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.

In honor of April Fools’ Day, I decided to write about a blockchain topic. The crypto economy is in the process of speedrunning their way from zero to a modern economy, and when you move that fast, a few things have to break along the way. One of those things is corporate governance.
Matt Levine’s “Money Stuff” is a financial newsletter that I can’t recommend enough. If you are at all interested in finance, stocks, and markets, it is funny and informative read.

Python and Assembly have one thing in common: as a professional software engineer, they are both languages that you probably should know how to read, but be terrified to write. These languages seem to be (and are) at opposite ends of the spectrum: One is almost machine code, and the other is almost a scripting language. One is beginner-friendly and the other is seen as hostile to experts. One is viciously versatile with tons of libraries and ports, and the other is ridiculously limited in its capabilities.

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.

This is the second part in a 2-part series on the “Fibonacci” interview problem. We are building off of a previous post, so take a look at Part I if you haven’t seen it.
Previously, we examined the problem and constructed a logarithmic-time solution based on computing the power of a matrix. Now we will derive a constant time solution using some more linear algebra. If you had trouble with the linear algebra in part I, it may help to read up on matrices, matrix multiplicaiton, and special matrix operations (specifically determinants and inverses) before moving on.

Few interview problems are as notorious as the “Fibonacci” interview question. At first glance, it seems good: Most people know something about the problem, and there are several clever ways to achieve a linear time solution. Usually, in interviews, the linear time solution is the expected solution. However, the Fibonacci problem is unique among interview problems in that the expected solution is not the optimal solution. There is an $O(1)$ solution, and to get there, we need a little bit of linear algebra.

Hello everyone, and welcome to my blog.
I am an ex-Google senior engineer focused on systems programming and performance optimization. My past experience includes hardware engineering, numerical analysis, and high-frequency trading.
Here, we will be talking about software engineering, performance, computer systems and foundations, interesting math concepts, electrical engineering, hardware acceleration, FPGAs, and more. We may also branch out to non-technical topics including companies, organizational psychology, and the stock market.