BLIS Retreat 2023: Aug. 28-29, UT Austin

Subsubsection 5.3.2.1 Codegen for GEMMFIP in BLIS

Related materials:

• Slides¹

• Towards a Unified Implementation of GEMM in BLIS² presented at ICS 2023.

• Arxiv: GEMMFIP: Unifying GEMM in BLIS³.

Subsubsection 5.3.2.2 AVX-512 optimizations for BLIS Level-3 routines

Subsubsection 5.3.2.3 Low Precision GEMM

Related materials

• Slides⁴

Subsubsection 5.3.2.4 Additional Discussion

Subsubsection 5.3.4.1 AOCL BLIS framework changes

Related materials

• Slides⁵

Subsubsection 5.3.4.2 BLIS for the Web: 2023 edition

Related materials

• Slides⁶

Subsubsection 5.3.4.3 The \(L T L^T \) factorization: A glimpse at what comes next

Collaborative work with Maggie Myers, Devangi Parikh, Devin Matthews, RuQing Xu, Tze Meng Low, Ishna Satyarth, Chao Yin, and others

Abstract:

We use the \(L T L^T \) factorization of a skew-symmetric matrix to illustrate opportunities that are available now that BLIS has been refactored to allow more flexible creation of custom functionality. It starts with extensions to the FLAME notation and the application of the FLAME methodology to derive new algorithms for computing. The best resulting algorithm casts most computation in terms of a skew-symmetric "sandwiched" rank-k update \(B := B + Y T Y^T \) where \(T \) is a skew-symmetric tridiagonal matrix. On the one hand, this operation can now be easily implemented in BLIS using the new plug-in facility. On the other hand, a proposed FLAME-like C++ interface allows unblocked and blocked algorithms to be elegantly represented in efficient code. This illustrates the tremendous potential of a new effort to reinvent higher level linear and multilinear algebra libraries.

Related materials

• Slides⁷

Subsubsection 5.3.4.4 Additional Discussion

Subsubsection 5.3.6.1 Plugin tutorial

Subsubsection 5.3.6.2 More informal brainstorming

Subsubsection 5.3.6.3

Subsubsection 5.3.6.4 Additional Discussion