LAProof: A Library of Formal Proofs of Accuracy and Correctness for Linear Algebra Programs

The LAProof library provides formal machine-checked proofs of the accuracy of basic linear algebra operations: inner product using conventional multiply and add, inner product using fused multiply-add, scaled matrix-vector and matrix-matrix multiplication, and scaled vector and matrix addition. Thes...

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Bibliographic Details
Published inProceedings - Symposium on Computer Arithmetic pp. 36 - 43
Main Authors Kellison, Ariel E., Appel, Andrew W., Tekriwal, Mohit, Bindel, David
Format Conference Proceeding
LanguageEnglish
Published IEEE 04.09.2023
Subjects
Error analysis
floating-point arithmetic
formal verification
Libraries
Mathematical models
program verification
rounding error analysis
Roundoff errors
Sparse matrices
Stability analysis
Vectors
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Summary:The LAProof library provides formal machine-checked proofs of the accuracy of basic linear algebra operations: inner product using conventional multiply and add, inner product using fused multiply-add, scaled matrix-vector and matrix-matrix multiplication, and scaled vector and matrix addition. These proofs can connect to concrete implementations of low-level basic linear algebra subprograms; as a proof of concept we present a machine-checked correctness proof of a C function implementing sparse matrix-vector multiplication using the compressed sparse row format. Our accuracy proofs are backward error bounds and mixed backward-forward error bounds that account for underflow, proved subject to no assumptions except a low-level formal model of IEEE-754 arithmetic. We treat low-order error terms concretely, not approximating as \mathcal{O}\left( {{u^2}} \right).
ISSN:2576-2265
DOI:10.1109/ARITH58626.2023.00021