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This talk was given as part of JuliaCon2021.

Abstract:
BLAS & LAPACK are integral components of many numerical algorithms. Due to their importance, a lot of effort has gone into optimizing ASM/C/Fortran implementations.
Nonetheless, early work demonstrated that Julia's implementations were often faster than competitors while laying the groundwork for new routines specialized for new problems.

We discuss a roadmap toward providing Julia BLAS and LAPACK libraries, from optimizations in LoopVectorization to libraries like Octavian and RecursiveFactorization.

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00:00 Welcome!
00:09 Introduction
01:00 Why do we want to create Julia's version of BLAS and LAPACK?
03:03 Performance
03:40 Commentary on LoopVectorization.jl
04:50 Multi-threaded matrix multiplication
05:51 Our biggest success: RecursiveFactorization.jl
07:25 Multi-threaded implementations are not always straightforward
08:58 Recursive factorization is fast even for relatively big matrices
11:16 Flexibility
13:49 Express operation as BLAS, or optimize direct?
15:14 Interoperability with the rest of the Julia ecosystem
16:00 Support for a wide variety of types
16:47 Julia multi-threading can lead to better workload balance
18:43 Roadmap

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