You don't even need to have specific knowledge of the hardware as long as you can identify cross-over points where one algorithm starts significantly outperforming others. An old HPC trick is to write software that thoroughly measures several algorithm strategies on your specific hardware environment and then code-gens an algorithm that has an optimal set of strategies and strategy-switching thresholds. The meta-algorithm is mostly focused on cheaply detecting these thresholds at runtime.
Where possible, I always liked arrays of function pointers for each next power of 2 in the input sizes. A few popcounts and a jump later, and you're executing the right routine. It's not great if you're throwing a general-purpose tool against tiny problems, but it's not a huge amount of overhead either, and it's dead simple to code.
Maybe that’s convex if you smooth enough. But depends on the buffer sizes.
There's a massive performance benefit to doing this at the cost of implementation complexity. I haven't studied the implementations or tried my hand one, but I get the impression that these are tough to implement correctly in a way that takes full advantage of the hardware.
(In that sense, it's awesome that the researchers also did the legwork to implement and maintain a library!)
The core here, which is bitmap storage and the basic optimization are simple, but solid and general. Mathematically it takes less space to store data as positions on a bitmap rather than fully spelt associations, and it takes even less space to seggregate the bitmaps in chunks.
This will hold and be smaller and faster in any computer. So, it's not some case of special case based on heuristics, either related to the specific frequencies or sample characteristics of some particular set of data, or of specific CPU peculiarities or whatever.
More exotic optimizations piled on top, sure. But "compressed bitmaps" themselves as a concept, not.
Given a large number of 32-bit integers, radix sort is indeed significantly faster.
While I would reach for a comparison sort method if I had a large number of arbitrary-length Unicode strings, which I wanted to sort in a case-ignoring order.
Also, I found timsort faster than radix sort when there was a small number (as I recall, <100 or so) of elements.
Most comparators are of the form "compare by this, then if tied, compare by that, then if tied, compare by the other thing" which is pretty well suited to radix sort. You are correct though.
> While I would reach for a comparison sort method if I had a large number of arbitrary-length Unicode strings, which I wanted to sort in a case-ignoring order.
It seems like the radix sort is likely to be a lot faster for this too, mainly due to cache effects. If you have a dataset in mind I'll be happy to give it a shot.
> Also, I found timsort faster than radix sort when there was a small number (as I recall, <100 or so) of elements.
For sure. 100 isn't so far from the threshold where a radix sort should fall back to something else anyway.
Yes, the general approach is to convert the input data into a fixed-length bit-string with the same sort order as the input.
Your example assumes that construction overhead is short. If tie-breaking is rare, and breaking the tie requires an expensive operation, then the trade-off point for radix might be much higher than 100 elements.
The fixed-length requirement works well for small items with relatively equal-length fields. Ragged items, like Wikipedia titles, causes a problem. There is one title which is 253 bytes long. Now, Wikipedia titles are limited to 255 bytes, so radix is certainly directly applicable, but 1) it changes the trade-off point, and 2) reduces cache effects.
Finally, it requires a sort-order-preserving transformation. I mentioned case-insensitive collation of Unicode strings as a well-known difficult problem. I do not believe there is mapping to an order-preserving representation which can be done bitwise. At the very least, it will be difficult to support all of the collation styles that currently exist (eg, French collation is different than Dutch).
In general MSB radix sort will have to look at the same parts of the input elements as multi-key quick sort, but one hopes that it gets to make fewer passes over the array. A comparator-based sort would look at about the same parts of the input elements as well, but it would look at them many times more than necessary.
> Finally, it requires a sort-order-preserving transformation. I mentioned case-insensitive collation of Unicode strings as a well-known difficult problem. I do not believe there is mapping to an order-preserving representation which can be done bitwise. At the very least, it will be difficult to support all of the collation styles that currently exist (eg, French collation is different than Dutch).
The requirements are a bit underspecified, but I think these can be solved by unicode normalization + tolower + codepoint-wise comparison, which is probably what you'd do in your comparator for a comparison-based sort as well.
[0]: https://github.com/bingmann/parallel-string-sorting/blob/mas...
[1]: https://github.com/dendibakh/perf-challenge6/blob/Solution_R...