performance stairs align with heuristics that prescribe certain decisions in a particular context. Stairs also tell us how to tailor the search engine of a DLA code generator to reduce the time it needs to find implementations that are as good or better than those crafted by experts.

Parallelizing dense matrix computations to distributed memory architectures is a well-studied subject and generally considered to be among the best understood domains of parallel computing. Two packages, developed in the mid 1990s, still enjoy regular use: ScaLAPACK and PLAPACK. With the advent of many-core architectures, which may very well take the shape of distributed memory architectures within a single processor, these packages must be revisited since the traditional MPI-based approaches will likely need to be extended. Thus, this is a good time to review lessons learned since the introduction of these two packages and to propose a simple yet effective alternative. Preliminary performance results show the new solution achieves competitive, if not superior, performance on large clusters.

A classical approach to program derivation is to progressively extend a simple specification and then incrementally refine it to an implementation. We claim this approach is hard or impractical when reverse engineering legacy software architectures. We present a case study that shows optimizations and pushouts---in addition to refinements and extensions---are essential for practical stepwise development of complex software architectures.

The efforts of an expert to parallelize and optimize a dense linear algebra algorithm for distributed-memory targets are largely mechanical and repetitive. We demonstrate that these efforts can be encoded and automatically applied to obviate the manual implementation of many algorithms in high-performance code.

SUMMARY A message passing, distributed‐memory parallel computer on a chip is one possible design for future, many‐core architectures. We discuss initial experiences with the Intel Single‐chip Cloud Computer research processor, which is a prototype architecture that incorporates 48 cores on a single die that can communicate via a small, shared, on‐die buffer. The experiment is to port a state‐of‐the‐art, distributed‐memory, dense matrix library, Elemental, to this architecture and gain insight from the experience. We show that programmability addressed by this library, especially the proper abstraction for collective communication, greatly aids the porting effort. This enables us to support a wide range of functionality with limited changes to the library code. Copyright © 2011 John Wiley & Sons, Ltd.