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.

> 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.

> 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.