{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T23:01:57Z","timestamp":1777676517422,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2013,6,19]],"date-time":"2013-06-19T00:00:00Z","timestamp":1371600000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p>Design by Transformation (DxT) is a top-down approach to mechanically derive high-performance algorithms for dense linear algebra. We use DxT to derive the implementation of a representative matrix operation, two- sided Trmm. We start with a knowledge base of transformations that were encoded for a simpler set of operations, the level-3 BLAS, and add only a few transformations to accommodate the more complex two- sided Trmm. These additions explode the search space of our prototype system, DxTer, requiring the novel techniques defined in this paper to eliminate large segments of the search space that contain suboptimal algorithms. Performance results for the mechanically optimized implementations on 8192 cores of a BlueGene\/P architecture are given.<\/jats:p>","DOI":"10.1177\/1094342013492178","type":"journal-article","created":{"date-parts":[[2013,6,19]],"date-time":"2013-06-19T22:04:05Z","timestamp":1371679445000},"page":"440-453","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["A case study in mechanically deriving dense linear algebra code"],"prefix":"10.1177","volume":"27","author":[{"given":"Bryan","family":"Marker","sequence":"first","affiliation":[{"name":"Department of Computer Science, The University of Texas at Austin, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Don","family":"Batory","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Texas at Austin, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"van de Geijn","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Texas at Austin, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,6,19]]},"reference":[{"key":"bibr1-1094342013492178","first-page":"231","volume-title":"ACM SIGPLAN symposium on languages, compilers, and tools for embedded systems","author":"Almagor L","year":"2004"},{"key":"bibr2-1094342013492178","volume-title":"LAPACK Users\u2019 Guide","author":"Anderson E","edition":"3"},{"key":"bibr3-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1080\/00268970500275780"},{"key":"bibr4-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1109\/FMPC.1992.234898"},{"key":"bibr5-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1145\/77626.79170"},{"key":"bibr6-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1145\/42288.42291"},{"key":"bibr7-1094342013492178","volume-title":"A systematic approach to the design and analysis of parallel dense linear algebra algorithms","author":"Gunnels J","year":"2001"},{"key":"bibr8-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840489"},{"key":"bibr9-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1145\/1509864.1509865"},{"key":"bibr10-1094342013492178","doi-asserted-by":"publisher","DOI":"10.1145\/355841.355847"},{"key":"bibr11-1094342013492178","unstructured":"Marker B, Batory D, Shepherd C (2012a) DxTer: A dense linear algebra program synthesizer. 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