Posted in Floating Point

Floating Point in the Browser, Part 3: When x+y=x (y != 0)

A few years ago I did a lot of thinking and writing about floating-point math. It was good fun, and I learned a lot in the process, but sometimes I go a long time without actually using that hard-earned knowledge. So, I am always inordinately pleased when I end up working on a bug which requires some of that specialized knowledge. Here then is the third of (at least) three tales of floating-point bugs that I have investigated in Chromium (part one is here, part two is here). It’s another variant on precision problems when pushing the limits – maybe I just keep encountering the same floating-point bug?

In this post I’ll also cover some debugging techniques you can apply if you ever want to explore the Chromium source code or investigate a crash.

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Floating Point in the Browser, Part 2: Bad Epsilon

A few years ago I did a lot of thinking and writing about floating-point math. It was good fun, and I learned a lot in the process, but sometimes I go a long time without actually using that hard-earned knowledge. So, I am always inordinately pleased when I end up working on a bug which requires some of that specialized knowledge. Here then is the second of (at least) three tales of floating-point bugs that I have investigated in Chromium (part one is here, part three is here). And this time I actually fixed the bug, both in Chromium, and then in googletest so that future generations will be spared some confusion.

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Floating Point in the Browser, Part 1: Impossible Expectations

A few years ago I did a lot of thinking and writing about floating-point math. It was good fun, and I learned a lot in the process, but sometimes I go a long time without actually using that hard-earned knowledge. So, I am always inordinately pleased when I end up working on a bug which requires some of that specialized knowledge. Here then is the first of (at least) three tales of floating-point bugs that I have investigated in Chromium (part two is here, part three is here). This is a short one.

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The Easy Ones – Three Bugs Hiding in the Open

I write a lot about investigations into tricky bugs – CPU defects, kernel bugs, transient 4-GB memory allocations – but most bugs are not that esoteric. Sometimes tracking down a bug is as simple as paying attention to server dashboards, spending a few minutes in a profiler, or looking at compiler warnings.

Here then are three significant bugs which I found and fixed which were sitting in the open, just waiting for somebody to notice.

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Exercises in Emulation: Xbox 360’s FMA Instruction

Years ago I worked in the Xbox 360 group at Microsoft. We were thinking about releasing a new console, and we thought it would be nice if that console could run the games of the previous console.

Emulation is always hard, but it is made more challenging when your corporate masters keep changing CPU types. The Xbox one – sorry, the original Xbox – used an x86 CPU. The Xbox two – sorry, the Xbox 360 – used a PowerPC CPU. The Xbox three – sorry, the Xbox One – used an x86/x64 CPU. These ISA flip-flops did not make life easy.

imageI made some contributions to the team that taught the Xbox 360 how to emulate a lot of the original Xbox games – emulating x86 on PowerPC – and was given the job title Emulation Ninja for that work*. Then I was asked to help investigate what it would take to emulate the Xbox 360’s PowerPC CPU with an x64 CPU. To set expectations, I’ll mention up front that I didn’t find a satisfactory solution.

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