[nkurz]

> Unfortunately although we cut the search space to 2/3 of what it was for binary search at each step (1/3 vs 1/2), we do 3/2 as many comparisons at each step (one comparison 50% of the time, two comparisons the other 50%), so it averages out to equivalence.

True, but is there some particular reason that you want to minimize the number of comparisons rather than have a faster run time? Daniel doesn't overly emphasize it, but as he mentions in the article: "The net result might generate a few more instructions but the number of instructions is likely not the limiting factor."

The main thing this article shows is that (at least sometimes on some processors) a quad search is faster than a binary search _despite_ the fact that that it performs theoretically unnecessary comparisons. While some computer scientists might scoff, I'd bet heavily that an optimized ternary search could also frequently outperform.

[jstanley]

You normally measure runtime of a sorting algorithm in terms of the number of comparisons it has to do.

Obviously real-world performance depends on other things as well.

[Someone]

Not “normally”, but “in computer science” and even then, mostly “in the past” and even then, only “typically” (there are sorting algorithms that make zero comparisons. See for example https://pages.cs.wisc.edu/~paton/readings/Old/fall01/LINEAR-...)

All other people live in the real world, and care about real-world performance, and modern computer scientists know that.

[alexfoo]

Those algorithms may not be doing any pairwise comparisons (e.g. between elements being sorted) but they still do plenty of comparisons.

And some of the algorithms, as described, still end up doing pairwise comparisons in all-but-optimal cases.

(Bucket sort requires items that end up in the same bucket to be sorted. This doesn't happen automatically via the algorithm as stated. Radix sort requires the items at each "level" to be sorted. Neither algorithm specifies how this should be done without pairwise comparisons.)

Counting Sort does work without pairwise comparisons, but is only efficient for small ranges of values, and if that's the case then it's obvious you don't need to apply a traditional sort if the number of elements greatly outnumbers the number of possible values.

Also, the algorithms still require some form of comparisons, just not pairwise comparisons.

> All other people live in the real world, and care about real-world performance, and modern computer scientists know that.

Yes, completely agree with that, but traditional "Comp Sci" is built on small building blocks of counting "comparisons" or "memory accesses". It's not designed to analyse prospective performance given modern processors with L1/L2/L3 caches, branch prediction, SIMD instructions, etc.