Algorithm 784: GEMM-based level 3 BLAS: portability and optimization issues

Reviewer: Timothy R. Hopkins

The basic linear algebra s ubroutines (BLAS) consist of three libraries (known as Levels 1, 2, and 3) and form an integral part of much of the important numerical software developed over the last two decades. Efficient implementations of these libraries often lead in turn to large gains in the efficiency of higher-level routines, such as the Lapack library of linear algebra software. Many vendors supply versions of the BLAS tuned to a particular platform, and these are often hand coded to extract the best performance from the target hardware. The hierarchical memory organization common to many current systems makes the development of efficient, plat form-specific Level 3 BLAS (which perform matrix-matrix operations) especially challenging and expensive. The authors of this pair of papers show how it is possible to produce an efficient BLAS Level 3 library based on highly optimized versions of the single Level 3 routine that performs a general matrix-matrix multiply (GEMM) and a small number of simpler Level 1 and Level 2 routines. They also provide a model implementation of their GEMM-based routines along with comprehensive benchmarking software that allows users to measure the quality of vendor implementations against an efficient, portable, Fortran 77 version of the library. The papers provide a detailed account of the strategies required to squeeze the last drop of efficiency from today's processors. Although targeted at the matrix-matrix multiply, the lessons and techniques employed will be valuable to anyone wishing to obtain similar performance from other higher-level numerical operations.