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

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floating-point arithmetic round-off errors.

interval analysis


continued fraction

möbius transformation


Data representation

Arithmetic operations

Comparisons

Foundations

History

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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

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

See also

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References

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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

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