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LINPACK initially referred to a numerical program library for solving systems of linear equations . Later the name was also used for a program for measuring the speed of a computer . In the original version of this measurement program, almost all of the work is done in two subroutines from the program library mentioned.


LINPACK, which stands for Lin ear System Pack age, was written in 1979 by Jack Dongarra , Cleve Moler , Gilbert W. Stewart for Fortran . The measurement program LINPACK is used to measure the performance of supercomputers , since the solution of linear systems of equations plays a decisive role in the implicit solution methods often implemented there. The result is given in floating point operations per second ( FLOPS ) and published in the TOP500 list of the fastest supercomputers. There are also versions of LINPACK for the programming languages C , C ++ , Pascal , Java and others. The LINPACK benchmark is now considered obsolete; the successor is LAPACK , which is particularly suitable for shared memory and vector supercomputers and which also runs on them with higher performance.

Structure of the benchmark

The benchmark is divided into three sub-tests.

Fortran n = 100 benchmark

The first benchmark consists in factoring a fully populated 100x100 matrix and solving a system of equations by decomposition.

The basic rules for running this benchmark are that no changes may be made to the Fortran code , and no comments may be changed or removed. Only compiler optimization can be used to increase performance.

Linpack n = 1000 benchmark

This test is quite similar to the first, with the difference that a 1000x1000 matrix has to be solved here, but both the solution algorithm and the programming language can be freely selected.

The only condition is that the result must have a certain degree of accuracy in order to be comparable with others.

Linpack's Highly Parallel Computing Benchmark

In this benchmark, in addition to the algorithm and the language, the size of the matrix can also be selected. However, here too there is the condition that the result must show a certain degree of accuracy.


The benchmark evaluates systems only in terms of their computing speed when solving linear systems of equations. The problem that the LINPACK benchmark tries to solve, however, represents an atypical application, since fully populated systems of equations are used here. The number of operations required with N unknowns and N equations is of the order of magnitude .

It is also criticized that the LINPACK benchmark measures performance, but does not take into account the efficiency of the supercomputer.

LINPACK benchmark results (as of November 2018)

Selected LINPACK benchmarks
Computer / CPU description Position
Rmax in Giga FLOPS
Summit Oak Ridge National Laboratory , Oak Ridge , USA 1. approx. 143,500,000
Sierra Lawrence Livermore National Laboratory , USA 2. approx. 94,640.0
Sunway TaihuLight National Supercomputing Center , Wuxi China 3. approx. 93,014.6
Tianhe-2 National Super Computer Center, Guangzhou


4th approx. 61,444.5
Piz Daint Swiss National Supercomputing Center , Switzerland 5. approx. 21,230.0
Trinity United States of America 6th approx. 20,158.7
AI Bridging Cloud Infrastructure National Institute of Advanced Industrial Science and Technology , Japan 7th approx. 19,880.0
SuperMUC-NG Leibniz Computing Center , Germany 8th. approximately 19,476.6
Titan (computer) Oak Ridge National Laboratory , USA 9. approx.17,590.0
Sequoia 10. approximately 17,173.2
2 × AMD Opteron 6274, 2.2 GHz Server in 2012 (64 bit) - approx. 204.9 
2 × Intel Xeon DP X5680, 3.33 GHz Workstation in 2010 (64 bit) - approx. 94.8 
Intel Core i7 , 3.20 GHz, 4 cores Standard PC in 2009 (64 bit) - approx. 33.0 
Intel Core 2 Quad , 2.66 GHz Standard PC in 2007 (64 bit) - approx. 23.5 
Intel Core 2 Duo , 2.66 GHz Standard PC in 2007 (64 bit) - approx. 12.5 
AMD Athlon 64 X2 6000+, 3.00 GHz Standard PC in 2007 (64 bit) - approx 8.4 
Intel Itanium 2 , 1.6 GHz Workstation (64 bit) - approx 6.4 
Intel Pentium 4 , 3.2 GHz Standard PC in 2003 - approx. 3.1 
Intel Pentium II , 450 MHz Standard PC in 1999 - approx. 0.4
Raspberry Pi , 700 MHz Educational Board - approx. 0.01625
Intel 386DX , 33 MHz Standard PC in 1989 - approx. 0.008

Web links

Individual evidence

  1. a b c Supercomputer benchmarks: Linpack page 3. July 21, 2006, accessed on May 26, 2019 .
  2. Linpack FAQ: n = 100 benchmarks. Retrieved May 26, 2019 .
  3. The US has the fastest. November 12, 2018, accessed May 26, 2019 .
  4. Top500 November 2018. Retrieved on May 26, 2019 .
  5. , created on April 24, 2012 with ACML (the AMD Core Math Library) and Open64 compiler under Suse Linux
  6. Tecchannel Linpack Benchmarks ( Memento from January 1, 2016 in the Internet Archive )
  7. , tested with only about 1.6 GB of memory usage
  8. a b c Tecchannel Linpack Benchmark ( Memento from December 9, 2015 in the Internet Archive )
  9. a b Cell Broadband Engine Architecture and its first implementation