\input{chapters/Background/Floats/Definition}
\subsection{Visualisation of Floating Point Representation}
\input{chapters/Background/Floats/Visualisation}


\subsection{Floating Point Operations}
{\bf FIXME:} Appendix?
\input{chapters/Background/Floats/Operations}


\subsection{Arbitrary Precision Floating Point Numbers}

Arbitrary precision floating point numbers are implemented in a variety of software libraries which will dynamically allocate extra bits for the exponent or mantissa as required. An example is the GNU MPFR library discussed by Fousse in 2007\cite{fousse2007mpfr}. Although many arbitrary precision libraries already existed, MPFR intends to be fully compliant with some of the more obscure IEEE-754 requirements such as rounding rules and exceptions. 

As we have seen, it is trivial to find real numbers that would require an infinite number of bits to represent exactly. Implementations of ``arbitrary'' precision must carefully determine at what point rounding should occur so as to balance performance with memory usage.
