RoundTowardInfinity

RoundTowardInfinity is a rounding mode used in floating-point and decimal arithmetic that maps a real number to the nearest representable value in the direction of positive infinity. In practice, it behaves like the ceiling function: for any real x, RoundTowardInfinity(x) equals ceil(x). When applied to numbers already representable as integers, the value remains unchanged; otherwise it rounds up to the next integer or higher-precision representation.

In IEEE 754 terminology, this mode is known as round toward +infinity and is one of the standard rounding modes available for reducing precision or converting real numbers to a lower-precision form. It is sometimes labeled as CEILING or RTP (round toward positive infinity) in various libraries. Many programming languages implement it via a ceiling function (for example, ceil in C, C++, and Python) or through a specific rounding mode in decimal or floating-point APIs.

Examples include: RoundTowardInfinity(3.2) = 4, RoundTowardInfinity(-2.7) = -2, and RoundTowardInfinity(5.0) = 5. This behavior makes the operation monotone nondecreasing with respect to the input.

Applications and considerations: RoundTowardInfinity is useful when underestimation must be avoided, such as certain display, allocation, or thresholding tasks. However, it introduces a positive bias in aggregation and may be inappropriate for statistics that assume symmetric rounding. In numerical libraries, it is important to distinguish this mode from rounding toward zero, toward negative infinity, or toward the nearest value.

See also: RoundTowardZero, RoundTowardNegativeInfinity, RoundToNearest, Floor, Ceiling.