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exo1_raffaele_ancarola.tex
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exo1_raffaele_ancarola.tex

\documentclass{article}
% Change "article" to "report" to get rid of page number on title page
\usepackage{amsmath,amsfonts,amsthm,amssymb}
\usepackage{setspace}
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{extramarks}
\usepackage{chngpage}
\usepackage{soul}
\usepackage[usenames,dvipsnames]{color}
\usepackage{graphicx,float,wrapfig}
\usepackage{ifthen}
\usepackage{listings}
\usepackage{courier}
\usepackage{makecell}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{wrapfig}
\usepackage{multicol}
\usepackage{float}
\usepackage{verbatim}
\usepackage[T1]{fontenc}
\usepackage{comment}
\usepackage{systeme}
\usepackage[table,xcdraw]{xcolor}
\usepackage{array}
\usepackage{physics}
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
%
% Here put your info (name, due date, title etc).
% the rest should be left unchanged.
%
%
%
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
% Homework Specific Information
\newcommand{\hmwkTitle}{Exercise 1}
\newcommand{\hmwkSubTitle}{}
\newcommand{\hmwkDueDate}{\today}
\newcommand{\hmwkClass}{Introduction to multiprocessor architecture}
\newcommand{\hmwkClassTime}{}
%\newcommand{\hmwkClassInstructor}{Prof. Oleg Yazyev}
\newcommand{\hmwkAuthorName}{Raffaele Ancarola}
%
%
% In case you need to adjust margins:
\topmargin=-0.45in %
\evensidemargin=0in %
\oddsidemargin=0in %
\textwidth=6.5in %
\textheight=9.5in %
\headsep=0.25in %
% This is the color used for comments below
\definecolor{MyDarkGreen}{rgb}{0.0,0.4,0.0}
% units of mesure
\usepackage{siunitx}
% comments
\usepackage{comment}
% pgfplots environment
%package setup for graphs
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usetikzlibrary{patterns}
\usepgfplotslibrary{external}
\pgfplotsset{compat=newest}
%pgfplot setup
\makeatletter
\pgfplotsset{
/pgfplots/flexible xticklabels from table/.code n args={3}{%
\pgfplotstableread[#3]{#1}\coordinate@table
\pgfplotstablegetcolumn{#2}\of{\coordinate@table}\to\pgfplots@xticklabels
\let\pgfplots@xticklabel=\pgfplots@user@ticklabel@list@x
},
% layer definition
layers/my layer set/.define layer set={
background,
main,
foreground
}{
% you could state styles here which should be moved to
% corresponding layers, but that is not necessary here.
% That is why we don't state anything here
},
% activate the newly created layer set
set layers=my layer set
}
\makeatother
\IfFileExists{./tikzext.perm}{\tikzexternalize[prefix=tikzext/]}{\tikzexternalize}
% pfgplots add graphics
\makeatletter
\newcommand\addplotgraphicsnatural[2][]{%
\begingroup
% set options in this local group (will be lost afterwards):
\pgfqkeys{/pgfplots/plot graphics}{#1}%
% measure the natural size of the graphics:
\setbox0=\hbox{\includegraphics{#2}}%
%
% compute the required unit vector ratio:
\pgfmathparse{\wd0/(\pgfkeysvalueof{/pgfplots/plot graphics/xmax} - \pgfkeysvalueof{/pgfplots/plot graphics/xmin})}%
\let\xunit=\pgfmathresult
\pgfmathparse{\ht0/(\pgfkeysvalueof{/pgfplots/plot graphics/ymax} - \pgfkeysvalueof{/pgfplots/plot graphics/ymin})}%
\let\yunit=\pgfmathresult
%
% configure pgfplots to use it.
% The \xdef expands all macros except those prefixed by '\noexpand'
% and assigns the result to a global macro named '\marshal'.
\xdef\marshal{%
\noexpand\pgfplotsset{unit vector ratio={\xunit\space \yunit}}%
}%
\endgroup
%
% use our macro here:
\marshal
%
\addplot graphics[#1] {#2};
}
\makeatother
% For faster processing, load Matlab syntax for listings
\lstloadlanguages{Matlab}%
\lstset{language=Matlab, % Use MATLAB
frame=single, % Single frame around code
basicstyle=\small\ttfamily, % Use small true type font
keywordstyle=[1]\color{Blue}\bf, % MATLAB functions bold and blue
keywordstyle=[2]\color{Purple}, % MATLAB function arguments purple
keywordstyle=[3]\color{Blue}\underbar, % User functions underlined and blue
identifierstyle=, % Nothing special about identifiers
% Comments small dark green courier
commentstyle=\usefont{T1}{pcr}{m}{sl}\color{MyDarkGreen}\small,
stringstyle=\color{Purple}, % Strings are purple
showstringspaces=false, % Don't put marks in string spaces
tabsize=3, % 5 spaces per tab
breaklines=True,
%
%%% Put standard MATLAB functions not included in the default
%%% language here
morekeywords={xlim,ylim,var,alpha,factorial,poissrnd,normpdf,normcdf},
%
%%% Put MATLAB function parameters here
morekeywords=[2]{on, off, interp},
%
%%% Put user defined functions here
morekeywords=[3]{FindESS, homework_example},
%
morecomment=[l][\color{Blue}]{...}, % Line continuation (...) like blue comment
numbers=left, % Line numbers on left
firstnumber=1, % Line numbers start with line 1
numberstyle=\tiny\color{Blue}, % Line numbers are blue
stepnumber=1 % Line numbers go in steps of 5
}
% Setup the header and footer
\pagestyle{fancy} %
\lhead{\hmwkAuthorName} %
%\chead{\hmwkClass\ (\hmwkClassInstructor\ \hmwkClassTime): \hmwkTitle} %
\rhead{\hmwkClass\ : \hmwkTitle} %
%\rhead{\firstxmark} %
\lfoot{\lastxmark} %
\cfoot{} %
\rfoot{Page\ \thepage\ of\ \protect\pageref{LastPage}} %
\renewcommand\headrulewidth{0.4pt} %
\renewcommand\footrulewidth{0.4pt} %
% This is used to trace down (pin point) problems
% in latexing a document:
%\tracingall
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Some tools
\newcommand{\enterProblemHeader}[1]{\nobreak\extramarks{#1}{#1 continued on next page\ldots}\nobreak%
\nobreak\extramarks{#1 (continued)}{#1 continued on next page\ldots}\nobreak}%
\newcommand{\exitProblemHeader}[1]{\nobreak\extramarks{#1 (continued)}{#1 continued on next page\ldots}\nobreak%
\nobreak\extramarks{#1}{}\nobreak}%
\newlength{\labelLength}
\newcommand{\labelAnswer}[2]
{\settowidth{\labelLength}{#1}%
\addtolength{\labelLength}{0.25in}%
\changetext{}{-\labelLength}{}{}{}%
\noindent\fbox{\begin{minipage}[c]{\columnwidth}#2\end{minipage}}%
\marginpar{\fbox{#1}}%
% We put the blank space above in order to make sure this
% \marginpar gets correctly placed.
\changetext{}{+\labelLength}{}{}{}}%
\setcounter{secnumdepth}{0}
\newcommand{\homeworkProblemName}{}%
\newcounter{homeworkProblemCounter}%
\newenvironment{homeworkProblem}[1][Problem \arabic{homeworkProblemCounter}]%
{\stepcounter{homeworkProblemCounter}%
\renewcommand{\homeworkProblemName}{#1}%
\section{\homeworkProblemName}%
\enterProblemHeader{\homeworkProblemName}}%
{\exitProblemHeader{\homeworkProblemName}}%
\newcommand{\problemAnswer}[1]
{\noindent\fbox{\begin{minipage}[c]{\columnwidth}#1\end{minipage}}}%
\newcommand{\problemLAnswer}[1]
{\labelAnswer{\homeworkProblemName}{#1}}
\newcommand{\homeworkSectionName}{}%
\newlength{\homeworkSectionLabelLength}{}%
\newenvironment{homeworkSection}[1]%
{% We put this space here to make sure we're not connected to the above.
% Otherwise the changetext can do funny things to the other margin
\renewcommand{\homeworkSectionName}{#1}%
\settowidth{\homeworkSectionLabelLength}{\homeworkSectionName}%
\addtolength{\homeworkSectionLabelLength}{0.25in}%
\changetext{}{-\homeworkSectionLabelLength}{}{}{}%
\subsection{\homeworkSectionName}%
\enterProblemHeader{\homeworkProblemName\ [\homeworkSectionName]}}%
{\enterProblemHeader{\homeworkProblemName}%
% We put the blank space above in order to make sure this margin
% change doesn't happen too soon (otherwise \sectionAnswer's can
% get ugly about their \marginpar placement.
\changetext{}{+\homeworkSectionLabelLength}{}{}{}}%
\newcommand{\sectionAnswer}[1]
{% We put this space here to make sure we're disconnected from the previous
% passage
\noindent\fbox{\begin{minipage}[c]{\columnwidth}#1\end{minipage}}%
\enterProblemHeader{\homeworkProblemName}\exitProblemHeader{\homeworkProblemName}%
\marginpar{\fbox{\homeworkSectionName}}%
% We put the blank space above in order to make sure this
% \marginpar gets correctly placed.
}%
%%% I think \captionwidth (commented out below) can go away
%%%
%% Edits the caption width
%\newcommand{\captionwidth}[1]{%
% \dimen0=\columnwidth \advance\dimen0 by-#1\relax
% \divide\dimen0 by2
% \advance\leftskip by\dimen0
% \advance\rightskip by\dimen0
%}
% Includes a figure
% The first parameter is the label, which is also the name of the figure
% with or without the extension (e.g., .eps, .fig, .png, .gif, etc.)
% IF NO EXTENSION IS GIVEN, LaTeX will look for the most appropriate one.
% This means that if a DVI (or PS) is being produced, it will look for
% an eps. If a PDF is being produced, it will look for nearly anything
% else (gif, jpg, png, et cetera). Because of this, when I generate figures
% I typically generate an eps and a png to allow me the most flexibility
% when rendering my document.
% The second parameter is the width of the figure normalized to column width
% (e.g. 0.5 for half a column, 0.75 for 75% of the column)
% The third parameter is the caption.
\newcommand{\scalefig}[3]{
\begin{figure}[ht!]
% Requires \usepackage{graphicx}
\centering
\includegraphics[width=#2\columnwidth]{#1}
%%% I think \captionwidth (see above) can go away as long as
%%% \centering is above
%\captionwidth{#2\columnwidth}%
\caption{#3}
\label{#1}
\end{figure}}
% Includes a MATLAB script.
% The first parameter is the label, which also is the name of the script
% without the .m.
% The second parameter is the optional caption.
\newcommand{\matlabscript}[2]
{\begin{itemize}\item[]\lstinputlisting[caption=#2,label=#1]{#1.m}\end{itemize}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Make title
%\title{\vspace{2in}\textmd{\textbf{\hmwkClass:\ \hmwkTitle\ifthenelse{\equal{\hmwkSubTitle}{}}{}{\\\hmwkSubTitle}}}\\\normalsize\vspace{0.1in}\small{Due\ on\ \hmwkDueDate}\\\vspace{0.1in}\large{\textit{\hmwkClassInstructor\ \hmwkClassTime}}\vspace{3in}}
\title{\vspace{2in}\textmd{\textbf{\hmwkClass:\ \hmwkTitle\ifthenelse{\equal{\hmwkSubTitle}{}}{}{\\\hmwkSubTitle}}}\\\normalsize\vspace{0.1in}\small{Due\ on\ \hmwkDueDate}\\\vspace{0.1in}\large{\textit{ \hmwkClassTime}}\vspace{3in}}
\date{}
\author{\textbf{\hmwkAuthorName}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
%\begin{spacing}{1.1}
\maketitle
% Uncomment the \tableofcontents and \newpage lines to get a Contents page
% Uncomment the \setcounter line as well if you do NOT want subsections
% listed in Contents
%\setcounter{tocdepth}{1}
%\newpage
%\tableofcontents
%\newpage
% When problems are long, it may be desirable to put a \newpage or a
% \clearpage before each homeworkProblem environment
%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{homeworkProblem}
\begin{homeworkSection}{(1)}
The boost of performance verified on the single-core processors is mainly due to
the exponential increasing of the number of transistors.
Precisely from the 90's, every two years the transistors number was doubling.
This allowed surely to increase the capacity of the chips, but without significantly improving the
performance. Required voltages also went down, giving more range for a clock frequency increase.
Such a possibility allowed to increase the clock risulting in faster CPU's and maintaining approximatively the same cost in energy.
That's here that a first idea of parallelism comes out: better distributing the consumed power over
multiple cores would have reduced the costs in energy because multiple units would have processed less
instructions at once and compared to the enormous gain of efficiency, the addictional cost in energy due to the alimentation
of all the cores was much smaller than the one got by alimenting a super-fast unit (but not fast enough to reach the multicore efficiency).
\end{homeworkSection}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{homeworkSection}{(2)}
ILP is defined as the simultaneous execution of multiple instructions during a program
belonging to the same task.
TLP is the technique of distributing tasks across different processor units. A task is generally a portion of code that can
be executed by a process or a thread.
The two differs mainly on the management of the execution: while ILP takes an input and process it
into different subsets of instructions synchronously, TLP assigns the execution to different threads.
Notice that TLP, instead of ILP, can apply
parallelism with differents clocks then the execution of a task is
asynchronous.
There are two basic approaches of ILP and TLP:
\begin{itemize}
\item Dynamic: let the hardware manage the parallelism over the executed instructions.
\item Static: involve software control over the executed instructions.
\end{itemize}
These two approaches are complementar and can be combined in order to obtain better performance.
A consequence of parallelism over instructions (then mainly ILP) are the three arising dependences: data dependency, name dependency and control dependency
marked as Ddep, Ndep and Cdep respectively in the following statements.
Let "i" and "j" be single instructions, then
\paragraph{Ddep}
"i" Ddep "j" if "i" produces a result that may be used by "j" and,
if "k" is another instruction, "j" Ddep "k" Ddep "i".
\paragraph{Ndep}
"i" Ndep "j" if "i" is antidependent or outputdependent on "j".
Generally, "i" is antidependent on "j" if "j" aptempts to write a memory location that "i" is reading.
On the other hand, "i" and "j" are outputdependent if both write on the same register.
In that case the depence can be avoided by thinking of a program structure which doesn't embed it.
The risk of this dependence is a "data hazard", or rather a violation of the program order, meaning that some registers
can be read and written at the same time from "i" and "j". The only case where there's no hazard is a simultaneous reading
of the same register.
\paragraph{Cdep}
Control dependence is explained imagining a tree of instructions representing its execution flow
and the instructions parallelism divergence in branches.
"i" Cdep "j" if there exists a branch ("j" -> "l") such that "i" post-dominate "l" and, if "i" doesn't post-dominate "j"
when "i" is different than "j".
"i" is said to post-dominate "j" if "i" appears on every path of the tree from "j" to the end of the execution.
\end{homeworkSection}
\begin{homeworkSection}{(3)}
NUMA is a specific build philosophy constructed for a system of multiple processing units.
In NUMA, individual processors work in parallel, sharing local memory in order to improve performance.
The main reason to prefer such a configuration is the gain in efficiency given by the reduction of the distance (in terms of units)
that a digital signal has to cover in order to pass from a memory to a process. This is achieved by placing intermediate shared memories
and avoid a lot of worthless uses of the bus. For example, when connected to a shared storage cache, a symmetric multiprocessing system can be implemented.
Sharing memory is also useful to avoid the need of storing duplicates values when more units want to read the same data.
\end{homeworkSection}
\end{homeworkProblem}
%\end{spacing}
\end{document}

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