heron_sqrt/bericht/bericht.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
% ******************************************************************************/

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  print,          % print optimized version of the thesis, standard option
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  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}
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\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}