From a957590287356c9dfb1d8069e6f33934e2ded473 Mon Sep 17 00:00:00 2001 From: Andre Meyering Date: Mon, 20 Nov 2017 12:31:49 +0100 Subject: [PATCH] =?UTF-8?q?[Kapitel]=20Neue=20Inhalte=20erg=C3=A4nzt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Bilder/Aufwand_Komparator.png | Bin 0 -> 68042 bytes Bilder/Cache_Aufbau.png | Bin 0 -> 46675 bytes Bilder/Cache_Komparator.png | Bin 0 -> 66566 bytes Bilder/Cache_Komparator_1.png | Bin 0 -> 30120 bytes Bilder/n-bit-Komparator.png | Bin 0 -> 69285 bytes Kapitel/02_Rechner.tex | 70 ----- Kapitel/03_Speicher.tex | 320 +++++++++++++++++++++++ Rechnerarchitektur_Roethig_Skript_AM.pdf | Bin 862743 -> 1135389 bytes Rechnerarchitektur_Roethig_Skript_AM.tex | 3 + 9 files changed, 323 insertions(+), 70 deletions(-) create mode 100644 Bilder/Aufwand_Komparator.png create mode 100644 Bilder/Cache_Aufbau.png create mode 100644 Bilder/Cache_Komparator.png create mode 100644 Bilder/Cache_Komparator_1.png 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y=hLjfXA_VZ6!3x1!_da=0GET`dqj-3|D0;x{!J6pVdQ-Z{Ag?HYgDK`2>X9ujrijL literal 0 HcmV?d00001 diff --git a/Kapitel/02_Rechner.tex b/Kapitel/02_Rechner.tex index dcf02b1..e2ebc20 100644 --- a/Kapitel/02_Rechner.tex +++ b/Kapitel/02_Rechner.tex @@ -1048,73 +1048,3 @@ In \autoref{tbl:risc_cisc} werden \acs{RISC} und \acs{CISC} verglichen. \label{tbl:risc_cisc} \end{table} - -\section{Speicher in Computern} \index{Speicher} - -\subsection{Speicherhierarchie} -\autoref{tbl:speicherhierarchie} zeigt die Speicherhierarchie in modernen Universalrechnern - -\begin{table}[ht] - \centering - \begin{tabular}{p{29mm}|p{36mm}|p{17mm}|p{34mm}|p{23mm}} - Speicher & von-Neumann-Rechner & Persistenz & Größe & Zugriffszeit \\ \midrule - \acs{CPU}-Register & Zentraleinheit (Rechen- und Steuerwerk) & flüchtig & $<1kB$ Byte & $\approx$ 200ps \\ \midrule - Cache \newline (\enquote{CPU-Cache}) & nicht vorhanden & flüchtig & \circa{4}MB \newline L1$\approx$64KB \newline L2$\approx$512KB & $\approx$ 10ns \\ \midrule - Hauptspeicher/ Primärspeicher & Speicherwerk & flüchtig & \circa{8}GB & $\approx$ 100ns \newline L1 schneller \\ \midrule - Sekundärspeicher & Peripheriegeräte an Ein- und Ausgabewerk & nicht flüchtig & HDD: 3T \newline SSD: 512GB \newline opt.~\acs{LW}: bis~100GB \newline \acs{BLW}: wenige TB & HDD~$\approx10ms$ \newline SSD~$\approx 10\mu s$\newline opt.~\acs{LW}~$\approx 1s$ \newline \acs{BLW}~$\approx 1min$ - \end{tabular} - \caption{Speicherhierarchie und -Daten} - \label{tbl:speicherhierarchie} -\end{table} - -\subsection{Sekundärspeicher} -Motivation für Sekundärspeicher: nicht-flüchtig, \dash der Speicherinhalt bleibt auch bei Stromausfall erhalten. - -\textbf{Anwendungen:} - -\begin{itemize}[noitemsep] - \item Programmcode (Betriebsystem, Anwendungsprogramme) - \item Nutzdaten - \item virtuelle Erweiterung des Speicherwerks (Swap-Datei/-Partition) - \item Hibernation (\enquote{Ruhezustand}) -\end{itemize} - -\subsection{CPU-Cache} -\begin{figure}[ht] - \centering - \begin{tikzpicture} - % CPU - \draw (-3, -0.5) rectangle ++(6,1); - \node at (0, 0) (SW) {Speicherwerk}; - - \draw (-2.5, 1.5) rectangle ++(5,1); - \node at (0, 2) (Ca) {CPU-Cache}; - - \draw (-2, 3.5) rectangle ++(4,1); - \node at (0, 4) (CPU) {Zentraleinheit (CPU)}; - - \draw ($(CPU)+(0,-0.5)$) -- ($(Ca)+(0,0.5)$) ($(Ca)+(0,-0.5)$) -- ($(SW)+(0,0.5)$); - \end{tikzpicture} - \caption{...} - \label{fig:cpu_cache} -\end{figure} - -Temporärer, flüchtiger, schneller Zwischenspeicher, um auf Informationen aus dem Hauptspeicher schneller zugreifen zu können. - -Eigenschaften des Cache: -\begin{itemize}[noitemsep] - \item flüchtig - \item kleiner als das zu cachende Medium (Hauptspeicher) - \item schneller als das zu cachende Medium (Hauptspeicher) - \item transparent, \dash es wird nicht auf den Cache, sondern auf das zu cachende Medium logisch zugegriffen (die \acs{CPU} adressiert den Hauptspeicher und nicht den Cache) - \item konsistent, \dash alle Instanzen derselben \acf{HSA} haben denselben Wert - \item kohärent, \dash beim Zugriff auf eine \acs{HSA} wird immer der aktuelle Wert geliefert -\end{itemize} - -\bigskip -\begin{Hinweis}[frametitle={Anmerkung: Kohärenz und Konsistenz}] - Kohärenz ist Pflicht und Konsistenz ist Wunsch, da aus Konsistenz Kohärenz folgt. Zeitweise kann aber auf Konsistenz verzichtet werden. -\end{Hinweis} - -Lokalität des Zugriffmusters \newline -$\Rightarrow$ verantwortlich dafür, dass der Cache Geschwindigkeitsvorteile bringen kann. diff --git a/Kapitel/03_Speicher.tex b/Kapitel/03_Speicher.tex new file mode 100644 index 0000000..f9f49e0 --- /dev/null +++ b/Kapitel/03_Speicher.tex @@ -0,0 +1,320 @@ + +\chapter{Speicher in Computern} \index{Speicher} + +\section{Speicherhierarchie} +\autoref{tbl:speicherhierarchie} zeigt die Speicherhierarchie in modernen Universalrechnern + +\begin{table}[ht] + \centering + \begin{tabular}{p{29mm}|p{36mm}|p{17mm}|p{34mm}|p{23mm}} + Speicher & von-Neumann-Rechner & Persistenz & Größe & Zugriffszeit \\ \midrule + \acs{CPU}-Register & Zentraleinheit (Rechen- und Steuerwerk) & flüchtig & $<1kB$ Byte & $\approx$ 200ps \\ \midrule + Cache \newline (\enquote{CPU-Cache}) & nicht vorhanden & flüchtig & \circa{4}MB \newline L1$\approx$64KB \newline L2$\approx$512KB & $\approx$ 10ns \\ \midrule + Hauptspeicher/ Primärspeicher & Speicherwerk & flüchtig & \circa{8}GB & $\approx$ 100ns \newline L1 schneller \\ \midrule + Sekundärspeicher & Peripheriegeräte an Ein- und Ausgabewerk & nicht flüchtig & HDD: 3T \newline SSD: 512GB \newline opt.~\acs{LW}: bis~100GB \newline \acs{BLW}: wenige TB & HDD~$\approx10ms$ \newline SSD~$\approx 10\mu s$\newline opt.~\acs{LW}~$\approx 1s$ \newline \acs{BLW}~$\approx 1min$ + \end{tabular} + \caption{Speicherhierarchie und -Daten} + \label{tbl:speicherhierarchie} +\end{table} + +\section{Sekundärspeicher} +Motivation für Sekundärspeicher: nicht-flüchtig, \dash der Speicherinhalt bleibt auch bei Stromausfall erhalten. + +\textbf{Anwendungen:} + +\begin{itemize}[noitemsep] + \item Programmcode (Betriebsystem, Anwendungsprogramme) + \item Nutzdaten + \item virtuelle Erweiterung des Speicherwerks (Swap-Datei/-Partition) + \item Hibernation (\enquote{Ruhezustand}) +\end{itemize} + +\section{CPU-Cache} + +Temporärer, flüchtiger, schneller Zwischenspeicher, um auf Informationen aus dem Hauptspeicher schneller zugreifen zu können. + +Eigenschaften des Cache: +\begin{itemize}[noitemsep] + \item flüchtig + \item kleiner als das zu cachende Medium (Hauptspeicher) + \item schneller als das zu cachende Medium (Hauptspeicher) + \item transparent, \dash es wird nicht auf den Cache, sondern auf das zu cachende Medium logisch zugegriffen (die \acs{CPU} adressiert den Hauptspeicher und nicht den Cache) + \item konsistent, \dash alle Instanzen derselben \acf{HSA} haben denselben Wert + \item kohärent, \dash beim Zugriff auf eine \acs{HSA} wird immer der aktuelle Wert geliefert +\end{itemize} + +\bigskip +\begin{Hinweis}[frametitle={Anmerkung: Kohärenz und Konsistenz}] + Kohärenz ist Pflicht und Konsistenz ist Wunsch, da aus Konsistenz Kohärenz folgt. Zeitweise kann aber auf Konsistenz verzichtet werden. +\end{Hinweis} + +\subsection{Lokalität des Zugriffmusters} \index{Lokalität} +Verantwortlich dafür, dass der Cache Geschwindigkeitsvorteile bringen kann. +\begin{description} + \item[räumliche Lokalität] Wenn auf eine Adresse zugegriffen wird, wird auch auf naheliegende Adressen zugegriffen. + \item[zeitlich Lokalität] Die Zugriffe (auf nahe beieinanderliegene Adressen) erfolgen in relativ geringem zeitlichen Aufwand +\end{description} +\medskip +\begin{Hinweis} + Hinweis: Insbesondere die räumliche Lokalität ist beim Zugriff auf Programmcode und Nutzdaten sehr unterschiedlich (Programmcode: sequentiell, Nutzdaten zufällig innterhalb von Speicherblöcken). + + $\Rightarrow$ Moderne \acsp{CPU} weisen getrennte Caches für Programmcode und Nutzdaten auf! +\end{Hinweis} + + +\subsection{Begriffe} +\begin{description} + \item[Hit]\index{Hit-Rate} Zugriff auf \acl{HS}-Daten, welcher aus dem Cache bedient werden kann + \item[Miss]\index{Miss-Rate} Zugriff auf \acl{HS}-Daten, welcher \textit{nicht} aus dem Cache bedient werden kann und deshalb der Cache die Daten erst aus dem \acl{HS} holen muss. + \item[Hit-Rate] Anteil der \enquote{erfolgreichen} Zugriffe an allen Zugriffen. \newline + Hit-Rate=$\frac{\text{\#Hits}}{\text{\#Zugriffe}}$ + \item[Miss-Rate] Anteil der \enquote{nicht erfolgreichen} Zugriffe an allen Zugriffen. \newline + Miss-Rate=$\frac{\text{\#Misses}}{\text{\#Zugriffe}}$ + \item[Zugriffe] Anzahl der Misses plus der Hits +\end{description} + +\columnratio{0.5} +\begin{paracol}{2} + \begin{tabular}{@{}ll} + \textbf{Anwendung}: & $0\leq$ Hit-Rate $\leq 1$ \\ + & $0\leq$ Miss-Rate $\leq 1$ \\ + & Hit-Rate + Miss-Rate $= 1$ + \end{tabular} + \switchcolumn + \begin{tabular}{ll} + \textbf{Ziel}: & Hit-Rate $\rightarrow 1$ (nicht realistisch) \\ + & Hit-Rate $\rightarrow 0$ \\ + & Hit-Rate $\rightarrow$ systembedingtes Maximum \\ + & \qquad (realistisch) + \end{tabular} +\end{paracol} + + +systembedingtes Maximum hängt ab von +\begin{itemize}[noitemsep] + \item Lokalität des Zugriffsmusters + \item Größe (und Größenverhältnis) von Cache und \acl{HS} +\end{itemize} + +Hinweis: $\text{Hit-Rate}_\text{erreicht} \geq \frac{\text{Größe (Cache)}}{\text{Größe HS}}$ (Wahrscheinlichkeit, das ein beliebiger Zugriff eine bereits im Cache gespeicherte Adresse betrifft) + +$\Rightarrow$ sobald das Zugriffsmuster Lokalität aufweist, ergibt sich eine bessere Hit-Rate + + +\subsection{Betriebszustände des Cache} +\begin{description} + \item[kalter Cache]\index{Cache!kalter Cache} bei Betriebsbeginn ist der Cache leer + \item[sich erwärmender Cache]\index{Cache!erwärmender Cache} Während des Betriebs wird der Cache mit immer mehr Daten geladen und die Hit-Rate steigt. + \item[heißer Cache]\index{Cache!heißer Cache} Der Cache ist (nahezu) voll nach einer gewissen Betriebszeit. Die Hit-Rate erreicht das systembedingte Maximum. +\end{description} + +\subsection{Cachearchitekturen}\index{Cache!Architektur} +\begin{figure}[!htb] + \medskip + \minipage{0.5\textwidth} + \begin{tikzpicture} + % CPU + \draw (-3, -0.5) rectangle ++(6,1); + \node at (0, 0) (SW) {Speicherwerk}; + + \draw (-2.5, 1.5) rectangle ++(5,1); + \node at (0, 2) (Ca) {CPU-Cache}; + + \draw (-2, 3.5) rectangle ++(4,1); + \node at (0, 4) (CPU) {Zentraleinheit (CPU)}; + + \draw ($(CPU)+(0,-0.5)$) -- ($(Ca)+(0,0.5)$) ($(Ca)+(0,-0.5)$) -- ($(SW)+(0,0.5)$); + \end{tikzpicture} + \caption{Look-Through-Cache} + \label{fig:cpu_cache_look_through} + \endminipage\hfill + \minipage{0.5\textwidth} + \begin{tikzpicture} + % CPU + \draw (-2.5, -0.5) rectangle ++(5,1); + \node at (0, 0) (SW) {Speicherwerk}; + + \draw (1.5, 1.5) rectangle ++(3,1); + \node at (3, 2) (Ca) {CPU-Cache}; + + \draw (-2, 3.5) rectangle ++(4,1); + \node at (0, 4) (CPU) {Zentraleinheit (CPU)}; + + \draw ($(CPU)+(0,-0.5)$) -- ($(SW)+(0,0.5)$); + \draw (0, 2) -- ($(Ca)+(-1.5,0)$); + \end{tikzpicture} + \caption{Look-Aside-Cache} + \label{fig:cpu_cache_look_aside} + \endminipage +\end{figure} + +\columnratio{0.5} +\begin{paracol}{2} + \textsf{\textbf{Look-Through-Cache}}\index{Cache!Look-Through} + + Wie in \autoref{fig:cpu_cache_look_through} zu sehen, ist die CPU nur mit dem Cache und der \acl{HS} ebenfalls nur mit dem Cache verbunden. + + CPU greift über den Cache auf den \acl{HS} zu: + + \begin{itemize}[leftmargin=5mm] + \item[$\ominus$] $t_\text{Miss}=t_\text{Cache}+t_\text{HS}$ \newline + Zugriffszeit bei Miss größer als ohne Cache + \item[$\oplus$] optimale Konsistenz + \end{itemize} + + \switchcolumn + \textsf{\textbf{Look-Aside-Cache}}\index{Cache!Look-Aside} + + In \autoref{fig:cpu_cache_look_aside} sind \acs{CPU}, Cache und \acs{HS} über einen Bus miteinander verbunden. Die Anfrage durch die CPU geht auf dem Bus an beide und ggf. antworten beide, \dash die schnellere Antwort gewinnt. + + \begin{itemize}[leftmargin=5mm] + \item[$\oplus$] $t_\text{Miss} > t_\text{HS}$ \newline + Zugriffszeit bei einem Miss genauso wie ohne Cache $\Rightarrow$ immer \enquote{beste} Zugriffszeit + \item[$\ominus$] Bus braucht Zugriffsprotokoll mit Overhead $\Rightarrow$ langsamer als 1:1 Verbindung + \item[$\ominus$] Konsistenz durch zweite Antwort potentiell gefährdet + \end{itemize} +\end{paracol} + +\subsection{Schreibstrategie} +\columnratio{0.5} +\begin{paracol}{2} + \textsf{\textbf{Write-Back}} + + Schreibzugriff durch die \acs{CPU} findet im Cache statt und der Cache aktualisiert die Daten bei nächster Gelegenheit im \acl{HS}. + \bigskip + \medskip + \begin{itemize}[leftmargin=5mm] + \item[$\ominus$] zeitwertige Inkonsistenz der Daten + \item[$\oplus$] Schreiben in Cache-Geschwindigkeit möglich + \end{itemize} + + \switchcolumn + \textsf{\textbf{Write-Through}} + + Schreibzugriffe durch die \acs{CPU} findet im \acl{HS} statt. Parallel dazu müssen die Daten im Cache invalidiert (schlecht) oder ebenfalls geschrieben werden (gut). + \begin{itemize}[leftmargin=5mm] + \item[$\oplus$] optimale Konsistenz der Daten + \item[$\ominus$] Schreiben nur in \acl{HS}-Geschwindigkeit möglich + \end{itemize} +\end{paracol} + +\begin{tabular}{p{32mm}|p{62mm}|p{62mm}} + \textbf{Cachearchitektur} \newline \newline \textbf{Schreibstrategie} + & \textbf{Write-Bac}k + & \textbf{Write-Through} \\ + \midrule + + \textbf{Look-Through} + & $\oplus$ gute klassische Kombination, da die physische Gegebenheit vorhanden sind, um direktes Schreiben in Cache und Rückschreiben vom Cache in \acs{HS} zu ermöglichen + & $\ominus$ Kombination nicht möglich, da kein direkter Zugriff der \acs{CPU} auf \acs{HS} physisch gegeben ist. + \\ \midrule + + \textbf{Look-Aside} + & $\ominus$ schlechte Kombination, da bei jedem Schreibzugriff der Bus zweimal belastet wird + & $\oplus$ gute klassische Kombination, da Schreibzugriffe parallel im \acs{HS} und Cache physisch gut machbar +\end{tabular} + +\subsection{Cache-Aufbau} + +\begin{figure}[ht] + \centering + \includegraphics[width=\textwidth]{./Bilder/Cache_Aufbau.png} + \caption{Aufbau des Caches} + \label{fig:cache_aufbau} +\end{figure} + +\begin{description} + \item[\acf{HSS}] gleich große Speicheranteile des Hauptspeichers. Eine \acs{HSS} sollte $2^m$ \acs{HSA} beinhalten, um eine einfache Umrechung von \acs{HSS}-Nummern und \acs{HSA} zu ermöglichen. + \item[\acf{CL}] Kopie einer \acl{HSS} im Cache + \item[Tag] Die um $m$ niederwertigsten Bit gekürzte \acs{HSA}, welche der \acs{HSS}-Nummer entspricht. + \item[Status] Zustandsinfo zur Cache-Line, \zB Valid-Flag und weiter Zustandsinfos abhängig von Verdrängungsstrategie + \item[Valid-Flag] Die Daten werden im Cache geändert und müssen noch in den \acs{HS} zurückgeschrieben werden (nur bei Write-Back-Schreibstrategie) +\end{description} + +\subsection{vollassoziativer Cache} +Jede \acl{HSS} kann in jeder \acl{CL} eingelagert werden (nicht gleichzeitig!) +\begin{itemize}[noitemsep] + \item[$\Rightarrow$] bei jedem Zugriff auf eine \acf{HSA} muss überprüft werden, ob die gekürzte \acs{HSA} einem der Tags von validen \acl{CL} entspricht! + \item[$\Rightarrow$] Vergleichen der gekkürzten \acs{HSA} mit allen Tags (von validen \acs{CL}) +\end{itemize} + +Wie kann verglichen werden? Welche Möglichkeiten des Vergleichs gibt es? + +\begin{itemize}[noitemsep] + \item sequentiell $\Rightarrow$ Nachteil: erhöhte Zugriffszeit + \item Parallel $\Rightarrow$ gleichzeitiges Vergleichen der angelegten (gekürzten) \acs{HSA} mit allen Tags über jeweils einen eigenen Komparator in jeder \acs{CL}. \newline + Nachteil: \acl{HW}-Aufwand für Komparator in jeder \acs{CL}. +\end{itemize} + + +\textsf{\textbf{Einschub: Schaltungssynthese Komparator}} \newline +Hier: Schaltnetz, welches zwei Zahlen auf Gleichheit, Größer und Kleiner vergleicht. + +\begin{figure}[!ht] + \centering + \includegraphics[width=6cm]{./Bilder/Cache_Komparator_1.png} + \caption{$n$-Bit-Komparator} + \label{fig:cache_komparator_1} +\end{figure} + +Möchte man eine Wertetabelle für einen $n$-Bit-Komparator erstellen, sieht man, dass zu viele Zeilen in der Wertetabelle ($2^{2n}$\ldots) sind $\Rightarrow$ besser mit kaskadierbaren 1-Bit-Komparatoren + +\textsf{\textbf{Komparator für Gleichheit}} \newline +\textit{Hinweis}: im Cache reicht der Vergleich auf Gleichheit. \autoref{fig:cache_komparator_3} zeigt 1-Bit-Komparatoren für einen Gleichheits-Komparator. +\begin{figure}[!ht] + \centering + \includegraphics[width=9cm]{./Bilder/Aufwand_Komparator.png} + \caption{Aufbau des Gleichheits-Komparators im Cache} + \label{fig:cache_komparator_3} +\end{figure} + +\subsubsection{Komparator} + +\begin{figure}[!h] + \centering + \includegraphics[width=\textwidth]{./Bilder/Cache_Komparator.png} + \caption{Aufbau des $n$-Bit-Komparator aus kaskadierbaren 1-Bit-Komparatoren} + \label{fig:cache_komparator_2} +\end{figure} + +Aus \autoref{fig:cache_komparator_2} ergibt sich folgende Tabelle: +\begin{center} + \ttfamily + \begin{tabular}{ccccc|ccc} + $b_n$ & $a_n$ & $a>b_{in}$ & $a=b_{in}$ & $ab_{out}$ & $a=b_{out}$ & $aWl)_>)2qpOY_w=8urj9;)(ib>$OQq^KU;rGP>47tlnCa)HkPMBkF!TV>&GyN_^@O~(Y>2_M z3z;Q$9RoC6^fzc(Z?m#-ul0Bo+%FC%WNdkzP2G>gA*|$~U7JflsS#V|eb+5AsshKH 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