argsort/sort with O(n) algorithms: counting-sort, radix-sort

You can already sort with couting-sort using numpy: as stated in an SO answer, it is simply:

np.repeat(np.arange(1+x.max()), np.bincount(x))

But there is no way (as far as I can tell) to do an argsort.

I think it would be fairly easy to implement and slot into the argsort/sort documentation. The benefit of counting sort is that it’s O(n), although it only works for not-too-large non-negative integers…however those are actually quite common in the real world! Pandas uses it behind the scenes apparently.

[d1manson]

Everyone loves a super fast sort!

In terms of API, why not keep the old kind kwarg for backward compatibility, but then add other keywords to control each requirement/hint. Any/all hint kwargs could be ignored in initial/future implementations:

• stable - True/False.
• nearly_sorted - True/False
• small_int_range - True/False
• small_float_set - True/False etc.

[hameerabbasi]

There are good implementations of radix/counting sort/argsort in this repo: https://github.com/eloj/radix-sorting

O(n) integer sort is important for PyData/Sparse as a lot of time is spent on integer sorting in many operations. See pydata/sparse#52. It’s also important to Zarr (zarr-developers/zarr#236)

Ideally, radix sort should be the default sort for integer arrays. The reason is that it’s O(n) instead of O(n log n). Benchmarks in the repository I linked show as much as a 7x speed up for moderately sized arrays.

Radix sort is also stable, which means it doesn’t change the relative ordering of any equal elements.

The only downside to radix sort is that it isn’t in-place: it needs a temporary array to get the work done.