A compiler for linear algebra operations

Barthels, Henrik

doi:10.1145/2984043.2998539

Cited by 2 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to being part of a compiler for linear algebra, it could even be used in interactive environments such as Julia. For the linear algebra compiler Linnea [5], the GMC algorithm allows to find good solutions while at the same time keeping the search space relatively small. e GMC algorithm can be extended even further in multiple ways.…”

Section: Discussionmentioning

confidence: 99%

“…Compared to GEMM, TRMM and SYMM perform half of the scalar operations. 5 is use of performance is, admi edly, a somewhat unfortunate choice of terminology adopted in the HPC community. said kernels in a way that results in a highly efficient evaluation.…”

Section: Related Workmentioning

confidence: 99%

“…To achieve optimal performance, it is necessary to manually map the expressions to optimized routines for basic linear algebra operations, for example as provided by libraries such as BLAS [16,17,30] and LAPACK [4]. To automate this task, the linear algebra compiler Linnea is developed [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The generalized matrix chain algorithm

Barthels

Copik

Bientinesi

2018

Proceedings of the 2018 International Symposium on Code Generation and Optimization

Self Cite

View full text Add to dashboard Cite

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts o en invest days or even weeks of works. e standard matrix chain problem consists in finding the parenthesization of a matrix product M := A 1 A 2 · · · A n that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated expressions, involving transposition, inversion, and matrix properties. Indeed, the computation of such expressions relies on a set of computational kernels that offer functionality well beyond the simple matrix product. e challenge then shi s from finding an optimal parenthesization to finding an optimal mapping of the input expression to the available kernels. Furthermore, it is o en the case that a solution based on the minimization of scalar operations does not result in the optimal solution in terms of execution time. In our experiments, the generated code outperforms other libraries and languages on average by a factor of about 9. e motivation for this work comes from the fact that-despite great advances in the development of compilers-the task of mapping linear algebra problems to optimized kernels is still to be done manually. In order to relieve the user from this complex task, new techniques for the compilation of linear algebra expressions have to be developed.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%