kokonaislukupohjaiset

Kokonaislukupohjaiset is a Finnish adjective used to describe something that is based on integers (kokonaisluvut) rather than on real numbers or floating-point representations. In mathematics, computer science and digital engineering, the term characterizes representations, calculations, or models that rely exclusively on integer values or integer arithmetic.

In practice, kokonaislukupohjaiset approaches include integer-based representations such as fixed-point arithmetic, where real numbers are scaled to integers for computation. They also encompass integer-based algorithms and methods, for example the Euclidean algorithm for greatest common divisor or modular arithmetic used in cryptography, which operate on integers and avoid floating-point rounding errors.

Advantages of integer-based approaches include exactness and predictability, as arithmetic with integers does not introduce rounding errors and aligns well with hardware that natively handles integer operations. They are particularly common in embedded systems, formal discrete mathematics, and many cryptographic protocols. Disadvantages can include the risk of overflow, the need for larger or arbitrary-precision integer types for very large values, and potential inefficiencies for certain numerical tasks where floating-point or real-number methods perform better.

The term is used in Finnish technical literature to distinguish integer-centered methods from those based on floating-point or real-number representations. It highlights a design choice that prioritizes exactness, deterministic behavior, and compatibility with integer hardware.