Computer arithmetic
type of arithmetic that uses computer representation of numbers
Computer arithmetic is the scientific field that deals with representation of numbers on computers and corresponding implementations of the arithmetic operations.
It includes:
Fixed-size arithmetic
"Integer arithmetic", which in practice is modular arithmetic by a power of 2.
Fixed-point arithmetic
Modular arithmetic
Multi-modular arithmetic
p-adic arithmetic, consisting of computing modulo a single prime number and retrieving the integer or rational result by using Hensel lifting
Finite field arithmetic
Floating-point arithmetic
Arbitrary-precision arithmetic
Interval arithmetic
Symmetric level-index arithmetic
Matrix arithmetic
In the cases where the size of the representation of a number is fixed (fixed-point, floating-point and interval arithmetic), the main concern is to control the computational error, as far as possible; see, for example IEEE 754.
In the other cases, where an exact result should be provided, the main concern is the practical efficiency, which is optimized by combining improvements of computational complexity with hardware specificities.
ARITH Symposium on Computer Arithmetic is an international symposium devoted to computer arithmetic.
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This entry incorporates text from “Computer arithmetic” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.