X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground%2FFloats.tex;fp=chapters%2FBackground%2FFloats.tex;h=17ec51cd357bd59ce9ea2e3b037838c00d84f291;hp=1be1113684ae7f2736c8761e36c289aba31b8d08;hb=a1ede3cfc3ef650aa0f7d3d06e78c6c6ef4cb0cc;hpb=7fe12ce195f039925222ad98b38018ad31d1b1f2 diff --git a/chapters/Background/Floats.tex b/chapters/Background/Floats.tex index 1be1113..17ec51c 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} +\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. -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. +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.