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Math. Softw."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Mixed precision \u201cmemory accessor\u201d approaches decouple storage and compute precisions (data are stored and accessed in low precision, but computations are kept in higher precision) to reduce data accesses, improve accuracy, and simplify programming. In this work, we develop such a memory accessor aimed at accelerating sparse direct solvers and propose several new improvements. In particular, we propose a BLAS-based block approach that can directly rely on BLAS libraries for efficiency and portability. When considering BLAS-2 memory-bound operations like triangular solves, we observe that the performance adequately matches the storage cost, in multiple parallel settings, provided that the conversion from storage to compute precision is efficient and that the block size is suitably chosen. For the storage precision, we leverage custom floating-point types unsupported by hardware, and we take advantage of the recent AVX512-VBMI instruction set to reach an improved efficiency. We also consider rank-structured matrix representations such as the Block Low-Rank (BLR) format and explain how to optimize the memory accessor for such matrices. We present preliminary performance experiments using the sparse direct solver MUMPS with adaptive precision BLR approximations. Our results confirm the potential of these memory accessor approaches to achieve efficiency while optimizing storage.<\/jats:p>","DOI":"10.1145\/3811406","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:29:06Z","timestamp":1776781746000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["BLAS-based Mixed Precision Block Memory Accessor with Applications to Sparse Direct Solvers"],"prefix":"10.1145","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8559-9600","authenticated-orcid":false,"given":"Patrick","family":"Amestoy","sequence":"first","affiliation":[{"name":"Mumps Technologies, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8682-3179","authenticated-orcid":false,"given":"Antoine","family":"Jego","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5804-993X","authenticated-orcid":false,"given":"Jean-Yves","family":"L\u2019Excellent","sequence":"additional","affiliation":[{"name":"Mumps Technologies, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9949-4634","authenticated-orcid":false,"given":"Theo","family":"Mary","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6298-703X","authenticated-orcid":false,"given":"Gr\u00e9goire","family":"Pichon","sequence":"additional","affiliation":[{"name":"LIP (Universit\u00e9 de Lyon, ENS de Lyon, UCBL, CNRS, Inria), Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Exploring Variable Accuracy Storage Through Lossy Compression Techniques in Numerical Linear Algebra: A First Application to Flexible GMRES","author":"Agullo Emmanuel","year":"2020","unstructured":"Emmanuel Agullo, Franck Cappello, Sheng Di, Luc Giraud, Xin Liang, and Nick Schenkels. 2020. 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