Mathround

Mathround is a commonly used name for a function that rounds a real number to the nearest integer. It appears in various programming languages and mathematical libraries as a convenience for converting floating-point results to whole numbers.

Behavior and rules often vary by language. In many implementations, Mathround follows round-half-away-from-zero: numbers with a fractional part of 0.5 or greater are rounded up (toward positive infinity for positives and toward negative infinity for negatives), while numbers with a fractional part less than 0.5 are rounded down. For example, Mathround(3.2) yields 3, Mathround(3.5) yields 4, and Mathround(-2.5) yields -3. Some languages implement bankers rounding (round-half-to-even), where 2.5 rounds to 2 and -2.5 rounds to -2. The exact behavior for halves, as well as the handling of special values like NaN or infinity, is language-specific.

Usage and return values depend on the language’s type system. In many environments, Mathround returns an integer type, while in others it returns a floating-point value that represents an integer. It is often used to convert floating-point results to discrete values, such as indices, counts, or pixel coordinates, where fractional parts are not meaningful.

Common alternatives include functions named round, floor, and ceil, which offer different rounding strategies or exact floor/ceiling operations. If a language lacks a built-in Mathround, it can typically be implemented with a combination of floor/ceil and sign-aware logic or via a library function that provides rounding to the nearest integer.