# integer_angles 0.1.0

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

## Angles Done With Integers

``````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.