What does HackerNews think of Octavian.jl?

They do, just not if they're using python. In Julia they absolutely do. Here's a matmul and LU respectively that are SOTA (especially for small matrices) https://github.com/JuliaLinearAlgebra/Octavian.jl and https://github.com/JuliaLinearAlgebra/RecursiveFactorization...

For some examples of people porting existing C++ Fortran libraries to julia, you should check out https://github.com/JuliaLinearAlgebra/Octavian.jl, https://github.com/dgleich/GenericArpack.jl, https://github.com/apache/arrow-julia (just off the top of my head). These are all ports of C++ or Fortran libraries that match (or exceed) performance of the original, and in the case of Arrow.jl is faster, more general, and 10x less code.

> But in the end, it's FORTRAN all the way down. Even in Julia.

That's not true. None of the Julia differential equation solver stack is calling into Fortran anymore. We have our own BLAS tools that outperform OpenBLAS and MKL in the instances we use it for (mostly LU-factorization) and those are all written in pure Julia. See https://github.com/YingboMa/RecursiveFactorization.jl, https://github.com/JuliaSIMD/TriangularSolve.jl, and https://github.com/JuliaLinearAlgebra/Octavian.jl. And this is one part of the DiffEq performance story. The performance of this of course is all validated on https://github.com/SciML/SciMLBenchmarks.jl

Well IMO it can definitely be rewritten in Julia, and to an easier degree than python since Julia allows hooking into the compiler pipeline at many areas of the stack. It's lispy an built from the ground up for codegen, with libraries like (https://github.com/JuliaSymbolics/Metatheory.jl) that provide high level pattern matching with e-graphs. The question is whether it's worth your time to learn Julia to do so.

You could also do it at the LLVM level: https://github.com/JuliaComputingOSS/llvm-cbe

One cool use case is in https://github.com/JuliaLinearAlgebra/Octavian.jl which relies on loopvectorization.jl to do transforms on Julia AST beyond what LLVM does. Because of that, Octavian.jl. a pure julia linalg library, beats openblas on many benchmarks

The initial results are that libraries like LoopVectorization can already generate optimal micro-kernels, and is competitive with MKL (for square matrix-matrix multiplication) up to around size 512. With help on macro-kernel side from Octavian, Julia is able to outperform MKL for sizes up to to 1000 or so (and is about 20% slower for bigger sizes). https://github.com/JuliaLinearAlgebra/Octavian.jl.

Or much faster (at small sizes): https://github.com/JuliaLinearAlgebra/Octavian.jl

> If you want performance benchmarks vs Fortran, https://benchmarks.sciml.ai/html/MultiLanguage/wrapper_packa... has benchmarks with Julia out-performing highly optimized Fortran DiffEq solvers, and https://github.com/JuliaLinearAlgebra/Octavian.jl shows that pure Julia BLAS implementations can compete with MKL and openBLAS, which are among the most heavily optimized pieces of code ever written.

That seems to be very Julia-specific comparisons, which I'm sure will be oriented towards the use cases Julia has been designed for. I'm more interested in "neutral" benchmarks and more general-purpose computing areas.

> Furthermore, Julia has been used on some of the world's fastest super-computers (in the performance critical bits), which as far as I know isn't true of Swift/Kotlin/C#.

That's more a reflection of culture than performance though. Back when I worked with a bunch of data scientists they would happily run Python or R on our Spark cluster, consuming oodles of resources to do not very much, but balked at writing Scala, even though their code would have run much faster.