Deriving Linear Algebra Libraries

نویسندگان

  • Robert van de Geijn
  • Tyler Rhodes
  • Maggie Myers
  • Field G. Van Zee
چکیده

Starting in the late 1960s computer scientists including Dijkstra and Hoare advocated goal-oriented programming and formal derivation of algorithms. The problem was that for loop-based programs, a priori determination of loop-invariants, a prerequisite for developing loops, was a task too complex for any but the simplest of operations. We believe that no practical progress was made in the field until around 2000 when we discovered how to systematically determine loop-invariants for operations in the domain of high-performance dense linear algebra libraries. This has led to a multitude of papers, mostly published in the ACM Transactions for Mathematical Software. It has yielded a system for mechanical derivation of algorithms and a high-performance linear algebra library, libflame, that is largely derived to be correct and includes more than a thousand algorithmic variants of algorithms for more than a hundred linear algebra operations. To our knowledge, this success story has unfolded without any awareness on the part the formal methods community. This paper is meant to raise that awareness.

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تاریخ انتشار 2011