Rounding
This variant is almost never used in most computations, except in situations where one wants to avoid rounding 0.5 or −0.5 to zero, or to avoid increasing the scale of numbers represented as floating point (with limited ranges for the scaling exponent), so that a non infinite number would round to infinite, or that a small denormal value would round to a normal non-zero value (these could occur with the round half to even mode). Effectively, this mode prefers preserving the existing scale of tie numbers, avoiding out of range results when possible.