That's it I give up

[ipdf/sam.git] / chapters / Progress.tex

diff --git a/chapters/Progress.tex b/chapters/Progress.tex
index a88e002..93b9b76 100644 (file)
--- a/chapters/Progress.tex
+++ b/chapters/Progress.tex
@@ -1,10 +1,9 @@
 \chapter{Progress Report}\label{Progress}
 
-We describe the current state of our research in relation to the aims outlined in Chapter \ref{Introduction}.
+We describe the current state of our project in relation to the aims outlined in Chapter \ref{Introduction}. At this stage work on the project has been done in collaboration with David Gow; however the Project Proposals and Literature Reviews were produced individually.
 
 \section{Literature Review}
-
-We have examined a range of literature that can be broadly classed into three different areas (with major references indicated):
+The literature examined in Chapter\ref{Background} can broadly classed into three different areas (with major references indicated):
 \begin{enumerate}
        \item Rendering Vector Graphics \cite{computergraphics2, knuth1983metafont, kilgard2012gpu}
        \begin{itemize}
@@ -22,17 +21,21 @@ We have examined a range of literature that can be broadly classed into three di
                \item Most document standards either specify, suggest, or imply a IEEE-754 floating point representation ({\TeX} is an exception)
                \item IEEE-754 is widely used, although there are instances of languages or processors which do not conform exactly to the standard
                \item Some GPUs in particular may not conform to IEEE-754, possibly trading some accuracy for performance
+               \item Arbitrary precision floating point arithmetic is possible through several libraries
        \end{itemize}
 \end{enumerate}
 
 To improve the Literature Review we could consider the following topics in more detail:
 \begin{enumerate}
-       \item Additional approaches to arbitrary or infinite precision, possibly including symbolic computation
+       \item Additional approaches to arbitrary precision possibly including symbolic computation
        \item Floating point errors in the context of computing B\'{e}zier Curves or similar
+       \item Algorithms for reducing overall error other than Fast2Sum
+       \item Alternative number representations such as rationals (eg: $\frac{1}{3}$)
        \item How well GPUs conform or do not conform to IEEE-754 in more detail
        \item Additional aspects of rendering vector documents including shading
 \end{enumerate}
 
+
 \section{Development of Testbed Software}
 
 We have produced a basic Document Viewer capable of rendering simple primitives under translation and scaling. The OpenGL 3.1 API is used to interface with graphics hardware. This software has the following features:
@@ -83,9 +86,9 @@ Deadlines enforced by the faculty of Engineering Computing and Mathematics are \
        $26^{\text{th}}$ May & \emph{Progress Report and Literature Review due.}\\
        \hline
        $9^{\text{th}}$ June & Demonstrations of limitations of floating point precision in the Testbed software. \\
-       $1^{\text{st}}$ July & At least one implementation of infinite precision for basic primitives (lines, polygons, curves) completed. Other implementations, advanced features, and areas for more detailed research identified. \\
+       $1^{\text{st}}$ July & At least one implementation of arbitrary precision for basic primitives (lines, polygons, curves) completed. Other implementations, advanced features, and areas for more detailed research identified. \\
        \hline
-       $1^{\text{st}}$ August & Experiments and comparison of various infinite precision implementations completed. \\
+       $1^{\text{st}}$ August & Experiments and comparison of various arbitrary precision implementations completed. \\
        \hline
        $1^{\text{st}}$ September & Advanced features implemented and tested, work underway on Final Report. \\
        \hline