X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;ds=sidebyside;f=chapters%2FBackground%2FFloats.tex;h=17ec51cd357bd59ce9ea2e3b037838c00d84f291;hb=e699a78987125e89a9f976067ecfb149409bb423;hp=7eba8a27bdb4c963fc54a389ad95e272e34525a7;hpb=9fcf44a0c34f393689118e913a2d17d907036c85;p=ipdf%2Fsam.git

diff --git a/chapters/Background/Floats.tex b/chapters/Background/Floats.tex
index 7eba8a2..17ec51c 100644
--- a/chapters/Background/Floats.tex
+++ b/chapters/Background/Floats.tex
@@ -7,8 +7,8 @@
 %\input{chapters/Background/Floats/Operations}
 
 
-\subsection{Arbitrary Precision Floating Point Numbers}
+\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 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. 
+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. 
 
-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 (size of the mantissa) be set; although it is possible to increase or decrease the precision of individual numbers as desired.