-\subsection{Scientific Computation Packages}
-
-The document and the code that produces it are one and the same.
-
-\begin{itemize}
- \item Numerical computation packages such as Mathematica and Maple use arbitrary precision floats
- \begin{itemize}
- \item Mathematica is not open source which is an issue when publishing scientific research (because people who do not fork out money for Mathematica cannot verify results)
- \item What about Maple? \cite{HFP} and \cite{fousse2007mpfr} both mention it being buggy.
- \item Octave and Matlab use fixed precision doubles
- \end{itemize}
- \item IPython is pretty cool guys
-\end{itemize}
-
-\section{Precision in Modern Document Formats}
-
-We briefly summarise the requirements of standard document formats in regards to the precision of number representations:
-\begin{itemize}
- \item {\bf PostScript} predates the IEEE-754 standard and originally specified a floating point representation with ? bits of exponent and ? bits of mantissa. Version ? of the PostScript standard changed to specify IEEE-754 binary32 ``single precision'' floats.
- \item {\bf PDF} has also specified IEEE-754 binary32 since version ?. Importantly, the standard states that this is a \emph{maximum} precision; documents created with higher precision would not be viewable in Adobe Reader.
- \item {\bf SVG} specifies a minimum of IEEE-754 binary32 but recommends more bits be used internally
- \item {\bf Javascript} uses binary32 floats for all operations, and does not distinguish between integers and floats.
- \item {\bf Python} uses binary64 floats
- \item {\bf Matlab} uses binary64 floats
- \item {\bf Mathematica} uses some kind of terrifying symbolic / arbitrary float combination
- \item {\bf Maple} is similar but by many accounts horribly broken
-
-\end{itemize}
+\subsection{PDF}
+PDF defines ``Real'' objects in a similar way to PostScript, but suggests a range of $\pm3.403\times10^{38}$ and smallest non-zero values of $\pm1.175\times10^{38}$\cite{pdfref17}. A note in the PDF 1.7 manual mentions that Acrobat 6 now uses IEEE-754 single precision floats, but ``previous versions used 32-bit fixed point numbers'' and ``... Acrobat 6 still converts floating-point numbers to fixed point for some components''.
+
+\subsection{\TeX and METAFONT}