integer_angles 0.1.0

Do math with angles, but represent them as integers to avoid using floats.
Documentation

Angles Done With Integers

Docs: https://docs.rs/integer_angles/

use integer_angles::Angle;

assert_eq!(Angle::pi_2().cos::<f64>(), 0.0f64);

Here we go, down the rabbit hole of floating-point instability and all sorts of crazy problems that come with representing angles within computers. The goal of this library is to solve the following problems:

  • If you have multiple angles, and you add them together, the result you get should be exactly correct.
  • If you add multiple angles together and end up with a full circle, that should be exactly a full circle.
  • If you do trigonometry of some multiple of pi radians, you should end up with the exact answer.
  • Keep track of the difference between a 0 radian angle, and a 2 pi radians angle.
  • Keep track of if the angle is going clockwise or counter-clockwise starting at the positive x axis.
  • Do not allow the user to represent an angle outside the range [-2 pi to 2 pi]

The way this library does it's magic is the following:

  • Stores the angle in units of [0..2**64) where each unit is 1/(2**64)th of a circle.
  • This means that adding and subtracting angles (with wrapping) will always be correct, and always within the specified range. (No more range reduction!)
  • This also means that you can (inside the library) cast an angle from u64 to i64 and end up with the same angle.
  • Set a flag for a full circle, and allow units to be 0 for a 0 degree angle.
  • This also means, for example, pi radians is exactly equal to 1<<63 units in this library.
  • Keep track of the clockwise/counterclockwise-ness of the angle using a separate flag.
  • Solves the Chebyshev to compute the sin/cos/tan using the new units (with more precision than the standard library).
  • Uses a binary search (at the moment) to compute asin/acos/atan/atan2.

Caveats:

  • This library is slower than using an f64 (about 10 times slower to compute cos. You've gotta wait a whole 80 ns to get the result!).
  • ... Probably other things.

License: MIT