heron_sqrt/bericht/bericht.tex
2014-01-02 13:01:07 +01:00

145 lines
5.8 KiB
TeX

%*******************************************************************************
% * Copyright (c) 2006-2013
% * Institute of Automation, Dresden University of Technology
% *
% * All rights reserved. This program and the accompanying materials
% * are made available under the terms of the Eclipse Public License v1.0
% * which accompanies this distribution, and is available at
% * http://www.eclipse.org/legal/epl-v10.html
% *
% * Contributors:
% * Institute of Automation - TU Dresden, Germany
% * - initial API and implementation
% ******************************************************************************/
\documentclass[
print, % print optimized version of the thesis, standard option
% alternative:
% screen, % makes the thesis better readable on screens (onesided, coloured links)
% use only 'print' OR 'screen'
% ATTENTION: 'screen' changes size of text area slightly. Always optimize document WITH
% 'print' option first for printing (size of graphics etc.) and convert afterwards
% in screen optimized version!
listoffigures, % includes list of figures
listoftables, % includes list of tables
listoflistings, % includes list of listings
abbrevations, % includes index of symbols and abbrevations
bibIfa, % citation style (IfA standard), alternatives: bibNumeric, bibHarvard
langDE % define the language (default: langDE)
]{ifathesis}
\ifaThesis{Belegarbeit}
\ifaAuthor{Jörg Thalheim}
\ifaAuthorBirthday{03.01.1992}
\ifaAuthorBirthplace{Großröhrsdorf}
\ifaAuthorCourse{Informationssystemtechnik}
\ifaAuthorYearOfMatriculation{2011}
\ifaKeywords{Praktikum, Schaltungsentwurf, Verilog} % Keywords included in pdf-file. Could be found e.g. by Windows file search.
\ifaTitleDE{Schaltkreis- und Systementwurf}
\ifaTitleEN{}
\ifaSupervisorA{Jens-Uwe Schlüßler}
\ifaProfessor{Prof. Dr.-Ing. habil. René Schüffny}
\ifaDayOfSubmission{\today}
\ifaTopicDescriptionPDF{parts/00_Aufgabenstellung.pdf}
\ifaAppendix{example_files/appendix}
\ifaAbstractDE{example_files/00_abstract_de__invalid}
\ifaAbstractEN{example_files/00_abstract_en__invalid}
\usepackage{tabularx}
\usepackage{graphicx}
\usepackage{color}
\definecolor{mygreen}{rgb}{0,0.6,0}
\definecolor{mygray}{rgb}{0.5,0.5,0.5}
\definecolor{mymauve}{rgb}{0.58,0,0.82}
\lstset{ %
backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}
basicstyle=\footnotesize, % the size of the fonts that are used for the code
breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
breaklines=true, % sets automatic line breaking
captionpos=b, % sets the caption-position to bottom
commentstyle=\color{mygreen}, % comment style
deletekeywords={...}, % if you want to delete keywords from the given language
escapeinside={\%*}{*)}, % if you want to add LaTeX within your code
extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
frame=single, % adds a frame around the code
keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
keywordstyle=\color{blue}, % keyword style
language=C, % the language of the code
morekeywords={*,...}, % if you want to add more keywords to the set
numbers=left, % where to put the line-numbers; possible values are (none, left, right)
numbersep=5pt, % how far the line-numbers are from the code
numberstyle=\tiny\color{mygray}, % the style that is used for the line-numbers
rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
showstringspaces=false, % underline spaces within strings only
showtabs=false, % show tabs within strings adding particular underscores
stepnumber=2, % the step between two line-numbers. If it's 1, each line will be numbered
stringstyle=\color{mymauve}, % string literal style
tabsize=2, % sets default tabsize to 2 spaces
title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title
}
\begin{document}
\chapter{Einleitung}
TODO Kapitel 5.1 -> Aufgabenstellung
\chapter{Beschreibung des Algorithmus}
\begin{align}
x_{n+1}=\frac{x_n + \frac{a}{x_n}}{2}
\end{align}
\section{Implementierung in C}
\begin{lstlisting}
typedef uint32_t u32;
void heron_sqrt(u32 *mem) {
int i = mem[0];
while (i > 0) {
u32 s = mem[i];
if (s > 1) {
// x_0 = (s + 1) / 2
// without increment to avoid overflow for 0xffffffff
u32 x = s >> 1;
u32 old_x = x;
while(1) {
// x_{n + 1} = (x_n + (s / x_n)) / 2
x = (x >> 1) + ((s/x) >> 1);
if (old_x <= x) {
break;
}
old_x = x;
}
mem[i] = x;
}
i--;
}
}
\end{lstlisting}
\subsection{Speicherbelegung}
Es wird angenommen, das jeder Speicherplatz 32 Bit breit ist.
Jedes Datenfeld wird als vorzeichenlose Festkommazahl interpretiert.
\begin{tabularx}{\textwidth}{X|X}
Speicherplatz & Beschreibung \\\hline
MEM[0] & Anzahl der Operanden (n) \\
MEM[1] & 1. Operand \\
MEM[2] & 2. Operand \\
$\ldots$ & $\dots$ \\
MEM[N] & N. Operand
\end{tabularx}
\subsection{Datenflussgraph}
\begin{figure}[ht]
\centering
\includegraphics[width=0.3\textwidth]{graph.pdf}
\label{fig1}
\end{figure}
\subsection{Datenpfad}
\end{document}