The most efficient/uniform representation is to store angle measures as fixed-point numbers in [–1, 1) representing [-π, π) radians, using two’s complement for

The most efficient/uniform representation is to store angle measures as fixed-point numbers in [–1, 1) representing [-π, π) radians, using two’s complement for negative numbers (so you can also think of this as [0, 2) with unsigned fixed-point numbers). This representation is called “binary angles”. You can think of it as an extended version of magnetic compass directions, or the corners of a regular polygon with 2^n sides. https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles Using IEEE floating point to represent angle measures is horribly wasteful of bits, regardless of how you do it. As an alternative, consider not storing angle measure at all, but instead using a stereographic projection (“half-angle tangent”) of the circle onto the whole line, and then using floating point numbers in the range (–∞, ∞] for your representation. https://en.wikipedia.org/wiki/Stereographic_projection https://en.wikipedia.org/wiki/Stereographic_projection What you really want as a working format for rotations, ray directions, or points on a circle is to use a 2-dimensional square-grid (Cartesian coordinate) format like unit-magnitude “complex numbers”. The angle measure or stereographic projection is primarily useful as a compression format when you need to save bits transferring or storing data. Angle measures work okay for this, but can be annoying for requiring transcendental function evaluations to convert them to/from Cartesian coordinates, whereas to take the stereographic projection or its inverse only requires a single multiplicative inverse (i.e. division operation) plus some addition and multiplication per point.