Cache Oblivious Algorithms (opens in new tab)

I implemented a bunch of cache oblivious search trees and benchmarked them against their classical counterparts. The results showed that while the cache oblivious ones were more cache efficient, they were slower overall.

The implementations and benchmarks can be found here if anyone is curious: https://gitlab.com/VladLazar/cache-oblivious-data-structures

I tried cache-oblivious algorithms for some numerical code, but found them underwhelming. The cache-oblivious model does not consider the effects of prefetching and cache line associativity. Both can make a huge difference.

They are a great starting point and work well for the RAM/Swap level of the memory hierarchy, but for the L1/L2 caches manual tuning still pays off. This unfortunately makes the implementation non-oblivious and even depended on the specific CPU used.

I'd not heard about van Emde Boas layout before, and it sounds super cool! I wish the author had included a simple example before focussing on the general case -- I find it hard to get an intuition for the general without a specific example! In particular, after some searching, I found the diagram at the top-left of page 4 of https://www.cs.au.dk/~gerth/papers/soda02.pdf to be immensely helpful in getting my head around the concept.

How hard is it to empirically detect cache size at startup and tune the algorithms based on that?

I guess you'd miss out on inlining / constant folding opportunities. If you didn't have a JIT.

I think there might be a mistake in this article, or at least something requiring clarification.

> For convenience, suppose the binary tree is complete and has height H=2^K.

What is K? It's never stated. I'd usually assume H = log N, if N is the number of nodes in a balanced tree.

I love cache oblivious algorithms in principle, but I feel they break my ultimate rule: you can’t please everyone. At the end of the day, the restrictions presented by your system are everything. Without those restrictions you have no problem to solve. Not taking them into account seems crazy.

However avoiding details as much as is feasible is very powerful and should be kept in mind. I feel like simple approaches like streaming computations (not necessarily cache oblivious) share many of the same underlying principles.

Don’t most CPUs have 64 byte cache lines anyway?

I remember my professor Michael Bender teaching those M/B stuff and it was interesting (somehow related to origami). Sadly I pretty much forgot everything now.