more-fixed-cpp

Single-header C++11 fixed-point arithmetic

• Use more::fixed16 as a drop-in replacement for float in existing code.
• No dependencies needed outside of the C++ standard library.
• Reasonable speed (but aggressive optimization is not a current goal).

This library may be useful if you'd like your mathematical calculations to be exactly reproducible (usually not the case with floating-point arithmetic). For example, in a game physics engine, you could run the same physics on two different machines and be sure of getting identical results.

How to use it

#include "more_fixed/more_fixed.h"

Use one of these types instead of float:

• more::fixed16: 16.16 bit fixed point. Aborts on overflow in debug builds.
• more::fixed16_safe: as above, but always aborts on overflow.
• more::fixed16_fast: as above, but ignores overflow.

Here's my Box2D fork that works with fixed-point: https://github.com/more-please/liquidfun

On x86_64, fixed16_fast seems to be about the same speed as float, while fixed16_safe is 1.5x--2x slower.

Things to watch out for

In general, this is still a work in progress, so use with caution. I don't have exhaustive unit tests yet, I'm just doing ad-hoc integration testing.

Build system

I'm using Clang with C++11 support. Other than fixing as many warnings as possible, I haven't put any special effort into making the code portable.

Reproducibility

Complete reproducibility is the goal, but I haven't actually checked this yet!

I currently have a cheesy implementation of sqrt, sin, cos etc, which is to convert values to float and just use math.h. That may actually be okay, if it always results in higher-precision results that are then truncated to fixed. (Probably it needs to be double rather than float, single precision doesn't have a full 32-bit mantissa.)