radix_sort_128x() produces unstable sorting output

[gsc74]

@lh3, I was benchmarking the radix_sort_128x() function from minimap2 to perform anchor sorting (map.c [Line 202, Line 289]). For small input sizes of anchors i.e. $\approx 10^5$, radix_sort_128x() produces stable sorting output. In contrast, the outputs are not stable for large inputs (checked for input anchors of size $10^6$). I have used std::stable_sort() to verify the stability of the implementation.

If I want to use std::stable_sort() to sort the anchors, then the PAF output is different for whole-genome alignment (i.e. the alignment of T2T assembly of HG002 against CHM13 v2.0).

Question: Let us say minimap2 produces three different PAF files, X, Y, and Z, by using std::sort(), radix_sort_128x() and std::stable_sort() for anchors sorting at [Line 202, Line 289] of map.c. Which output is preferable to use and why?

The key used for sorting the anchors in std::stable_sort() is specified here, and this repository (https://github.com/gsc74/test_ksort.git) contains the code for verification.