A modern CPU is an incredible machine. It can execute many instructions at the same time, it can re-order instructions to ensure that memory accesses and dependency chains don’t impact performance too much, it contains hundreds of registers, and it has huge areas of silicon devoted to predicting which branches your code will take. However, if you have a tight loop and you are interested in optimizing the hell out of it, the same mechanisms that make your code run fast can make your job very difficult.
In performance work, you will often find many distributions that are weirdly shaped: fat-tailed distributions, distributions with a hard lower bound at a non-zero number, and distributions that are just plain odd. Particularly when you look at latency distributions, it is extremely common for the 99th percentile to be a lot further from the mean than the 1st percentile. These sorts of asymmetric fat-tailed distributions come with the business.
Often times, when performance engineers need to be scientific about their work, they will take samples of these distributions, and put them into into a $t$-test to get a $p$-value for the significance of their improvements.
When we think of how to represent fractional numbers in code, we reach for double and float, and almost never reach for anything else. There are several alternatives, including constructive real numbers that are used in calculators, and rational numbers. One alternative predates all of these, including floating point, and actually allows you to compute faster than when you use floating point numbers. That alternative is fixed point: a primitive form of decimal that does not offer any of the conveniences of float, but allows you to do decimal computations more quickly and efficiently.
I have been working on another post recently, also related to division, but I wanted to address a comment I got from several people on the previous division article. This comment invariably follows a lot of articles on using math to do things with chars and shorts. It is: “why are you doing all of this when you can just use a lookup table?”
Even worse, a stubborn and clever commenter may show you a benchmark where your carefully-crafted algorithm performs worse than their hamfisted lookup table.
Occasionally, I like to peruse uops.info. It is a great resource for micro-optimization: benchmark every x86 instruction on every architecture, and compile the results. Every time I look at this table, there is one thing that sticks out to me: the DIV instruction. On a Coffee Lake CPU, an 8-bit DIV takes a long time: 25 cycles. Cannon Lake and Ice Lake do a lot better, and so does AMD. We know that divider architecture is different between architectures, and aggregating all of the performance numbers for an 8-bit DIV, we see:
A lot of the time, when engineers think of performance work, we think about looking at benchmarks and making the numbers smaller. We anticipate that we are benchmarking the right pieces of code, and we take it for granted that reducing some of those numbers is a benefit, but also “the root of all evil” if done prematurely. If you are a performance-focused software engineer, or you are working with performance engineers, it can help to understand the value proposition of performance and when to work on it.
When you design software to achieve a particular level of performance, it can be a good idea to be familiar with the general speed regimes you are working with: fundamental limitations like storage devices and networks can drive software architecture. Here are a set of common benchmark numbers that can help you anchor performance conversations and think about the components that your software will interact with. As with all guidelines, these numbers are all slightly wrong, but still useful.