GPUCompiler.jl VS RecursiveFactorization.jl

I don't think it's frowned upon to compile, many people want this capability as well. If you had a program that could be proven to use no dynamic dispatch it would probably be feasible to compile it as a static binary. But as long as you have a tiny bit of dynamic behavior, you need the Julia runtime so currently a binary will be very large, with lots of theoretically unnecessary libraries bundled into it. There are already efforts like GPUCompiler[1] that do fixed-type compilation, there will be more in this space in the future.

[1] https://github.com/JuliaGPU/GPUCompiler.jl

Julia's compiler is made to be extendable. GPUCompiler.jl which adds the .ptx compilation output for example is a package (https://github.com/JuliaGPU/GPUCompiler.jl). The package manager of Julia itself... is an external package (https://github.com/JuliaLang/Pkg.jl). The built in SuiteSparse usage? That's a package too (https://github.com/JuliaLang/SuiteSparse.jl). It's fairly arbitrary what is "external" and "internal" in a language that allows that kind of extendability. Literally the only thing that makes these packages a standard library is that they are built into and shipped with the standard system image. Do you want to make your own distribution of Julia that changes what the "internal" packages are? Here's a tutorial that shows how to add plotting to the system image (https://julialang.github.io/PackageCompiler.jl/dev/examples/...). You could setup a binary server for that and now the first time to plot is 0.4 seconds.

Julia's arrays system is built so that most arrays that are used are not the simple Base.Array. Instead Julia has an AbstractArray interface definition (https://docs.julialang.org/en/v1/manual/interfaces/#man-inte...) which the Base.Array conforms to, and many effectively standard library packages like StaticArrays.jl, OffsetArrays.jl, etc. conform to, and thus they can be used in any other Julia package, like the differential equation solvers, solving nonlinear systems, optimization libraries, etc. There is a higher chance that packages depend on these packages then that they do not. They are only not part of the Julia distribution because the core idea is to move everything possible out to packages. There's not only a plan to make SuiteSparse and sparse matrix support be a package in 2.0, but also ideas about making the rest of linear algebra and arrays themselves into packages where Julia just defines memory buffer intrinsic (with likely the Arrays.jl package still shipped with the default image). At that point, are arrays not built into the language? I can understand using such a narrow definition for systems like Fortran or C where the standard library is essentially a fixed concept, but that just does not make sense with Julia. It's inherently fuzzy.

A fun fact is that the GPUCompiler, which compiles the code to run in GPU's, is the current way to generate binaries without hiding the whole ~200mb of julia runtime in the binary.

https://github.com/JuliaGPU/GPUCompiler.jl/ https://github.com/tshort/StaticCompiler.jl/

What about the other benchmarks on the same site? https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Bio/BCR/ BCR takes about a hundred seconds and is pretty indicative of systems biological models, coming from 1122 ODEs with 24388 terms that describe a stiff chemical reaction network modeling the BCR signaling network from Barua et al. Or the discrete diffusion models https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Jumps/Dif... which are the justification behind the claims in https://www.biorxiv.org/content/10.1101/2022.07.30.502135v1 that the O(1) scaling methods scale better than O(log n) scaling for large enough models? I mean.

> If you use special routines (BLAS/LAPACK, ...), use them everywhere as the respective community does.

It tests with and with BLAS/LAPACK (which isn't always helpful, which of course you'd see from the benchmarks if you read them). One of the key differences of course though is that there are some pure Julia tools like https://github.com/JuliaLinearAlgebra/RecursiveFactorization... which outperform the respective OpenBLAS/MKL equivalent in many scenarios, and that's one noted factor for the performance boost (and is not trivial to wrap into the interface of the other solvers, so it's not done). There are other benchmarks showing that it's not apples to apples and is instead conservative in many cases, for example https://github.com/SciML/SciPyDiffEq.jl#measuring-overhead showing the SciPyDiffEq handling with the Julia JIT optimizations gives a lower overhead than direct SciPy+Numba, so we use the lower overhead numbers in https://docs.sciml.ai/SciMLBenchmarksOutput/stable/MultiLang....

> you must compile/write whole programs in each of the respective languages to enable full compiler/interpreter optimizations

You do realize that a .so has lower overhead to call from a JIT compiled language than from a static compiled language like C because you can optimize away some of the bindings at the runtime right? https://github.com/dyu/ffi-overhead is a measurement of that, and you see LuaJIT and Julia as faster than C and Fortran here. This shouldn't be surprising because it's pretty clear how that works?

I mean yes, someone can always ask for more benchmarks, but now we have a site that's auto updating tons and tons of ODE benchmarks with ODE systems ranging from size 2 to the thousands, with as many things as we can wrap in as many scenarios as we can wrap. And we don't even "win" all of our benchmarks because unlike for you, these benchmarks aren't for winning but for tracking development (somehow for Hacker News folks they ignore the utility part and go straight to language wars...).

If you have a concrete change you think can improve the benchmarks, then please share it at https://github.com/SciML/SciMLBenchmarks.jl. We'll be happy to make and maintain another.

Ask them to download Julia and try it, and file an issue if it is not fast enough. We try to have the latest available.

See for example: https://github.com/JuliaLinearAlgebra/RecursiveFactorization...

Julia defaults to OpenBLAS but libblastrampoline makes it so that `using MKL` flips it to MKL on the fly. See the JuliaCon video for more details on that (https://www.youtube.com/watch?v=t6hptekOR7s). The recursive comparison is against OpenBLAS/LAPACK and MKL, see this PR for some (older) details: https://github.com/YingboMa/RecursiveFactorization.jl/pull/2... . What it really comes down to in the end is that OpenBLAS is rather bad, and MKL is optimized for Intel CPUs but not for AMD CPUs, so when the best CPUs are now all AMD CPUs, having a new set of BLAS tools and mixing that with recursive LAPACK tools is either as good or better on most modern systems. Then we see this in practice even when we build BLAS into Sundials for 1,000 ODE chemical reaction networks (https://benchmarks.sciml.ai/html/Bio/BCR.html).

>I hope those benchmarks are coming in hot

M1 is extremely good for PDEs because of its large cache lines.

https://github.com/SciML/DiffEqOperators.jl/issues/407#issue...

The JuliaSIMD tools which are internally used for BLAS instead of OpenBLAS and MKL (because they tend to outperform standard BLAS's for the operations we use https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...) also generate good code for M1, so that was giving us some powerful use cases right off the bat even before the heroics allowed C/Fortran compilers to fully work on M1.

Not necessarily true with Julia. Many libraries like DifferentialEquations.jl are Julia all of the way down because the pure Julia BLAS tools outperform OpenBLAS and MKL in certain areas. For example see:

https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...

So a stiff ODE solve is pure Julia, LU-factorizations and all.

Also, the major point is that BLAS has little to no role played here. Algorithms which just hit BLAS are very suboptimal already. There's a tearing step which reduces the problem to many subproblems which is then more optimally handled by pure Julia numerical linear algebra libraries which greatly outperform OpenBLAS in the regime they are in:

https://github.com/YingboMa/RecursiveFactorization.jl#perfor...

And there are hooks in the differential equation solvers to not use OpenBLAS in many cases for this reason:

https://github.com/SciML/DiffEqBase.jl/blob/master/src/linea...

Instead what this comes out to is more of a deconstructed KLU, except instead of parsing to a single sparse linear solve you can do semi-independent nonlinear solves which are then spawning parallel jobs of small semi-dense linear solves which are handled by these pure Julia linear algebra libraries.

And that's only a small fraction of the details. But at the end of the day, if someone is thinking "BLAS", they are already about an order of magnitude behind on speed. The algorithms to do this effectively are much more complex than that.