Fans of a 2013 Japanese soccer game tracked down a bizarre floating point bug

The Arm ARM says FNMADD is "Floating-point Negated fused Multiply-Add", so the position of the hyphens points strongly to "n(madd)" rather than "(nm)add".

Nothing was really broken, the problem was just that the 3 CPU architectures, POWER, Intel/AMD and 64-bit ARM include in their instruction sets slightly different FMA instructions, so porting a program between them requires care.

The fused multiply-add instructions (FMA) have been used for the first time in 1990, in the first IBM POWER CPUs.

Some years later FMA instructions have been included in many other CPUs from various vendors, the main exceptions being the Intel/AMD CPUs (where the first CPU with FMA was AMD Bulldozer in 2011, 21 years later than POWER) and the ARM CPUs, which also added FMA quite late, but before the introduction of the 64-bit variant.

The problem is that both Intel and ARM have chosen to define FMA instructions that differ between themselves and also from POWER, in the position of the negation signs.

With real numbers of unlimited precision, that would not have mattered, because the negation is commutative with the multiplication and distributive over addition.

However with floating-point numbers these mathematical properties do not hold exactly, which is what the developers of the Dolphin emulator have discovered now.

This is a general rule for any floating-point computation, that changing a formula using associativity/distributivity/commutativity is not guaranteed to produce the same results.

Sometimes the differences are too small to matter, but in this case they made a game unplayable in the emulator, so they had to emulate the exact formula used in the original game, without trying to reduce the execution time by reducing the number of emulated instructions (emulating the original formula requires 2 instructions, while they initially optimized the code to use a single instruction but that computed a formula with the negation sign moved in another place).

Based on the article it sounds like the main difference comes down to calculations resulting in +0 or -0. As long as the architecture is self-consistent, it wouldn’t be a problem. Once that floating point value is sent to another architecture, things could go bad. I suppose sending FP values over the wire and used for dsync detection doesn’t happen often?

What I find interesting in addition to that is how much slack most software allows. I remember lurking on the alt groups when emus were being discussed for things like an amiga or pc. They were talking sub cycle accuracy would be totally necessary for anything to work at all. Yet most software seems pretty chill with 'sort of close' results. It is oddly counter intuitive. Intuitively they were right but ended up being wrong (mostly). Some bits though you need that accuracy. Mostly you dont.

I think a lot of software companies would do like what you did. Where they would check for some sort of thing that should be there, or not, or too much of something. But the emulator would or would not have it. I think in many cases it would be things like checking to see if 512k of memory was available, when the real box would have 128k. That was usually for things like copiers I think?

Is it weird that you sound proud about this? Is there something noble about doing work that makes lives harder for hobbyists trying to preserve video games for the future, and has nearly zero impact on the actual sales of the game at release?

If we're following HN guidelines correctly, the title should be 'Dolphin Progress Report: August 2021' -- what has been submitted has been editorialised.

I overlooked the URL. Seeing that or the original title I would have understood what this was.

But now, my first guess was actually that this was about some much debated football match and that the floating point bug was present in some software used by the referees when reviewing replays.

I can personally attest to creating and fixing floating point bugs to do with real life football games.

Counterpoint: I assumed real life scoreboard.

I was immediately trying to figure out if it somehow had to do with a stop watch being used in meatspace.