roundawayfromzero

Round away from zero is a rounding mode used to convert a real number to an integer by increasing its magnitude away from zero. In this scheme, positive values are moved upward, negative values downward, and zero remains zero.

Formally, if x > 0 then round_away(x) = ceil(x); if x < 0 then round_away(x) = floor(x); if x = 0 then 0. This guarantees that nonzero values round to the next integer in their sign direction. Examples: 3.2 becomes 4; 3.0 stays 3; -2.8 becomes -3; -0.1 becomes -1; 0 stays 0.

Some uses describe a related variant as rounding to the nearest integer with ties broken away from zero, so 1.5 → 2 and -1.5 → -2.

Round away from zero is distinct from round toward zero (which truncates toward zero) and from round to nearest (which selects the closest integer, sometimes with different tie rules). It is used in contexts where a magnitude-preserving step is required, such as certain numerical methods, graphics, or user-facing interfaces that must avoid underestimating a magnitude.

Implementation notes: in many languages you can implement as described above with existing ceiling and floor functions: if x > 0, use ceil(x); if x < 0, use floor(x). Be mindful of floating-point precision near integers and special values such as NaN or infinities, which should be handled according to the language's rules.