Using 'Turns' Instead of Radians Simplifies Trigonometric Calculations in Code

The Problem with Radians in Code

Programmers frequently convert angular values to radians when calling trigonometric functions like `sin()` or `cos()`. This is a common practice, as radians are the standard unit for these mathematical functions. However, this often leads to redundant calculations within the software stack.

Redundant Conversions in Math Libraries

Many trigonometric function implementations, such as those found in AVX2 libraries, internally convert the radian input back to a different scale. For example, an input multiplied by `2 * pi` by the programmer might immediately be multiplied by `4 / pi` inside the `sin()` function, effectively canceling out the `pi` factor. This means the code is performing a conversion to radians only for the library to convert it back, creating an unnecessary computational step.

Introducing 'Turns' for Simplicity

The article proposes using 'turns' as a unit for angular measurement, where one turn represents a full circle (0 to 1). If a value `h` is already periodic on the range 0 to 1, directly passing it to a trigonometric function designed to accept 'turns' would eliminate the need for `pi` or `tau` multiplications. This would simplify the calling code and remove the redundant conversions performed by the underlying math libraries.

Impact on Code Efficiency and Readability

Adopting 'turns' could lead to slightly more efficient code by removing unnecessary arithmetic operations. More significantly, it could improve code readability by making the intent clearer when dealing with periodic values that naturally range from 0 to 1. This change, while minor, addresses an overlooked opportunity for optimization and clarity in common programming practices.