User:Ndcroos/Exact real arithmetic
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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
[edit]floating-point arithmetic round-off errors.
Data representation
Arithmetic operations
Comparisons
Foundations
History
[edit]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
Implementations
[edit]The implementations differ on the programming paradigm used (e.g. functional or object oriented), lazy or eager evaluation, efficiency.(irram18)
See also
[edit]References
[edit]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
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