In that case, the CPU will speculate loads reasonably far ahead, and because both choices tend to be in the same cacheline, this prefetch is rarely wasted.
In other words, the big win isn't about reducing the number of cacheline fetched, it's about reducing the effective latency of those fetches.
That said, using a similar layout with higher fan-out and SIMD ops doesn't benefit from this effect and is probably still better.
The pointers are wholly implicit. E.g. assuming you let the index 0 be empty, the left pointer for a node k is at 2k and the right node is at 2k+1.
In terms of benefit here, the main benefit appears to be that since you always know where the children will be, you can trade bandwidth for latency and trigger pre-fetching of the next step down before you've even decided if you're going left or right.
But seems they did as well. See the graph at the bottom which compares against a (Eytzinger-style) B-tree, which is basically taking that approach. You do more comparisons per node to figure out which branch to take, but fetch less memory.
Given the overall performance they show is very similar, the question if you want to scale this basically becomes whether your system saturates available cores or available memory bandwidth first.
(Would have been interesting to see comparisons of a quaternary and octonary version as well, though as their B-tree test seems to rely on 16 branches, and maybe the sweet spot is somewhere in between)
https://en.wikipedia.org/wiki/B-tree
With caching on modern CPUs, as opposed to databases on disks, there are multiple levels of caching and you may not know the size of the caches. And the caches can be shared with other work you're doing, or other processes are doing, so the effective size can be smaller. So there's some benefit to algorithms that are independent of cache size.
When retrieving from disk you have far more cycles to work with before less disk-read sized blocks can get close to competitive.
Ya I agree re latency. In fact there’s no other option afaict. CPU always loads 64 bytes, just like Postgres always loads data in 8kb chunks (unless you compile Postgres to use different size)
So you get at most seven 8bit data nodes or twelve 4bit data nodes per cache line. This would save you 2 or ~3.6 memory/highercache reads respectively.
The odds of this strategy helping past the first few layers seems unlikely. So for 100k elements binary tree, this should be a 13% or 18% performance improvement respectively. That’s 17 vs 15 and 17 vs 14.4 reads.
And this would not help much for string data values unless the strings are at most 8 characters long :-)
This same thinking can be used to optimize database queries. Given several table and index layouts how many 8kb disk reads will be needed in each case. Wish I could get a job doing that kind of design work!