> 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.

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.

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

No.

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.

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.