I got really excited that stuff had been pushed to the repo and then I saw it was just the IRC logs again.
*.bbl
*.blg
*.toc
+*.pyg
+*.geany
+*.dat
+*.exe
+*.dll
data/*
+.geany
--- /dev/null
+\documentclass[11pt]{article}
+\input{template}
+
+\begin{document}
+\title{Arbitrary Sized Integers}
+\author{Sam Moore, David Gow}
+\maketitle
+
+\section*{Abstract}
+We have implemented arbitrary sized integers which sometimes don't segfault, using a combination of the C++ standard library and stand alone x86-64 assembly. Performance tests reveal that we would have been better off just using the GNU Multiprecision Library (GMP).
+
+\section{Integer Representation}
+
+A positive integer (natural number) can be written as the sum of smaller integers ``digits'' multiplied by powers of a base.
+\begin{align}
+ z &= \displaystyle\sum_{i=0}^{\infty} d_i \beta^{i}
+\end{align}
+Where each digit $d_i < \beta$ the base. A set of $\beta$ unique symbols are used to represent values of $d_i$.
+A fixed size representation truncates the sum at some $i=N$, which can represent all values $0 \leq z \leq \beta^{n+1}-1$.
+
+A seperate sign symbol (eg: '-') can be used to represent negative integers using the same digit sum.
+
+Example in base 10 (decimal):
+\begin{align}
+ 5682_{10} &= 5\times10^3 + 6\times10^2 + 8\times10^1 + 2\times10^0
+\end{align}
+In base 2 (binary) the same integer is:
+\begin{align}
+ 1011000110010_2 &= 1\times2^{12} + 0\times2^{11} + \text{ ...} + 0\times2^0
+\end{align}
+
+\subsection{Representation on computer hardware}
+
+Computer hardware implements operations for fixed size integers. The base is $\beta = 2$ and the digits are $\{0, 1\}$. The most significant bit can be reserved for the sign instead of a digit.
+
+We can construct larger size integers by considering some sequence of fixed size integers to be individual digits. In practice we will still be limited by the memory and processing time required for ``big'' integers.
+
+For example, we can represent $5682_{10}$ as a single 16 bit digit or as the sum of two 8 bit digits.
+Each digit is being written in base 2 or 10 because there is not a universal base with $\geq2^8$ unique symbols.
+
+\begin{align}
+ 5682_{10} &= 0001011000110010_2 = 10110_2\times2^8+ 110010_2\times 2^0 \\
+ &= 22_{10}\times2^{8} + 50_{10}\times2^{0}
+\end{align}
+
+\section{Addition Algorithms}
+
+
+
+\section{Subtraction Algorithms}
+
+\section{Multiplication Algorithms}
+
+\section{Division Algorithms}
+
+\subsection{Naive Algorithm}
+
+\subsection{Shifting Algorithm}
+
+\section{Base conversion}
+
+Since humans are not very good at understanding binary, it is convenient to convert integer representations from one base to another.
+
+
+\section{IPDF Integer Representations}
+
+
+
+
+\end{document}
\documentclass[8pt]{extreport}
-\usepackage{graphicx}
-\usepackage{caption}
-\usepackage{amsmath} % needed for math align
-\usepackage{bm} % needed for maths bold face
- \usepackage{graphicx} % needed for including graphics e.g. EPS, PS
-\usepackage{fancyhdr} % needed for header
-%\usepackage{epstopdf} % Converts eps to pdf before including. Do it manually instead.
-\usepackage{float}
-\usepackage{hyperref}
-
- \topmargin -1.5cm % read Lamport p.163
- \oddsidemargin -0.04cm % read Lamport p.163
- \evensidemargin -0.04cm % same as oddsidemargin but for left-hand pages
- \textwidth 16.59cm
- \textheight 21.94cm
- %\pagestyle{empty} % Uncomment if don't want page numbers
- \parskip 8.2pt % sets spacing between paragraphs
- %\renewcommand{\baselinestretch}{1.5} % Uncomment for 1.5 spacing between lines
- \parindent 0pt % sets leading space for paragraphs
-\linespread{1}
-
-
-\newcommand{\vect}[1]{\boldsymbol{#1}} % Draw a vector
-\newcommand{\divg}[1]{\nabla \cdot #1} % divergence
-\newcommand{\curl}[1]{\nabla \times #1} % curl
-\newcommand{\grad}[1]{\nabla #1} %gradient
-\newcommand{\pd}[3][ ]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} %partial derivative
-%\newcommand{\d}[3][ ]{\frac{d^{#1} #2}{d #3^{#1}}} %full derivative
-\newcommand{\phasor}[1]{\tilde{#1}} % make a phasor
-\newcommand{\laplacian}[1]{\nabla^2 {#1}} % The laplacian operator
-
-\usepackage{color}
-\usepackage{listings}
-
-\definecolor{darkgray}{rgb}{0.95,0.95,0.95}
-\definecolor{darkred}{rgb}{0.75,0,0}
-\definecolor{darkblue}{rgb}{0,0,0.75}
-\definecolor{pink}{rgb}{1,0.5,0.5}
-\lstset{language=XML}
-\lstset{backgroundcolor=\color{darkgray}}
-%\lstset{numbers=left, numberstyle=\tiny, stepnumber=1, numbersep=5pt}
-%\lstset{keywordstyle=\color{darkred}\bfseries}
-%\lstset{commentstyle=\color{darkblue}}
-%\lstset{stringsyle=\color{red}}
-%\lstset{showstringspaces=false}
-%\lstset{basicstyle=\small}
-
-\newcommand{\shell}[1]{\texttt{#1}}
-\newcommand{\code}[1]{\texttt{#1}}
-
+\input{template}
\begin{document}
all but guaranteed that this is the method we will be using for compositing
document elements in our project.
-{\bf Some issues with the statements made here...}
-When introducing Bresenham's algorithm below you say modern graphics systems ``will often use Wu's line-drawing algorithm instead, \emph{as it produces antialiased lines}'' (and don't give a citation). Here you say OpenGL uses Porter-Duff compositing ``almost exactly''. But in their introduction they say: ``
-\begin{enumerate}
-\
\section{Bresenham's Algorithm: Algorithm for computer control of a digital plotter \cite{bresenham1965algorithm}}
Bresenham's line drawing algorithm is a fast, high quality line rasterization
%% Sam again
-\section{Boost Multiprecision Library \cite{boost_multiprecision}}
+\section{Boost Multiprecision Library}
\begin{itemize}
\item ``The Multiprecision Library provides integer, rational and floating-point types in C++ that have more range and precision than C++'s ordinary built-in types.''
\begin{figure}[H]
\centering
-\begin{lstlisting}[language=XML,basicstyle=\ttfamily]
+\begin{minted}{xml}
<?xml version="1.0"?>
<mesh name="mesh_root">
<!-- here is a mesh node -->
</node>
</mesh>
<?include somedata?>
-\end{lstlisting}
+\end{minted}
\includegraphics[width=0.6\textwidth]{references/pugixmlDOM-dom_tree.png}
\caption{Tree representation of the above listing \cite{pugixmlDOM}}
An example is this Fortran compiler ``nasty bug'' where the compiler replaces $s$ with $x$ in line 4 and thus a rounding operation is lost.
-\begin{lstlisting}[language=Fortran, basicstyle=\ttfamily]
+\begin{minted}{Fortran}
real(8) :: x, y % double precision (or extended as real(12))
real(4) :: s, t % single precision
s = x % s should be rounded
t = (s - y) / (...) % Compiler incorrectly replaces s with x in this line
-\end{lstlisting}
+\end{minted}
\subsection{The Baleful Influence of Benchmarks \cite{kahan1996ieee754} pg 20}
TARGETS = LiteratureNotes.pdf
-all : $(TARGETS) clean
+all : $(TARGETS)
rebuild :
make clean_full
%.pdf : %.tex papers.bib
# Incoming wall of text
- pdflatex $*
+ pdflatex -shell-escape $*
bibtex $*
- pdflatex $*
- pdflatex $*
+ pdflatex -shell-escape $*
+ pdflatex -shell-escape $*
clean :
# LaTeX makes way too many output files; get rid of them all
--- /dev/null
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--- /dev/null
+<?xml version="1.0"?>
+
+<?include somedata?>
keywords={Calculators;Character recognition;Engine cylinders;Engineering drawings;Hardware;History;Information analysis;Information processing;Permission;Time sharing computer systems},
doi={10.1109/MAHC.1982.10042},
ISSN={0164-1239},}
+
+@article{heckmann1998bigintegers,
+ author = "Reinhold Heckmann",
+ title = "Big Integers and Complexity Issues in Exact Real Arithmetic",
+ journal = "Electronic Notes in Theoretical Computer Science",
+ Volume = 13,
+ year = 1998,
+ pages = 69,
+ doi = "10.1016/S1571-0661(05)80215-4"
+}
--- /dev/null
+
+\usepackage{makeidx}
+\usepackage{graphicx}
+\usepackage{caption}
+\usepackage{amsmath} % needed for math align
+\usepackage{bm} % needed for maths bold face
+ \usepackage{graphicx} % needed for including graphics e.g. EPS, PS
+\usepackage{fancyhdr} % needed for header
+%\usepackage{epstopdf} % Converts eps to pdf before including. Do it manually instead.
+\usepackage{float}
+\usepackage{hyperref}
+\usepackage{setspace}
+\usepackage{anyfontsize}
+\usepackage{mdframed}
+\usepackage[compact]{titlesec}
+\usepackage[table]{xcolor}
+
+ \topmargin -1.5cm % read Lamport p.163
+ \oddsidemargin -0.04cm % read Lamport p.163
+ \evensidemargin -0.04cm % same as oddsidemargin but for left-hand pages
+ \textwidth 16.59cm
+ \textheight 21.94cm
+ %\pagestyle{empty} % Uncomment if don't want page numbers
+ \parskip 8.2pt % sets spacing between paragraphs
+ %\renewcommand{\baselinestretch}{1.5} % Uncomment for 1.5 spacing between lines
+ \parindent 0pt % sets leading space for paragraphs
+\linespread{1}
+
+
+\newcommand{\vect}[1]{\boldsymbol{#1}} % Draw a vector
+\newcommand{\divg}[1]{\nabla \cdot #1} % divergence
+\newcommand{\curl}[1]{\nabla \times #1} % curl
+\newcommand{\grad}[1]{\nabla #1} %gradient
+\newcommand{\pd}[3][ ]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} %partial derivative
+%\newcommand{\d}[3][ ]{\frac{d^{#1} #2}{d #3^{#1}}} %full derivative
+\newcommand{\phasor}[1]{\tilde{#1}} % make a phasor
+\newcommand{\laplacian}[1]{\nabla^2 {#1}} % The laplacian operator
+
+\usepackage{color}
+
+\usepackage{minted} % For code snippets
+\AtBeginEnvironment{minted}{\singlespacing\fontsize{7}{7}\selectfont}
+\definecolor{pink}{rgb}{1.0,0.5,0.5}
+\definecolor{darkgray}{rgb}{0.1,0.1,0.1}
+\definecolor{lightgray}{rgb}{0.95,0.95,0.95}
+\definecolor{gray}{rgb}{0.5,0.5,0.5}
+\definecolor{darkred}{rgb}{0.75,0,0}
+\definecolor{darkblue}{rgb}{0,0,0.35}
+\definecolor{green}{rgb}{0,0.70,0}
+\definecolor{black}{rgb}{0,0,0}
+
+\newcommand{\shell}[1]{\texttt{#1}}
+\newcommand{\code}[1]{\texttt{#1}}
+\renewcommand{\url}[1]{$\langle$\href{#1}{\underline{\color{blue}{#1}}}$\rangle$}
+
+
git.ucc.asn.au / ipdf / documents.git / commitdiff
UCC git Repository :: git.ucc.asn.au
