JUNE 19–23, 2016

Presentation Details

Name: (A11) HPC in Asia Award Winning Poster: Performance of Quadruple Precision Eigenvalue Solver Libraries QPEigenK & QPEigenG on the K Computer
Time: Wednesday, June 22, 2016
10:00 am - 11:00 am
Room:   Analog 1+2
Messe Frankfurt
Breaks:10:00 am - 11:00 am Coffee Break
Presenter:   Yusuke Hirota, RIKEN/AICS
Abstract:   In this study, we evaluate the performance of the high performance quadruple precision eigensolver libraries QPEigenK and QPEigenG. In many computational science applications, it is required to solve large dense standard eigenvalue problems and generalized ones. The numerical solution of the eigenvalue problems generally become less accurate as the matrix dimension increases due to rounding errors. In this study, it is essential to take account of the double-double arithmetic as a quadruple precision format from the viewpoint of accuracy and performance. In 2012, we started to develop a quadruple precision version of eigensolver libraries for a standard eigenproblem and a generalized eigenproblem: QPEigenK and QPEigenG, respectively. The solvers are developed by using MPI/OpenMP hybrid parallelization. Due to a technical reason, a significant computing part of the back transformation is inappropriately parallelized in a thread fashion by OpenMP. However, the current implementation of each solver shows an excellent performance and reaches a good scalability as follows. The execution time for a standard eigenproblem with n = 10,000 is 118 seconds on 16,384 nodes of the K computer, which is only 31 times longer than the case of a double precision solver. The execution time for a generalized problem with n = 5,000 is 171 seconds on 8,192 nodes, which is about five times longer than the case of the same dimensional standard eigenproblem.

Yusuke Hirota, RIKEN AICS; Susumu Yamada, Japan Atomic Energy Agency; Toshiyuki Imamura, RIKEN AICS; Narimasa Sasa, Japan Atomic Energy Agency; Masahiko Machida, Japan Atomic Energy Agency