Prospectus for the Next LAPACK and Scalapack Libraries
Prospectus for the Next LAPACK and ScaLAPACK Libraries James Demmel1, Jack Dongarra23, Beresford Parlett1, William Kahan1, Ming Gu1, David Bindel1, Yozo Hida1, Xiaoye Li1, Osni Marques1, E. Jason Riedy1, Christof Voemel1, Julien Langou2, Piotr Luszczek2, Jakub Kurzak2, Alfredo Buttari2, Julie Langou2, Stanimire Tomov2 1 University of California, Berkeley CA 94720, USA, 2 University of Tennessee, Knoxville TN 37996, USA, 3 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, 1 Introduction Dense linear algebra (DLA) forms the core of many scienti¯c computing appli- cations. Consequently, there is continuous interest and demand for the devel- opment of increasingly better algorithms in the ¯eld. Here 'better' has a broad meaning, and includes improved reliability, accuracy, robustness, ease of use, and most importantly new or improved algorithms that would more e±ciently use the available computational resources to speed up the computation. The rapidly evolving high end computing systems and the close dependence of DLA algo- rithms on the computational environment is what makes the ¯eld particularly dynamic. A typical example of the importance and impact of this dependence is the development of LAPACK [1] (and later ScaLAPACK [2]) as a successor to the well known and formerly widely used LINPACK [3] and EISPACK [3] libraries. Both LINPACK and EISPACK were based, and their e±ciency depended, on optimized Level 1 BLAS [4]. Hardware development trends though, and in par- ticular an increasing Processor-to-Memory speed gap of approximately 50% per year, started to increasingly show the ine±ciency of Level 1 BLAS vs Level 2 and 3 BLAS, which prompted e®orts to reorganize DLA algorithms to use block matrix operations in their innermost loops.
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