For those of you who aren’t aware, the Mojo SDK was recently released, so I thought I would take the opportunity to start benchmarking some Julia code against Mojo. As a first test, I am calculating the Mandelbrot set using the code provided by Modular . This is my Julia implementation: using Plots…

This one runs 5x 8x faster then the original julia example posted here, and illustrates nicely how something like ComplexSIMD can be defined quite easily in Julia: const xn = 960 const yn = 960 const xmin = -2.0 const xmax = 0.6 const ymin = -1.5 const ymax = 1.5 const MAX_ITERS = 200 struct Compl…

Am I right in thinking that the main issue for speed here is the branch abs2(z)>4? In this case, could we make a package to handle this branching in parallel loops?

Yes, the main issue is that the branch exits the loop. Also, that the optimal loop to SIMD is not the inner most loop. LLVM is really bad whenever that’s the case, so it needs help. SIMD.jl and LoopVectorization.jl can both help there, but LoopVectorization.jl also doesn’t handle early-stopping lo…

Since not exiting the loop exactly on time in mandelbrot_kernel, does not change the output values (because of inactive mask), perhaps checking the condition less than every time can improve performance. For example, check condition when i is a power of 2. …or sampling a point in a bunch of vectors…

[image] Dan: perhaps checking the condition less than every time can improve performance. yeah, I was thinking that. basically do an internal loop: @inline function mandelbrot_kernel(c) z = c iesc = 0 for i = 1:8:MAX_ITERS @turbo for j in 1:8 z = z * z + c if iesc == …

It is much better to parallelize an outer loop, and perform multiple mandelbrot_kernels in parallel like both my code and sdanisch’s code does, than it is to try and parallelize the mandelbrot_kernel’s iterations.

Oh right, the inner_turbo, moving along a scanline makes good sense, each pixel is totally independent.

Almost the only case where @simd does anything is where a loop is computing a floating-point reduction and allowing reassociation of + or * lets the compiler convert a left-to-right reduction into a vectorized reduction. But sum and prod and reduce already do this in a cleverer and faster way, so yo…

[image] StefanKarpinski: But sum and prod and reduce already do this in a cleverer and faster way It’s going to be machine and size-dependent, but Base.sum lags behind for larger arrays that are still small enough to fit in cache: Benchmarking over lengths 1:2 in a random order: Base.sum: …

Can we improve reduce/sum/prod then? After all they should have full license to associate operations however they want. Of course there’s also recursive pairwise summation for accuracy, which may be contributing some overhead.

[image] StefanKarpinski: Can we improve reduce/sum/prod then? After all they should have full license to associate operations however they want. I think we can improve them without loss of accuracy. It’s worth asking what the best approach at an implementation is. E.g., we don’t have details…

Julia & Mojo Mandelbrot Benchmark

General Usage

mbauman Split this topic October 15, 2023, 4:17pm 58

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Julia & Mojo Mandelbrot Benchmark

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