The Student Supercomputer Challenge Guide by ASC Community

The Student Supercomputer Challenge Guide by ASC Community

Author:ASC Community
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore


5.2.1.3 Floating-Point Performance Evaluation Program HPL

High Performance LINPACK Benchmark (HPL) is currently the most well-known high-performance computer performance benchmark software, and the evaluation results of HPL have become a basis for supercomputers’ performance ranking of the world’s TOP500 list and the TOP100 list in China.

LINPACK (LINear algebra PACKage) is the function library for solving linear algebra problems (solving equations, least squares, etc.), written by Jack Dongarra and colleagues in the 1970s and the 1980s. To help users estimate the time needed to solve equations using LINPACK, LINPACK developers wrote the first version of the LINPACK Benchmark, and provided the test data sets: according to a problem with the 100 × 100 matrix, they gave the test results (run time) conducted in many popular computer systems (a total of 23 kinds) at that time. In this way, users can infer the time required to solve the problem of their own matrix. In June 1993, HPL results were introduced in the global TOP500 list of supercomputers’ performance, and replaced the original peak performance ranking as the new basis. This new ranking basis was widely accepted and received quickly. Thereafter until today, HPL has been the most important high-performance computing performance evaluation program.

HPL uses the time taken for solving a dense linear equations Ax = b to evaluate the computer’s floating-point performance. In order to ensure the fairness of the evaluation results, HPL does not allow the user to modify the basic algorithm (using Gaussian elimination of the LU decomposition) that is, the user must ensure the same total number of floating-point calculations. For the N × N matrix A, the total number of floating-point calculations for solving Ax = b is (2/3 × N3−2 × N2). Therefore, as long as the size of the problem N is given, and the system computation time T is measured, we can compute the HPL floating-point performance as (2/3 × N3−2 × N2)/T, with the unit of FLOPS.

HPL allows the user to select any N scale, and modifying the algorithm and program without changing the total number of floating-point operations and computation accuracy. This prompts the users to put all their efforts into obtaining a better value of HPL performance.

Common HPL optimization strategies or approaches include:(1)Select an N as large as possible. Before the system runs out of memory, the larger N, the higher the HPL performance. (Why is that? Think about the reasons.)



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