User:Ndcroos/Exact real arithmetic

In computer science and numerical computing, exact real arithmetic is way to implement real numbers on computers. It is an alternative to limited precision arithmetic.

Introduction

floating-point arithmetic round-off errors.

interval analysis

continued fraction

möbius transformation

Data representation

Arithmetic operations

Comparisons

Foundations

History

computability theory

Computable function Church Turing

Computable number, also called recursive, representable or constructive

representation: cauchy sequence, dedekind cut, interval, continued fraction

Dana Scott proposed interval domains domain theory 1970

PCF

Implementations

The implementations differ on the programming paradigm used (e.g. functional or object oriented), lazy or eager evaluation, efficiency.(irram18)

References

Jean Vuillemin Exact real computer arithmetic with continued fractions

limitations of rational numbers: computing roots, pi, exponential function

Exact real arithmetic: Formulating real numbers as functions

Exact real arithmetic: A case study in higher order programming

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.28.1539&rep=rep1&type=pdf

Type classes for efficient exact real arithmetic in Coq

External links

• https://wiki.haskell.org/Exact_real_arithmetic

• https://members.loria.fr/PZimmermann/irram18.pdf

• https://ncatlab.org/nlab/show/computable+real+number

• https://ncatlab.org/nlab/show/exact+real+computer+arithmetic