1 \input{chapters/Background/Floats/Definition}
2 \subsection{Visualisation of Floating Point Representation}
3 \input{chapters/Background/Floats/Visualisation}
6 \subsection{Floating Point Operations}
7 \input{chapters/Background/Floats/Operations}
10 \subsection{Arbitrary Precision Floating Point Numbers}
12 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.
14 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 be set; although it is possible to increase or decrease the precision of individual numbers as desired.