Lesson plan
Computer arithmetic
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.
Article summary
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.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.