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


%\subsection{Floating Point Operations}
%\input{chapters/Background/Floats/Operations}


\section{Arbitrary Precision Floating Point Numbers}\label{Arbitrary Precision Floating Point Numbers}

Arbitrary precision floating point numbers are implemented in a variety of software libraries which will 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. 

It is trivial to find real numbers that would require an infinite number of bits to represent exactly (for example, $\frac{1}{3} = 0.333333\text{...}$). The GMP and MPFR libraries require a fixed but arbitrarily large precision (size of the mantissa) be set; although it is possible to increase or decrease the precision of individual numbers as desired.
