array
cadabra2
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array | cadabra2 | |
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5 | 2 | |
188 | 215 | |
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6.9 | 8.1 | |
4 months ago | 10 days ago | |
C++ | C++ | |
Apache License 2.0 | GNU General Public License v3.0 only |
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array
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Einsum in 40 Lines of Python
I wrote a library in C++ (I know, probably a non-starter for most reading this) that I think does most of what you want, as well as some other requests in this thread (generalized to more than just multiply-add): https://github.com/dsharlet/array?tab=readme-ov-file#einstei....
A matrix multiply written with this looks like this:
enum { i = 2, j = 0, k = 1 };
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Benchmarking 20 programming languages on N-queens and matrix multiplication
I should have mentioned somewhere, I disabled threading for OpenBLAS, so it is comparing one thread to one thread. Parallelism would be easy to add, but I tend to want the thread parallelism outside code like this anyways.
As for the inner loop not being well optimized... the disassembly looks like the same basic thing as OpenBLAS. There's disassembly in the comments of that file to show what code it generates, I'd love to know what you think is lacking! The only difference between the one I linked and this is prefetching and outer loop ordering: https://github.com/dsharlet/array/blob/master/examples/linea...
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A basic introduction to NumPy's einsum
If you are looking for something like this in C++, here's my attempt at implementing it: https://github.com/dsharlet/array#einstein-reductions
It doesn't do any automatic optimization of the loops like some of the projects linked in this thread, but, it provides all the tools needed for humans to express the code in a way that a good compiler can turn it into really good code.
cadabra2
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A basic introduction to NumPy's einsum
If you're into tensor algebra i can only recommend the beautiful piece of Software Cadabra is:
https://cadabra.science/
We wrote an article with it once, 40th order in the Lagrangian, perhaps 50k pages of calculations when all printed. Amazing tool! Thanks Kasper!
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Help with compiling Cadabra2 on Fedora
Before these suggestions come up, let me note that I did submit a bug report about a month ago, which was so far unaddressed by the developer. If I can't get it to work here, I also plan to email the developer directly since he said
What are some alternatives?
optimizing-the-memory-layout-of-std-tuple - Optimizing the memory layout of std::tuple
fricas - Official repository of the FriCAS computer algebra system
NumPy - The fundamental package for scientific computing with Python.
OpenGL-Particle-Motion - This project simulates the motion of electrons and protons using Coulomb's Law. The simulation is visually represented on-screen using OpenGL.
alphafold2 - To eventually become an unofficial Pytorch implementation / replication of Alphafold2, as details of the architecture get released
einops - Flexible and powerful tensor operations for readable and reliable code (for pytorch, jax, TF and others)
Einsum.jl - Einstein summation notation in Julia
julia - Simple fractal drawing software
c-examples - Example C code
einshape
calc - C-style arbitrary precision calculator