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Daniele G. Spampinato and Markus Püschel (Proc. International Symposium on Code Generation and Optimization (CGO), pp. 117-127, 2016)

**A basic linear algebra compiler for structured matrices**

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Bibtex

Many problems in science and engineering are in practice modelled and solved through matrix computations. Often, the matrices involved have structure such as symmetric or triangular, which reduces the operations count needed to perform a computation. For example, dense linear systems of equations are solved by first converting to triangular form and optimization problems may yield matrices with any kind of structure. The well-known BLAS (basic linear algebra subprograms) interface provides a small set of structured matrix computations, chosen to serve a certain set of higher level functions (LAPACK). However, if a user encounters a computation or structure that is not supported, she has to forego the benefits of the structure and choose a generic functionality. In this paper, we address this problem by providing a compiler that translate a given basic linear algebra computation on structured matrices into optimized C code, optionally vectorized with intrinsics. Our work combines prior work on the Spiral-like LGen compiler with techniques from polyhedral compilation to mathematically capture matrix structures. In the paper we consider upper/lower triangular and symmetric matrices but the approach is extensible to a much larger set including blocked structures. We run experiments on a modern Intel platform against the Intel MKL library and a baseline implementation showing competitive performance results for both BLAS and non-BLAS functionalities.

SIMD vectorization, Synthesis, Linear algebra

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