Angles

The Player's yaw (facing) is a float (from $-180.0$ to $180.0$ )

An angle is an integer (from $0$ to $2^{16}-1$ )

Angles and Half Angles
Minecraft relies on angles for movement calculations, which means the Player's yaw has to be converted before being used.

This conversion induces some imprecision, as information is lost when casting a float to an int.

This also means two close (but different) facings can result in the same significant angle being used (a single angle spans across ~$$0.0055°$$).

Sin and Cos source code (from MathHelper): Note:   is the same as  , which is the remainder of a division by 65536 ( $$2^{16}$$)

By analyzing the sin and cos function from the source code, we can notice that the yaw-to-angle conversion is not exactly the same for both functions.

Because floats are rather imprecise for larger values, this means the same value could potentially be converted differently.

Half angles are such values, and can found between consecutive angles (hence the name).

Half angles don't have much use outside of Tool-Assisted Parkour: their effect on jump distance is negligible (±0.0001 for Tier 0), and they can hardly be reached with mouse movement.


 * Positive half-angles increase the Player's speed. They can be found (rarely) in the North-West quadrant (90° to 180°)
 * Negative half-angles decrease the Player's speed. They can be found (abundantly) in the South-East quadrant (-90° to 0°).

The best half-angle is 135.0055° (combined with 45° Strafe)

Note: Fast Math is an Optifine feature that reduces the number of angles to 4096 ( $$2^{12}$$). With Fast Math, half angles are fewer in number, but are up to 16x more effective. For example, it makes a no-sprint 3b jump possible with only flat momentum.