Stream-K: Work-centric Parallel Decomposition for Dense Matrix-Matrix Multiplication on the GPU

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<div class="modal-body"> <div class="paper-implementations"> <div class="row align-items-center"> <div class="col-md-5"> <div class="paper-impl-cell"> <a href="https://github.com/NVIDIA/cutlass" class="code-table-link"> <span class=" icon-wrapper icon-ion" data-name="logo-github"><svg xmlns="http://www.w3.org/2000/svg" width="512" height="512" viewBox="0 0 512 512"><path d="M256 32C132.3 32 32 134.9 32 261.7c0 101.5 64.2 187.5 153.2 217.9a17.56 17.56 0 0 0 3.8.4c8.3 0 11.5-6.1 11.5-11.4 0-5.5-.2-19.9-.3-39.1a102.4 102.4 0 0 1-22.6 2.7c-43.1 0-52.9-33.5-52.9-33.5-10.2-26.5-24.9-33.6-24.9-33.6-19.5-13.7-.1-14.1 1.4-14.1h.1c22.5 2 34.3 23.8 34.3 23.8 11.2 19.6 26.2 25.1 39.6 25.1a63 63 0 0 0 25.6-6c2-14.8 7.8-24.9 14.2-30.7-49.7-5.8-102-25.5-102-113.5 0-25.1 8.7-45.6 23-61.6-2.3-5.8-10-29.2 2.2-60.8a18.64 18.64 0 0 1 5-.5c8.1 0 26.4 3.1 56.6 24.1a208.21 208.21 0 0 1 112.2 0c30.2-21 48.5-24.1 56.6-24.1a18.64 18.64 0 0 1 5 .5c12.2 31.6 4.5 55 2.2 60.8 14.3 16.1 23 36.6 23 61.6 0 88.2-52.4 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class="author-span"> Duane Merrill</span>, <span class="author-span"> Cris Cecka</span>, <span class="author-span"> Michael Garland</span>, <span class="author-span"> John D. Owens</span> <span class="hidden-element">路 </span><button type="button" class="badge-edit" data-bs-toggle="modal" data-bs-toggle="modal" data-bs-target="#loginModal"> <span class=" icon-wrapper icon-fa icon-fa-solid" data-name="edit"><svg viewBox="0 0 576 514.999" xmlns="http://www.w3.org/2000/svg"><path d="M402.6 85.198l90.2 90.2c3.8 3.8 3.8 10 0 13.8l-218.399 218.4-92.8 10.3c-12.4 1.4-22.9-9.1-21.5-21.5l10.3-92.8 218.4-218.4c3.799-3.8 10-3.8 13.799 0zm162-22.9c15.2 15.2 15.2 39.9 0 55.2l-35.4 35.4c-3.8 3.8-10 3.8-13.8 0l-90.2-90.2c-3.8-3.8-3.8-10 0-13.8l35.4-35.4c15.3-15.2 40-15.2 55.2 0zM384 348.198c0-3.2 1.3-6.2 3.5-8.5l40-40c7.6-7.5 20.5-2.2 20.5 8.5v157.8c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48v-352c0-26.5 21.5-48 48-48h285.8c10.7 0 16.1 12.9 8.5 20.5l-40 40c-2.3 2.2-5.3 3.5-8.5 3.5H64v320h320v-101.8z"/></svg></span> <span>Edit social preview</span> </button> </p> </div> </div> </div> </div> <div class="paper-abstract"> <div class="row"> <div class="col-md-12"> <p> We introduce Stream-K, a work-centric parallelization of matrix multiplication (GEMM) and related computations in dense linear algebra. Whereas contemporary decompositions are primarily tile-based, our method operates by partitioning an even share of the aggregate inner loop iterations among physical processing elements. This provides a near-perfect utilization of computing resources, regardless of how efficiently the output tiling for any given problem quantizes across the underlying processing elements. On GPU processors, our Stream-K parallelization of GEMM produces a peak speedup of up to 14$\times$ and 6.7$\times$, and an average performance response that is both higher and more consistent across 32,824 GEMM problem geometries than state-of-the-art math libraries such as CUTLASS and cuBLAS. Furthermore, we achieve this performance from a single tile size configuration per floating-point precision, whereas today's math libraries employ complex kernel-selection heuristics to select from a large ensemble of kernel variants. </p> <a href="https://arxiv.org/pdf/2301.03598v1.pdf" onclick="captureOutboundLink('https://arxiv.org/pdf/2301.03598v1.pdf'); return true;" class="badge badge-light badge-cs"> <span class=" icon-wrapper icon-fa icon-fa-regular" data-name="file-pdf"><svg viewBox="0 0 384 513.795" xmlns="http://www.w3.org/2000/svg"><path d="M369.9 98.88c9 9 14.1 21.3 14.1 34v332.1c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48v-416c0-26.5 21.5-48 48-48.1h204.1c12.7 0 24.9 5.1 33.9 14.1zm-37.8 30.1L256 52.88v76.1h76.1zM48 464.98h288v-288H232c-13.3 0-24-10.7-24-24v-104H48v416zm250.2-143.7c10.5 10.5 8 38.7-17.5 38.7-14.8 0-36.9-6.8-55.8-17-21.6 3.6-46 12.7-68.4 20.1-50.1 86.4-79.4 47-76.1 31.2 4-20 31-35.9 51-46.2 10.5-18.4 25.4-50.5 35.4-74.4-7.4-28.6-11.4-51-7-67.1 4.8-17.7 38.4-20.3 42.6 5.9 4.7 15.4-1.5 39.9-5.4 56 8.1 21.3 19.6 35.8 36.8 46.3 17.4-2.2 52.2-5.5 64.4 6.5zm-198.1 77.8c0 .7 11.4-4.7 30.4-35-5.9 5.5-25.299 21.3-30.4 35zm81.6-190.6c-2.5 0-2.6 26.9 1.8 40.8 4.9-8.7 5.6-40.8-1.8-40.8zm-24.4 136.6c15.9-6.1 34-14.9 54.8-19.2-11.199-8.3-21.8-20.4-30.1-35.5-6.7 17.7-15 37.8-24.7 54.7zm131.6-5c3.6-2.4-2.2-10.4-37.3-7.8 32.3 13.8 37.3 7.8 37.3 7.8z"/></svg></span> <span>PDF</span> </a> <a href="https://arxiv.org/abs/2301.03598v1" onclick="captureOutboundLink('https://arxiv.org/abs/2301.03598v1'); return true;" class="badge badge-light badge-cs"> <span class=" icon-wrapper icon-fa icon-fa-regular" data-name="file"><svg viewBox="0 0 384 513.795" xmlns="http://www.w3.org/2000/svg"><path d="M369.9 98.88c9 9 14.1 21.3 14.1 34v332.1c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48v-416c0-26.5 21.5-48 48-48.1h204.1c12.7 0 24.9 5.1 33.9 14.1zm-37.8 30.1L256 52.88v76.1h76.1zM48 464.98h288v-288H232c-13.3 0-24-10.7-24-24v-104H48v416z"/></svg></span> <span>Abstract</span> </a> </div> </div> </div> <div class="row"> <div class="col-md-7 paper-section-first" id="code"> <div class="paper-section-title"> <div class="row"> <div class="col-md-12"> <h2>Code <div class="float-right"> <div class="dropdown edit-button"> <button class="dropdown-toggle badge badge-edit" type="button" id="codeEditMenu" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> <span class=" icon-wrapper icon-fa icon-fa-solid" data-name="edit"><svg viewBox="0 0 576 514.999" xmlns="http://www.w3.org/2000/svg"><path d="M402.6 85.198l90.2 90.2c3.8 3.8 3.8 10 0 13.8l-218.399 218.4-92.8 10.3c-12.4 1.4-22.9-9.1-21.5-21.5l10.3-92.8 218.4-218.4c3.799-3.8 10-3.8 13.799 0zm162-22.9c15.2 15.2 15.2 39.9 0 55.2l-35.4 35.4c-3.8 3.8-10 3.8-13.8 0l-90.2-90.2c-3.8-3.8-3.8-10 0-13.8l35.4-35.4c15.3-15.2 40-15.2 55.2 0zM384 348.198c0-3.2 1.3-6.2 3.5-8.5l40-40c7.6-7.5 20.5-2.2 20.5 8.5v157.8c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48v-352c0-26.5 21.5-48 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<h2>Categories</h2> <hr/> </div> </div> <div class="paper-tasks"> <div class="row"> <div class="col-md-12"> <span class="badge badge-primary badge-primary-nohover"> Data Structures and Algorithms </span> <span class="badge badge-primary badge-primary-nohover"> Distributed, Parallel, and Cluster Computing </span> </div> </div> </div> </div> </div> </div> <div class="row"> <div class="col-md-12 paper-section paper-evaluation-section-title" id="datasets"> <div class="paper-section-title"> <div class="row"> <div class="col-md-12 zero-padding-datasets"> <h2>Datasets <div class="float-right"> <div class="dropdown edit-button"> <button class="dropdown-toggle badge badge-edit" type="button" id="datasetEditMenu" data-bs-toggle="modal" data-bs-target="#loginModal" aria-haspopup="true" aria-expanded="false"> <span class=" icon-wrapper icon-fa icon-fa-solid" data-name="edit"><svg viewBox="0 0 576 514.999" xmlns="http://www.w3.org/2000/svg"><path d="M402.6 85.198l90.2 90.2c3.8 3.8 3.8 10 0 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