Restructure chapters, delete a bunch of words, add more words, do some things, panic...

[ipdf/sam.git] / chapters / Background / Floats.tex

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+\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}
+
+
+\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.