The Relevance of New Data Structure Approaches for Dense Linear Algebra in the New Multi-Core / Many Core Environments
For about ten years now, Bo Kågström’s Group in Umea, Sweden, Jerzy Waśniewski’s Team at Danish Technical University in Lyngby, Denmark, and I at IBM Research in Yorktown Heights have been applying recursion and New Data Structures (NDS) to increase the performance of Dense Linear Algebra (DLA) factorization algorithms. Later, John Gunnels, and later still, Jim Sexton, both now at IBM Research also began working in this area. For about three years now almost all computer manufacturers have dramatically changed their computer architectures which they call Multi-Core, (MC). It turns out that these new designs give poor performance for the traditional designs of DLA libraries such as LAPACK and ScaLAPACK. Recent results of Jack Dongarra’s group at the Innovative Computing Laboratory in Knoxville, Tennessee have shown how to obtain high performance for DLA factorization algorithms on the Cell architecture, an example of an MC processor, but only when they used NDS. In this talk we will give some reasons why this is so.
Unable to display preview. Download preview PDF.
- 1.Agarwal, R.C., Gustavson, F.G., Zubair, M.: Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms. IBM Journal of Research and Development 38(5), 563–576 (1994)Google Scholar
- 5.Chatterjee, S., et al.: Design and Exploitation of a High-performance SIMD Floating-point Unit for Blue Gene/L. IBM Journal of Research and Development 49(2-3), 377–391 (2005)Google Scholar
- 9.Gustavson, F.G.: Recursion Leads to Automatic Variable Blocking for Dense Linear-Algebra Algorithms. IBM Journal of Research and Development 41(6), 737–755 (1997)Google Scholar
- 10.Gustavson, F.G., Jonsson, I.: Minimal Storage High Performance Cholesky via Blocking and Recursion. IBM Journal of Research and Development 44(6), 823–849 (2000)Google Scholar
- 13.Gustavson, F.G.: New Generalized Data Structures for Matrices Lead to a Variety of High performance Dense Linear Algorithms. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 11–20. Springer, Heidelberg (2006)Google Scholar
- 16.IBM. IBM Engineering and Scientific Subroutine Library for AIX Version 3, Release 3. IBM Pub. No. SA22-7272-00 (February 1986)Google Scholar