Computer Arithmetic
Floating‑point arithmetic
Floating‑point arithmetic is a method of approximating real‑number calculations on digital computers using finite precision formats defined by standards such as IEEE 754 (2019) and its international adoption ISO/IEC 60559:2020. It specifies binary and decimal formats, rounding rules, special values, status flags, and required operations used by most modern hardware and software environments. [IEEE SA](https://standards.ieee.org/standard/60559-2020.html); [ISO](https://www.iso.org/standard/80985.html).
Interval arithmetic
Interval arithmetic is a numerical framework in which numbers are represented as closed intervals and arithmetic operations are extended so that the exact result is guaranteed to lie within computed bounds. It underpins validated numerics, enabling mathematically rigorous control of rounding and data uncertainty in scientific computing, optimization, and computer‑assisted proofs. The approach has been formalized in the IEEE 1788 standard and is implemented in several software libraries across programming languages.