Floor vs Ceil when identifying the index

[karayusuf]

I recently noticed that the library floors the result when determining the bin index.
However, the paper seems to indicate the we should ceil the result.

The floor logic is consistent across the various language implementations, so I assume it is correct.
Could someone please explain the difference? Perhaps I'm just looking at the wrong thing?

---

[CharlesMasson]

It doesn't matter as long as the computation of the quantile from the index stays consistent with the calculation of the index from the value. Essentially, the libraries shift indexes by 1 when compared to the paper, but when recomputing the quantile, the opposite shift is applied. The motivation for using the floor in the libraries was leveraging intrinsics for more performant bucket indexing, as floor intrinsics are more widely available across architectures than ceil intrinsics, and more easily accessible when implementing across languages.

[dlu-tech]

@CharlesMasson Thanks for the response! The explanation helps a lot.
Just wondering for a special case where input value x = 1 , wouldn't this logic fail ? Or maybe there's some special treatment in the code for it?
I was just thinking doesn't the bin_index_that_takes_floor != bin_ndex_that_takes_ceil - 1 when log_gamma(x) is an integer?