102 lines
3.8 KiB
TeX
102 lines
3.8 KiB
TeX
\documentclass[a4paper,landscape]{scrartcl}
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\usepackage[T1]{fontenc}
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\usepackage{amsmath, amsthm, amssymb}
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\usepackage[ansinew]{inputenc}
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\usepackage{listings}
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\usepackage{tabularx}
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\usepackage{graphicx}
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\usepackage{color}
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\definecolor{mygreen}{rgb}{0,0.6,0}
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\definecolor{mygray}{rgb}{0.5,0.5,0.5}
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\definecolor{mymauve}{rgb}{0.58,0,0.82}
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\lstset{ %
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backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}
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basicstyle=\footnotesize, % the size of the fonts that are used for the code
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breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
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breaklines=true, % sets automatic line breaking
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captionpos=b, % sets the caption-position to bottom
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commentstyle=\color{mygreen}, % comment style
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deletekeywords={...}, % if you want to delete keywords from the given language
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escapeinside={\%*}{*)}, % if you want to add LaTeX within your code
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extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
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frame=single, % adds a frame around the code
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keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
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keywordstyle=\color{blue}, % keyword style
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language=C, % the language of the code
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morekeywords={*,...}, % if you want to add more keywords to the set
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numbers=left, % where to put the line-numbers; possible values are (none, left, right)
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numbersep=5pt, % how far the line-numbers are from the code
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numberstyle=\tiny\color{mygray}, % the style that is used for the line-numbers
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rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
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showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
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showstringspaces=false, % underline spaces within strings only
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showtabs=false, % show tabs within strings adding particular underscores
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stepnumber=2, % the step between two line-numbers. If it's 1, each line will be numbered
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stringstyle=\color{mymauve}, % string literal style
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tabsize=2, % sets default tabsize to 2 spaces
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title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title
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}
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\begin{document}
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\subsection{Algorithmus}
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\begin{align}
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x_{n+1}=\frac{x_n + \frac{a}{x_n}}{2}
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\end{align}
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\subsection{Implementierung in C}
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\begin{lstlisting}
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typedef uint32_t u32;
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void heron_sqrt(u32 *mem) {
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int i = mem[0];
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while (i > 0) {
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u32 s = mem[i];
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if (s > 1) {
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// x_0 = (s + 1) / 2
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// without increment to avoid overflow for 0xffffffff
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u32 x = s >> 1;
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u32 old_x = x;
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while(1) {
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// x_{n + 1} = (x_n + (s / x_n)) / 2
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x = (x >> 1) + ((s/x) >> 1);
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if (old_x <= x) {
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break;
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}
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old_x = x;
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}
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mem[i] = x;
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}
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i--;
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}
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}
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\end{lstlisting}
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\subsection{Speicherbelegung}
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Es wird angenommen, das jeder Speicherplatz 32 Bit breit ist.
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Jedes Datenfeld wird als vorzeichenlose Festkommazahl interpretiert.
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\begin{tabularx}{\textwidth}{X|X}
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Speicherplatz & Beschreibung \\\hline
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MEM[0] & Anzahl der Operanden (n) \\
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MEM[1] & 1. Operand \\
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MEM[2] & 2. Operand \\
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$\ldots$ & $\dots$ \\
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MEM[N] & N. Operand
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\end{tabularx}
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\subsection{Datenflussgraph}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=0.5\textwidth]{graph.pdf}
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\label{fig1}
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\end{figure}
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\subsection{Datenpfad}
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\end{document}
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