Programmers urged to swap radians for 'turns' to fix floating-point errors

A technical proposal is gaining traction among developers suggesting that programmers replace radians with 'turns' as the primary unit for trigonometric calculations. The shift aims to eliminate redundant conversions and resolve persistent floating-point precision issues in software development.

In this system, a 'turn' is a mathematical unit where 1.0 represents a full 360-degree circle, 0.5 represents 180 degrees, and 0.25 represents 90 degrees. The author of the proposal, writing for Computer Enhance, argues that current programming practices are inefficient because calling code often multiplies values by pi only for the underlying library to immediately divide them back out. "It’s literally a conversion to radians and back for no reason," the author stated.

The Precision Problem

The primary technical driver for this change is how computers handle binary floating-point numbers. Common cardinal angles, such as 90 degrees, can be represented exactly as 0.25 turns. In contrast, the radian equivalent (pi/2) is an irrational number that cannot be represented exactly in binary, leading to small but cumulative rounding errors.

Some high-performance tools already utilize similar logic. For instance, the CUDA sincospi intrinsic computes the sine and cosine of an input multiplied by pi, effectively operating in half-turns rather than standard radians. This suggests that the industry already has a precedent for bypassing traditional radian inputs to achieve better performance or accuracy.

Industry Implications

For graphics programmers and game developers, adopting turns could result in cleaner code and fewer errors when calculating cardinal directions. By removing the need for pi and tau constants in many contexts, developers could potentially see a slight performance gain by stripping away redundant multiplications from their execution loops.

This debate extends the long-standing argument over whether pi or tau should be the fundamental constant of a circle. However, this proposal goes further by suggesting the removal of irrational constants entirely in favor of a normalized [0, 1] range.

The Calculus Conflict

Despite the benefits for precision, the proposal faces pushback from those who rely on the mathematical properties of radians. Critics argue that radians remain essential for calculus, specifically when calculating rates of change. As Hacker News user 'traes' noted, turns are convenient until a developer needs to calculate a derivative, as the derivative of sin(2pi x) requires the 2pi constant to remain mathematically correct.

Whether the industry will move toward a normalized unit depends on if the precision gains for graphics outweigh the disruption of changing standard trigonometric function signatures across global libraries.