## 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