Turns are Better than Radians

Casey Muratori challenges the conventional use of radians and tau in software development, advocating for a lesser-known unit called 'turns'. He argues that while many championed 'tau' (2π) over 'pi' for representing a full circle, an even more impactful optimization is to eliminate explicit radian conversions altogether.

• Muratori observes that programmers often convert values to radians (multiplying by π or τ) before calling trigonometric functions. However, the internal implementations of these functions immediately convert the input back (dividing by π or τ) to work with their own optimized representations.
• This results in redundant and computationally expensive multiplication/division operations, which also introduce floating-point inaccuracies because irrational constants like π or τ cannot be perfectly represented.
• He proposes using 'turns' where a full circle is represented by 1. In this system, common angles like 90 degrees become 0.25, 180 degrees become 0.5, and 360 degrees become 1.0. These values are exactly representable as floating-point numbers, unlike their radian equivalents.
• The article demonstrates that 'turns' are not a novel concept but a legitimate mathematical unit. Switching to turns simplifies code by removing unnecessary constants and improving clarity.
• For existing codebases, Muratori suggests adjusting sin and cos functions to accept turns, or leveraging platform-specific intrinsics like CUDA's sincospi which already operate on a 'half-turn' (input multiplied by pi) basis.

By adopting turns, developers can streamline trigonometric calculations, enhance numerical precision for common angles, and eliminate superfluous constants from their code, leading to cleaner and potentially faster programs.