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0 pointsadrian_b21d ago0 comments

There are applications where the difference between fixed-point and floating-point numbers matters, i.e. the difference between having a limit for the absolute error or for the relative error.

The applications where the difference does not matter are those whose accuracy requirements are much less than provided by the numeric format that is used.

When using double-precision FP64 numbers, the rounding errors are frequently small enough to satisfy the requirements of an application, regardless if those requirements are specified as a relative error or as an absolute error.

In such cases, floating-point numbers must be used, because they are supported by the existing hardware.

But when an application has more strict requirements for the maximum absolute error, there are cases when it is preferable to use smaller fixed-point formats instead of bigger floating-point formats, especially when FP64 is not sufficient, so quadruple-precision floating-point numbers would be needed, for which there is only seldom hardware support, so they must be implemented in software anyway, preferably as double-double-precision numbers.

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larrry21d ago

The core of my multiplayer arena game is in fixed point

I wanted absolute certainty that the rollback netcode would result in identical simulations on any platform, and integer math provides that. With set of wrapper functions and look up tables for trig it’s not that much worse than using regular floats

I am still uncertain if I actually would have been fine with floats, being diligent to round frequently and staying within true integer representable range… but now at least I’m far less afraid of game desyncs and it wasn’t that much work

Cross platform, cross USA games have been stable and fun to play, no fixed point complaints here

AlotOfReading21d ago

Floating point determinism has been a personal bugbear of mine for a number of years. You still have to be careful, but it's at the point where it's less work than switching to fixed point (cheap as that may be). There are even libraries [0] [1] that implement full reproducibility with negligible overhead. Compilers shipping incorrectly rounded stdlib functions remains an issue, but they're slowly improving. Language level support for float reproducibility is in the C++ pipeline, and already a design consideration on the Rust side. In a decade or so determinism issues might be a distant memory once you've ensured same inputs to the same instructions in the same order.

[0] https://github.com/J-Montgomery/rfloat

[1] https://github.com/sixitbb/sixit-dmath

AlotOfReading21d ago

    i.e. the difference between having a limit for the absolute error or for the relative error.

The masking procedure I mentioned gives uniform absolute error in floats, at the cost of lost precision in the significand. The trade-off between the two is really space and hence precision.

I'm not saying fixed point is never useful, just that it's a very situational technique these days to address specific issues rather than an alternative default. So if you aren't even doing numerical analysis (as most people don't), you should stick with floats.

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larrry21d ago

The core of my multiplayer arena game is in fixed point

Cross platform, cross USA games have been stable and fun to play, no fixed point complaints here

AlotOfReading21d ago

[0] https://github.com/J-Montgomery/rfloat

[1] https://github.com/sixitbb/sixit-dmath

AlotOfReading21d ago

    i.e. the difference between having a limit for the absolute error or for the relative error.

The masking procedure I mentioned gives uniform absolute error in floats, at the cost of lost precision in the significand. The trade-off between the two is really space and hence precision.

j / k navigate · click thread line to collapse