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

> Even in Julia. Unless you're using [Octavian.jl](https://github.com/JuliaLinearAlgebra/Octavian.jl) or such for your linear algebra in place of BLAS. But yes, it is always interesting how many people do not know how much of modern software is built on Fortran!

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

> The biggest reason is because some function of the high level language is incompatible with the application domain. Like garbage collection in hot or real-time code or proprietary compilers for processors. Julia does not solve these problems. The presence of garbage collection in julia is not a problem at all for hot, high performance code. There's nothing stopping you from manually managing your memory in julia. The easiest way would be to just preallocate your buffers and hold onto them so they don't get collected. Octavian.jl is a BLAS library written in julia that's faster than OpenBLAS and MKL for small matrices and saturates to the same speed for very large matrices [1]. These are some of the hottest loops possible! For true, hard-real time, yes julia is not a good choice but it's perfectly fine for soft realtime. [1] https://gith

> 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.

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. 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#. Expressiveness is hard to judge objectively, but in my opinion at least, Multiple Dispatch is a massive win for writing composable, re-usable code, and there really isn't anything that compares on that front to Julia.

Not necessarily. All of the DifferentialEquations.jl defaults use pure Julia BLASes which outperform the Fortran BLASes. Mainly, RecursiveFactorization.jl and Octavian.jl, which tend to match or outperform MKL and OpenBLAS on our benchmarking computers, form our workhorse. https://raw.githubusercontent.com/JuliaLinearAlgebra/Octavia... https://github.com/JuliaLinearAlgebra/Octavian.jl https://github.com/YingboMa/RecursiveFactorization.jl

The pure Julia (sub)BLAS (because they are incomplete right now) that benchmarks the best right now are Octavian and PaddedMatrices.jl. On Ryzen these BLAS's are doing extremely well: https://github.com/JuliaLinearAlgebra/Octavian.jl/issues/24#... but also on Intel: https://chriselrod.github.io/PaddedMatrices.jl/dev/arches/ca... I personally wouldn't spend too much time on BLAS-limited applications though, and this kind of circuit modeling is not one of them as I describe in another post. Also, it's 1000x at 99% accuracy: it's essentially a form of automated model order reduction which allows you to choose a tolerance and get more speedup matching the original circuit to the given tolerance.

I'm not sure that's a particularly convincing argument. Bolting a type system on a dynamic language is incredibly hard to do if you're trying to make a type system that's worth using. It's a fundamental language design problem, and if the type system is doing anything worth while, it'd probably take around a decade to make one that is reasonably sound and robust. At that level of commitment, one can just turn around and look at your static language and say "Well, couldn't you just implement a new language with a new type system in your language?" (assuming your language is turing complete). This really isn't that different. Meanwhile, Julia's type system is actually a fundamental player in it's optimization schemes (the compiler essentially breaks up programs into statically typed chunks and optimizes those separately), so rather than ind