Angles are a measurement of a separation between two rays. Using trigonometry, angles give substantial information relating to the position and velocity of an object.
Yaw, Pitch and Roll
Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.
Instead of calculating them in real time, the game uses a look-up table for values of the trigonometric functions Sine and Cosine.
An angular unit or angle unit is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for PU movement).