Algorithm 784: GEMM-based level 3 BLAS: portability and optimization issues

ABSTRACT

This companion article discusses portability and optimization issues of the GEMM-based level 3 BLAS model implementations and the performance evaluation benchmark. All software comes in all four data types (single- and double-precision, real and complex) and are designed to be easy to implement and use on different platforms. Each of the GEMM-based routines has a few machine-dependent parameters that specify internal block sizes, cache characteristics, and branch points for alternative code sections. These parameters provide means for adjustment to the characteristics of a memory hierarchy.

REFERENCES

• 1: E. Anderson , Z. Bai , C. Bischof , J. Demmel , J. Dongarra , J. Du Croz , A. Greenbaum , S. Hammarling , A. McKenney , S. Ostrouchov , D. Sorensen, LAPACK's user's guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
• 2: David H. Bailey, Unfavorable strides in cache memory systems (RNR Technical Report RNR-92-015), Scientific Programming, v.4 n.2, p.53-58, Summer 1995
• 3: J. J. Dongarra , Jeremy Du Croz , Sven Hammarling , I. S. Duff, A set of level 3 basic linear algebra subprograms, ACM Transactions on Mathematical Software (TOMS), v.16 n.1, p.1-17, March 1990 [doi>10.1145/77626.79170]
• 4: J. J. Dongarra , Jermey Du Cruz , Sven Hammerling , I. S. Duff, Algorithm 679; a set of level 3 basic linear algebra subprograms: model implementation and test programs, ACM Transactions on Mathematical Software (TOMS), v.16 n.1, p.18-28, March 1990 [doi>10.1145/77626.77627]
• 5: Bo Kågström , Per Ling , Charles van Loan, GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark, ACM Transactions on Mathematical Software (TOMS), v.24 n.3, p.268-302, Sept. 1998 [doi>10.1145/292395.292412]

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing; Efficiency; Reliability and robustness

General Terms:
Algorithms, Measurement, Performance

Keywords:
GEMM-based level 3 BLAS, blocked algorithms, matrix-matrix kernels, memory hierarchy, parallelization, vectorization