This is not a new algorithm. The same algorithm is described in Figure 4 (Theorem 3.1) of https://arxiv.org/pdf/2310.01655.pdf
(Disclaimer: I am an author on the linked paper)
(Disclaimer: I am an author on the linked paper)
Also I note the only thing you have posted before is a link to this paper in particular.
The posted algorithm and the one mentioned in my paper are very similar. It is just that the cumulative sum computation is parallelized in the posted website.