By Richard P. Brent (auth.), Jack Dongarra, Kaj Madsen, Jerzy Waśniewski (eds.)
Introduction The PARA workshops some time past have been dedicated to parallel computing equipment in technology and know-how. there were seven PARA conferences to this point: PARA’94, PARA’95 and PARA’96 in Lyngby, Denmark, PARA’98 in Umea, ? Sweden, PARA 2000 in Bergen, N- means, PARA 2002 in Espoo, Finland, and PARA 2004 back in Lyngby, Denmark. The ?rst six conferences featured lectures in smooth numerical algorithms, laptop technological know-how, en- neering, and commercial functions, all within the context of scienti?c parallel computing. This assembly within the sequence, the PARA 2004 Workshop with the name “State of the paintings in Scienti?c Computing”, used to be held in Lyngby, Denmark, June 20–23, 2004. The PARA 2004 Workshop was once equipped via Jack Dongarra from the collage of Tennessee and Oak Ridge nationwide Laboratory, and Kaj Madsen and Jerzy used to be ´niewski from the Technical collage of Denmark. The emphasis right here was once shifted to high-performance computing (HPC). the continuing improvement of ever extra complicated desktops presents the opportunity of fixing more and more dif?cult computational difficulties. in spite of the fact that, given the complexity of contemporary computing device architectures, the duty of figuring out this power wishes cautious cognizance. for instance, the failure to use a computer’s reminiscence hello- archy can degrade functionality badly. a prime difficulty of HPC is the advance of software program that optimizes the functionality of a given machine. The excessive fee of cutting-edge pcs might be prohibitive for lots of places of work, specially if there's in simple terms an occasional want for HPC.
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Additional info for Applied Parallel Computing. State of the Art in Scientific Computing: 7th International Workshop, PARA 2004, Lyngby, Denmark, June 20-23, 2004. Revised Selected Papers
Also, we introduce RFP format which is a variant of hybrid full packed (HFP) format. HFP format is described in  of these proceedings. RFP format is a rearrangement of standard full storage holding a symmetric / triangular matrix A into a compact full storage rectangular array AR that uses minimal storage NT=N(N+1)/2. Therefore, level 3 BLAS can be used on AR. In fact, with the equivalent Lapack algorithm, using AR instead of A, gives slightly better performance. This offers the possibility to replace all packed or full Lapack routines with equivalent Lapack routines that work on AR.
We shall make eight points below. Points 1 to 3 are commonly accepted architecture facts about many of today’s processors. Points 4 to 6 are dense linear algebra algorithms facts that are easily demonstrated or proven. Points 7 and 8 are an obvious conclusion based on the AA approach. 1. Floating point arithmetic cannot be done unless the operands involved first reside in the L1 cache. 2. Two-dimensional Fortran and C arrays do not map nicely into L1 cache. (a) The best case happens when the array is contiguous and properly aligned.
In addition to general ideas and techniques, detailed case studies of matrix computations are presented, which only briefly have been dicussed here. Some of the main points are the following: – Recursion creates new algorithms for linear algebra software. – Recursion can be used to express dense linear algebra algorithms entirely in terms of level 3 BLAS-like matrix-matrix operations. – Recursion introduces an automatic variable blocking that targets every level of a deep memory hierarchy. – Recursive blocking can also be used to define data formats for storing block-partitioned matrices.