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While working on the Roc compiler, we regularly dive deep on computer science topics. A recurring theme is speed, both the runtime performance of the code that we generate, as well as the performance of our compiler itself.

One extremely useful technique that we have been playing with is data-oriented design: the idea that the actual data you have should guide how code is structured.

Google recently published a blog article and paper introducing their SIMD-accelerated sorting algorithm.

SIMD stands for single instruction, multiple data. A single instruction is used to apply the same operation to multiple pieces of data. The prototypical example is addition, where one instruction can do e.g. 4 32-bit additions. A single SIMD addition should be roughly 4 times faster than performing 4 individual additions.

This kind of instruction-level parallelism has many applications in areas with a lot of number crunching, e.g. machine learning, physics simulations, and game engines. But how can this be used for sorting? Sorting does not involve arithmetic, and the whole idea of sorting is that each element moves to its unique correct place in the output. In other words, we don't want to perform the same work for each element, so at first sight it's hard to see where SIMD can help.

To understand the basic concepts, I played around with the ideas from the paper Fast Quicksort Implementation Using AVX Instructions by Shay Gueron and Vlad Krasnov. They provide an implementation in (surprisingly readable) assembly on their github. Let's see how we can make SIMD sort.