Abstract
We present new abstract domains to prove automatically the functional correctness of algorithms implementing matrix operations, such as matrix addition, multiplication, GEMM (general matrix multiplication), or more generally BLAS (Basic Linear Algebra Subprograms). In order to do so, we introduce a family of abstract domains parameterized by a set of matrix predicates and by a numeric domain. We show that our analysis is robust enough to prove the functional correctness of several versions of matrix addition and multiplication codes resulting from loop reordering, loop tiling, inverting the iteration order, line swapping, and expression decomposition. Finally, we extend our method to enable modular analysis on code fragments manipulating matrices by reference, and show that it results in a significant analysis speedup.
This work is partially supported by the European Research Council under Consolidator Grant Agreement 681393 – MOPSA.
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Notes
- 1.
\(\triangledown _p\) can not be used when the two abstract states do not have the same shape, in which case the analyzer will perform a join. However, ultimately, the shape will stabilize, thus allowing the analyzer to perform a widening. This widening technique is similar to the one proposed by [18] on cofibred domains.
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Journault, M., Miné, A. (2016). Static Analysis by Abstract Interpretation of the Functional Correctness of Matrix Manipulating Programs. In: Rival, X. (eds) Static Analysis. SAS 2016. Lecture Notes in Computer Science(), vol 9837. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53413-7_13
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