Theseus | modern OS written from scratch in Rust
kandi X-RAY | Theseus Summary
kandi X-RAY | Theseus Summary
Theseus is a new OS written from scratch in Rust to experiment with novel OS structure, better state management, and how to leverage intralingual design principles to shift OS responsibilities like resource management into the compiler. For more info, check out Theseus's documentation or our published academic papers, which describe Theseus's design and implementation. Theseus is under active development, and although it is not yet mature, we envision that Theseus will be useful in high-end embedded systems or edge datacenter environments. We are continually working to improve the OS, including its fault recovery abilities for higher system availability without redundancy, as well as easier and more arbitrary live evolution and runtime flexbility.
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QUESTION
I am working on a object storage project where I need to understand Reed Solomon error correction algorithm,
I have gone through this Doc as a starter and also some thesis paper.
1. content.sakai.rutgers.edu
2. theseus.fi
but I can't seem to understand the lower part of the identity matrix (red box), where it is coming from. How this calculation is done?
Can anyone please explain this.
...ANSWER
Answered 2020-May-23 at 14:08The encoding matrix is a 6 x 4 Vandermonde matrix using the evaluation points {0 1 2 3 4 5} modified so that the upper 4 x 4 portion of the matrix is the identity matrix. To create the matrix, a 6 x 4 Vandermonde matrix is generated (where matrix[r][c] = pow(r,c) ), then multiplied with the inverse of the upper 4 x 4 portion of the matrix to produce the encoding matrix. This is the equivalent of "systematic encoding" with Reed Solomon's "original view" as mentioned in the Wikipedia article you linked to above, which is different than Reed Solomon's "BCH view", which links 1. and 2. refer to. The Wikipedia's example systematic encoding matrix is a transposed version of the encoding matrix used in the question.
https://en.wikipedia.org/wiki/Vandermonde_matrix
The code to generate the encoding matrix is near the bottom of this github source file:
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Install Theseus
Obtain the Theseus repository (with all submodules): git clone --recurse-submodules https://github.com/theseus-os/Theseus.git
Install Rust: curl https://sh.rustup.rs -sSf | sh
Install dependencies: sudo apt-get install make gcc nasm pkg-config grub-pc-bin mtools xorriso qemu qemu-kvm
Build and run (in QEMU): cd Theseus make run To exit QEMU, press Ctrl + A, then X.
First, install Rust by following the setup instructions here. On Linux, just run:.
Our personal preference is to use VS Code, which has excellent cross-platform support for Rust. Other options are available here.
rust-analyzer, by matklad
Better TOML, by bungcip
x86 and x86_64 Assembly, by 13xforever
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