Looks good to me. Have you considered adding a really practical realworld example? As someone who loves looking at examples I like your small examples in the readme, but it still leaves me wondering a bit what I actually would use this library for.

Many people don't know what you would use wavelets for or where they really shine. I for example know wavelets are used in image compression algorithms but that's about it. I am curious where else this could be applied.

Thanks for the feedback! You're right, just listing features doesn't make the use cases very clear. I'm planning to add more concrete, real-world examples to the README and examples to better show where wavelet matrices really shine.

Can a wavelet be used with SIMD 128bit operations? Or are they used with 4x4 Matrix operators? Are wavelets good for that kind of math?

> Can a wavelet be used with SIMD 128bit operations?

Popcount works great in this context, but that only gives you linear speedups. Doing rank/select in O(1) instead of O(N) is a bigger win, and you get that by precomputing superblocks.

> Or are they used with 4x4 Matrix operators? Are wavelets good for that kind of math?

Nope, different kind of matrix. Just refers to a nicer packing of a wavelet tree with space wasted by bookkeeping pointers between tree nodes.

Does this contain unsafe? Even the Linux kernel's Rust code have memory safety bugs. https://news.ycombinator.com/item?id=46309536

No, the library itself does not use unsafe Rust at all. The Python bindings are built using PyO3, which internally uses unsafe (as required to interface with the CPython C API), but that is fully encapsulated within PyO3. The core data structure and algorithms remain purely safe Rust.

> git clone https://github.com/math-hiyoko/wavelet-matrix.git && find wavelet-matrix -type f -name '*.rs' -exec grep 'unsafe' {} +

No.

Thank you for sharing! It's great to have more wavelet libraries. I don't often use those, but when I do the choice is scarce. It's great to have another option!

What's a good reference to learn about Wavelet Matrices?

Start with Wavelet trees (much more intuitive): https://www.alexbowe.com/wavelet-trees/

The matrix version is just an implementation detail to store the tree in a less tree-like shape so you don't need as many pointers.