X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;ds=sidebyside;f=chapters%2FBackground%2FFloats.tex;h=1be1113684ae7f2736c8761e36c289aba31b8d08;hb=ae8d5f837db032eb4d9e9666f5026fab7e3e8e4a;hp=7eba8a27bdb4c963fc54a389ad95e272e34525a7;hpb=9fcf44a0c34f393689118e913a2d17d907036c85;p=ipdf%2Fsam.git

diff --git a/chapters/Background/Floats.tex b/chapters/Background/Floats.tex
index 7eba8a2..1be1113 100644
--- a/chapters/Background/Floats.tex
+++ b/chapters/Background/Floats.tex
@@ -3,12 +3,12 @@
 \input{chapters/Background/Floats/Visualisation}
 
 
-%\subsection{Floating Point Operations}
-%\input{chapters/Background/Floats/Operations}
+\subsection{Floating Point Operations}
+\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.
+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.