Implementing BLAS Level 3 on the CAP-II ∗
Peter E Strazdins, Richard P. Brent · 2008
The Basic Linear Algebra Subprogram (BLAS) library is widely used in many supercomputing applications, and is used to implement more extensive linear algebra subroutine libraries, such as LINPACK and LAPACK. The use of BLAS aids in the clarity, portability and maintenance of mathematical software. BLAS level 1 routines involve vector-vector operations, level 2 routines involve matrix-vector operations, and level 3 routines involve matrix-matrix operations. To take advantage of the high degree of parallelism of architectures such as the CAP-II, BLAS level 3 routines are desirable. These routines are not I/O bound; for n × n matrices, the order of arithmetic operations is O(n 3) whereas the order of I/O operations is only O(n 2). We are concerned with implementing BLAS level 3 for real matrices on the CAP-II, with emphasis on obtaining the highest possible performance, without sacrificing numerical stability. While the CAP-II has many features that make it very well-suited for this purpose, there are also many new challenges in implementing BLAS level-3 on a distributed memory parallel computer (these are currently being considered also by the authors of BLAS-3, who