truncate, ceiling, floor, and...? Truncation rounds negative numbers upwards, and positive numbers downwards. Floor rounds all numbers downwards, and ceiling rounds all numbers upwards. Is there a term/notation/whatever for the fourth operation, which rounds negative numbers downwards, and positive numbers upwards? That is, one which maximizes magnitude as truncation minimizes magnitude?

The fourth operation is called "round towards infinity" or "round away from zero". It can be implemented by

$$y=\text{sign} (x)\text{ceil}(|x|)$$