Arytmetype

Arytmetype is a term occasionally used to describe a data type that participates in arithmetic operations within a programming language or a formal mathematical model. In this sense, an arytmetype consists of a carrier set of values together with a defined set of operations such as addition, subtraction, multiplication and division, and often includes rules for remainder, comparison, and conversion between types. The concept is commonly discussed in the context of type systems, numeric libraries, and language design.

Operations on an arytmetype are expected to be closed under the defined arithmetic operators, yielding results that are either of the same arytmetype or of a promoted type when mixed with other arytmetypes. Semantics such as overflow, rounding, and exceptional cases (for example, division by zero or NaN in floating-point arytmetypes) vary by language and implementation. Some systems also specify how arytmetypes interact through type promotion or coercion when expressions combine values of different arytmetypes.

Common variants of arytmetype include integer arytmetype, floating-point arytmetype, fixed-point arytmetype, and complex arytmetype. Each variant has its own representation, range, precision, and behavior under operations. Representation details—such as bit width, sign, and whether overflow is wraparound, saturated, or checked—affect performance and correctness. In mathematical modeling, arytmetype can be analyzed as algebraic structures (for example, semirings or rings) to study properties of the supported operations.

Note that arytmetype is not a widely standardized term; most literature refers to arithmetic types or numeric types. See also arithmetic operators, numeric types, type promotion, and overflow behavior.