The LINPACK benchmark: Past, present and future

Concurrency and Computation: Practice and Experience

Volumn 15, Issue 9, 2003, Pages 803-820

  Dongarra, Jack J ^a   Luszczek, Piotr ^a   Petite, Antoine ^b  

^a University of Tennessee   (United States)

^b SUN MICROSYSTEMS   (United States)

Author keywords

Benchmarking; BLAS; High performance computing; HPL; Linear algebra; LINPACK; TOP500

Indexed keywords

ALGORITHMS; BENCHMARKING; CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; DIGITAL ARITHMETIC; EXTRAPOLATION; FORTRAN (PROGRAMMING LANGUAGE); LINEAR EQUATIONS; MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS; VECTORS;

BASIC LINEAR ALGEBRA SUBROUTINES; HIGH PARALLEL COMPUTING; HIGH PERFORMANCE COMPUTING; SOFTWARE PACKAGE LINPACK;

COMPUTER SOFTWARE SELECTION AND EVALUATION;

EID: 0042674307     PISSN: 15320626     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpe.728     Document Type: Article

References (57)

1. The LINPACK 1000x1000 benchmark program. (http://www.netlib.org/benchmark/1000d for source code.).
2. Dongarra JJ, Bunch J, Moller C, Stewart GW. LINPACK User's Guide. SIAM: Philadelphia, PA, 1979.
3. Lawson C, Hanson R, Kincaid D, Krogh F. Basic Linear Algebra Subprograms for Fortran usage. ACM Transactions on Mathematical Software 1979;5:308-323.
4. Dongarra JJ. Performance of various computers using standard linear equations software. Technical Report CS-89-85, University of Tennessee, 2002. (An updated version of this report can be found at benchmark/performance.ps).
5. Pager D. Some notes on speeding up certain loops by software, firmware, and hardware means. IEEE Transactions on Computers 1972; 97-100.
6. Dongarra JJ, Hinds A. Unrolling loops in Fortran. Software-Practice and Experience 1979; 9:219-226.
7. Knuth D. An empirical study of Fortran programs. Software-Practice and Experience 1971; 1:105-133.
8. Dongarra JJ, Du Croz J, Hammarling S, Hanson R. An extended set of Fortran Basic Linear Algebra Subprograms. ACM Transactions on Mathematical Software 1988; 14:1-17.
9. Dongarra JJ, Duff IS, Sorensen DC, van der Vorst HA. Numerical Linear Algebra for High-Performance Computers. SIAM: Philadelphia, PA, 1998.
10. Dongarra JJ, Hewitt T. Implementing dense linear algebra algorithms using mutlitasking on CRAY X-MP-4. SIAM Journal of Science and Statistics in Computing 1986; 7(1):347-350.
11. Dongarra JJ, Sorensen DC. Linear algebra on high-performance computers. Proceedings Parallel Computing 85, Schendel U (ed.). North Holland, 1986; 3-32.
12. Dongarra JJ, Du Croz J, Duff IS, Hammarling S. A set of Level 3 Fortran Basic Linear Algebra Subprograms. ACM Transactions on Mathematical Software 1990; 16:1-17.
13. Barron DW, Swinnerton-Dyer HPF. Solution of simultaneous linear equations using a magnetic tape store. Computer J. 1990; 3:28-33.
14. Calahan DA. Block-oriented local-memory-based linear equation solution on the CRAY-2: Uniprocessor algorithms. Proceedings International Conference on Parallel Processing, August 1986, Schendel U (ed). IEEE Computer Society Press, 1986; 375-378.
15. Chartres B. Adaption of the Jacobi and Givens methods for a computer with magnetic tape backup store. Technical Report 8, University of Sydney, 1960.
16. Dave AK, Duff IS. Sparse matrix calculations on the CRAY-2. Technical Report CSS 197, AERE Harwell, 1986.
17. DuCroz J, Nugent S, Reid J, Taylor D. Solving large full sets of linear equations in a paged virtual store. ACM Transactions on Mathematical Software 1981; 7(4):527-536.
18. McKellar AC, Coffman EG Jr. Organizing matrices and matrix operations for paged memory systems. Communications of the ACM 1969; 12(3):153-165.
19. Berry M, Gallivan K, Harrod W, Jalby W, Lo S, Meier U, Philippe B, Sameh A. Parallel algorithms on Cedar system. Technical Report Report No. 581, CSRD, 1986.
20. Bischof C, Van Loan CF. The WY representation for products of Householder matrices. SIAM SISSC 1987; 8(2).
21. Bucher I, Jordan T. Linear algebra programs for use on a vector computer with a secondary solid state storage device. Advances in Computer Methods for Practical Differential Equations, Vichnevetsky R, Stepleman R (eds). IMACS, 1984; 546-550.
22. IBM. Engineering and Scientific Subroutine Library. IBM, 1986. Program Number: 5668-863.
23. Robert Y, Suguazerro P. The LU decomposition algorithm and its efficient Fortran implementation on the IBM 3090 vector multiprocessor. Technical Report ECSEC Report ICE-0006, IBM, March 1987.
24. Schreiber R. Engineering and Scientific Subroutine Library, Module Design Specification. SAXPY Computer Corporation, 255 San Geronimo Way, Sunnyvale, CA 94086, 1986.
25. Dongarra JJ, Eijkhout V, Luszczek P. Recursive approach in sparse matrix LU factorization. Scientific Programming 2001; 9(1):51-60.
26. Duff IS. Full matrix techniques in sparse Gaussian elimination. Numerical Analysis Proceedings, Dundee, 1981 (Lecture Notes in Mathematics, vol. 912). Springer: Berlin, 1981; 71-84.
27. George A, Rashwan H. Auxiliary storage methods for solving finite element systems. SIAM SISSC 1985; 6:882-910.
28. Gustavson FG. Recursion leads to automatic variable blocking for dense linear-algebra algorithms. IBM Journal of Research and Development 1997; 41(6):737-755.
29. Toledo S. Locality of reference in LU decomposition with partial pivoting. SIAM Journal on Matrix Analysis and Applications 1997; 18(4).
30. Anderson E, Bai Z, Bischof C, Blackford SL, Demmel JW, Dongarra JJ, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Sorensen DC. LAPACK User's Guide (3rd edn). Society for Industrial and Applied Mathematics: Philadelphia, PA, 1999.
31. Toledo S, Gustavson FG. The design and implementation of Solar, a portable library of resealable out-of-core linear algebra computations. Proceedings of the 4th Annual Workshop on I/O in Parallel and Distributed Systems, May 1996. ACM Press, 1996; 28-40.
32. Dongarra JJ, Petitet A, Whaley RC. Automated empirical optimization of software and the Atlas project. Parallel Computing 2001; 27(1-2):3-25.
33. Dongarra JJ, Whaley RC. Automatically tuned linear algebra software (ATLAS). Proceedings SC'89 Conference. IEEE, 1998.
34. Meuer HW, Strohmaier E, Dongarra JJ, Simon HD. Top500 Supercomputer Sites, 17th edition, November 2 2001. (The report can be downloaded from http://www.netlib.org/benchmark/top500.html).
35. Ahrendt G. Weekly postings to comp.sys.super [1993].
36. Kahaner D. Kahaner report on supercomputer in Japan. Technical Report, The Computer Science Department, University of Arizona, 1992. ftp://ftp.cs.arizona.edu/japan/kahaner.reports/jsuper.92.
37. Bailey D, Lee K, Simon H. Using Strassen's algorithm to accelerate the solution of linear systems. Journal of Supercomputing 1990; 4:357-371.
38. Grayson B, van de Geijn R. A high performance parallel Strassen implementation. Parallel Processing Letters 1996; 6(1):3-12.
39. Paprzycki M, Cyphers C. Using Strassen's matrix multiplication in high performance solution of linear systems. Computers and Mathematics with Applications 1996; 31(4/5):55-61.
40. Strassen V. Gaussian elimination is not optimal. Numerical Mathematics 1969; 13:354-356.
41. Coppersmith D, Winograd S. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 1990; 9:251-280.
42. Petitet A, Whaley RC, Dongarra JJ, Cleary A. HPL-A Portable Implementation of the High-Performance Linpack Benchmark for Distributed-Memory Computers. Innovative Computing Laboratory, September 2000. Available at http://icl.cs.utk.edu/hpl/ and http://www.netlib.org/benchmark/hpl/.
43. High Performance Fortran Forum. High Performance Fortran Language specification. Version 1.1. Technical Report, Rice University, November 1994.
44. High Performance Fortran Forum. High Performance Fortran Language specification. version 2.0. Technical Report, Rice University, January 1997.
45. IBM. Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3. IBM, 2001.
46. van de Geijn RA. Using PLAPACK. The MIT Press. 1997.
47. Blackford LS, Choi J, Cleary A, D'Azevedo E, Demmel JW, Dhillon IS, Dongarra JJ, Hammarling S, Henry G, Petitet A, Stanley K, Walker DW, Whaley RC. ScaLAPACK Users' Guide. Society for Industrial and Applied Mathematics: Philadelphia, PA, 1997.
48. Openmp: Simple, portable, scalable smp programming. http://www.openmp.org/.
49. International Organization for Standardization. Information technology-Portable operating system interface (POSIX)-Part 1: System Application Programming Interface (API) [C language]. ISO/IEC 9945-1:1996, Geneva, Switzerland, 1996.
50. Shwartz DA, Judd RR, Harrod WJ, Manley DP. VSIPL 1.02 API. http://www.vsipl.org/ [26 February 2002].
51. Message Passing Interface Forum. MPI: A Message-Passing Interface Standard (version 1.1). http://www.mpi-forum.org/ [1995].
52. Message Passing Interface Forum. MPI-2: Extensions to the Message-Passing Interface. http://www.mpi-forum.org/ [July 1997].
53. Chtchelkanova A, Gunnels J, Morrow G, Overfelt J, van de Geijn R. Parallel implementation of BLAS: General techniques for Level 3 BLAS. Concurrency: Practice and Experience 1997, 9(9):837-857.
54. Dongarra JJ, van de Geijn R, Walker DW. Scalability issues in the design of a library for dense linear algebra. Journal of Parallel and Distributed Computing 1994: 22(3):523-537. (Also LAPACK Working Note No. 43).
55. van de Geijn R. Massively parallel LINPACK Benchmark on the Intel Touchstone DELTA and iPSC/860 systems. 1991 Annual Users Conference Proceedings, Dallas, Texas. Intel Supercomputer Users Group, 1991.
56. van de Geijn R, Watts J. SUMMA: Scalable universal matrix multiplication algorithm. Concurrency: Practice and Experience 1997; 9(4):255-274.
57. Moore GE. Cramming more components onto integrated circuits. Electronics 1965; 38(8).