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preamble.tex
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preamble.tex
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\documentclass[article, onecolumn]{IEEEtran}
\usepackage{cite}
\ifCLASSINFOpdf
\usepackage[pdftex]{graphicx}
\graphicspath{{./tikz_figures/}}
\DeclareGraphicsExtensions{.pdf,.jpeg,.png, .jpg, .PNG}
\else
\fi
\usepackage{amsmath,bm}
\interdisplaylinepenalty=2500
\ifCLASSOPTIONcompsoc
\usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
\else
\usepackage[caption=false,font=footnotesize]{subfig}
\fi
\usepackage{url}
\usepackage{amsfonts} % for \mathbb{}
\usepackage{listings} % For writing math in verbatim
\usepackage{enumerate}
\usepackage[showlabels,sections,floats,textmath,displaymath]{preview}
\usepackage{amssymb} %% For showing special symbols like \bigstar
\usepackage{pifont} %% For showing circled numbers
\usepackage{array}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{ifthen}
\usepackage{dirtree}
\setlength{\DTbaselineskip}{13pt}
\renewcommand*\DTstyle{}
\DTsetlength{.2em}{1em}{.2em}{.4pt}{2pt}
\newcommand{\mathnew}{\mathit}
% for nice reference
\newcommand{\fsp}{{\;}}
\newcommand{\Fig}{\figurename \fsp}
\newcommand{\Sec}{Sec.\fsp}
\newcommand{\Eq}{Eq.\fsp}
\newcommand{\Tab}{Tab.\fsp}
\newcommand{\Alg}{Alg.\fsp}
\newcommand{\etal}{\textit{et al}. }
\newcommand{\ie}{\textit{i}.\textit{e}. }
\newcommand{\eg}{\textit{e}.\textit{g}. }
\newcommand{\Prop}{Property }
\DeclareMathOperator*{\argminB}{argmin}
\hyphenation{temperature} % correct bad hyphenation here
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{intersections}
\usetikzlibrary{calc, quotes}
\usetikzlibrary{external}
\tikzexternalize[prefix=tikz_figures/]%
\pgfdeclarelayer{bg} % declare background layer
\pgfsetlayers{bg,main} % set the order of the layers (main is the standard layer)
\usetikzlibrary{patterns, patterns.meta}
\usetikzlibrary{decorations.pathreplacing,calligraphy}
\renewcommand\thesection{\arabic{section}}
\renewcommand\thesubsectiondis{\textbf{\thesection.\arabic{subsection}}} %% This is to change the looking of subsection heading number
\renewcommand\thesubsection{\thesection.\arabic{subsection}} %% This is to change the numbering by \ref{}
\renewcommand\thesubsubsectiondis{\ding{42}\;\thesection.\arabic{subsection}.\arabic{subsubsection}}
\setcounter{tocdepth}{1} % Show sections
%\setcounter{tocdepth}{2} % + subsections
%\setcounter{tocdepth}{3} % + subsubsections
%\setcounter{tocdepth}{4} % + paragraphs
%\setcounter{tocdepth}{5} % + subparagraphs
%% The following commands are used to reduce the space before and after formula
%% in align and equation environments
%\setlength{\abovedisplayskip}{1pt}
%\setlength{\belowdisplayskip}{0pt}
%\setlength{\abovedisplayshortskip}{0pt}
%\setlength{\belowdisplayshortskip}{0pt}
%%
%% The following definition is a remedy of the fact that
%% IEEEtrans class does not define subparagraph.
%% Check this post for details
%% https://tex.stackexchange.com/a/8362/172530
\newcommand{\subparagraph}{}
\usepackage{titlesec} % for controlling vertical space around section headers
\titlespacing\section{0pt}{8pt plus 2pt minus 2pt}{4pt plus 2pt minus 2pt}
\titlespacing\subsection{0pt}{6pt plus 2pt minus 2pt}{2pt plus 2pt minus 2pt}
\titlespacing\subsubsection{0pt}{4pt plus 2pt minus 2pt}{2pt plus 1pt minus 1pt}
\titleformat{\subsection}
{\normalfont\bfseries}
{\thesubsection}{1em}{}
%%
%% Check this post for how to write properly-sized ceiling operator
%% https://tex.stackexchange.com/a/367035/172530
%%
\usepackage{mathtools}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
%% For text color
\usepackage{xcolor}
%% For drawing boxes around text
%% https://tex.stackexchange.com/a/234195/172530
\newcommand\textbox[2]{%
\tikz[baseline]\node[%
inner ysep=0pt,
inner xsep=2pt,
anchor=text,
rectangle,
rounded corners=1mm,
#1] {\strut#2};%
}
%% package for highlighting text
%% Usage: \hl{text to be highlighted}
\usepackage{soul}
\sethlcolor{yellow}
%% underlining for emphasis
%% Examples:
%% \uline{important} underline
%% \uuline{urgent} double-underline
%% \uwave{boat} wavy underline like
%% \sout{wrong} line struck through word
%% \xout{removed} removed
%% \dashuline{dashing} dashed
%% \dotuline{dotty} dotted
\usepackage[normalem]{ulem}
%% define a red check mark
\newcommand\redcheck{
{\textcolor{red}{\ding{52}}}
}
\usepackage{dblfloatfix} % To enable figures at the bottom of page
\usepackage{wrapfig}
\usepackage{siunitx}
% Overlay question mark on equal mark
\def\qeq{\mathrel{%
\mathchoice{\QEQ}{\QEQ}{\scriptsize\QEQ}{\tiny\QEQ}%
}}
\def\QEQ{{%
\setbox0\hbox{=}%
\rlap{\hbox to \wd0{\hss?\hss}}\box0
}}
%% Package for theorem-like blocks
\usepackage{amsthm}
\renewcommand\qedsymbol{$\blacksquare$}
\newtheorem{prop}{Property}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Tikz figure commands
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\defs}[1]{
%% #1: gap
\def\latalu{6}
\def\latmem{24}
\def\unit{.1}
\def\h{.2}
\def\scale{.7}
\def\alpha{6}
\def\numwarps{6}
\def\gap{#1}
\pgfmathsetmacro\latwarp{\alpha*\latalu*\unit+\latmem*\unit+\alpha*\gap*\unit-\gap*\unit}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap+\numwarps-1}
}
\newcommand{\cycles}[2]{
%% #1: height of the line
%% #2: number of cycles
\foreach \i in {0,...,#2}
{
\draw [ultra thin, red] ($(TL)+(\i*.1, 0)$) -- ++(0, -#1);
}
}
\newcommand{\mylabel}[4]{
%% #1 width of the label
%% #2 text for the label
%% #3 scale
%% #4 below of above
%% The left is defined as the coordinate before calling this command
\coordinate (right) at ($(left)+(#1, 0)$);
\node [scale=#3, #4, inner xsep=0] (label) at ($(left)!.5!(right)$) {#2};
\draw [ultra thin] (left) |- (label.west);
\draw [ultra thin] (right) |- (label.east);
}
\newcommand{\latlabel}[1]{
%% #1: scale of the text
%% (left) should be defined as the topleft of the warp
\mylabel{\latalu*\unit}{$\text{lat}_\text{alu}$}{\scale}{above};
\coordinate (left) at ($(left)+(\alpha*\latalu*\unit+\alpha*\gap*\unit-\gap*\unit, 0)$);
\mylabel{\latmem*\unit}{$\text{lat}_\text{mem}$}{\scale}{above};
}
\newcommand{\coord}[3]{
%% origin is defined as a coordinate
%% #1: x length
%% #2: y length
%% #3: scale
\draw [fill=black] (origin) circle (2pt);
\draw [thick, ->, >=stealth, name path=x] (origin) -- ++(#1, 0)
node [scale=#3, right] {$n$};
\draw [thick, ->, >=stealth, name path=y] (origin) -- ++(0, #2)
node [scale=#3, above] {$\text{thr}_\text{warp}$};
}
\newcommand{\maxthralu}[4]{
%% #1: \alpha, i.e. number of alu insts per warp
%% #2: number of warps
%% #3: starting index of the first warp in this group
%% #4: gap between consecutive alu insts
%% (TL) should already be defined
\pgfmathsetmacro\alp{int(#1-1)}
\pgfmathsetmacro\warps{int(#2-1)}
\foreach \w in {0,...,\warps} {
\pgfmathsetmacro\z{int(#3+\w)}
\node [left, scale=.9*\scale] at ($(TL)+(\w*\unit,-\w*\h-.5*\h)$) {w\z};
\foreach \i in {0,...,\alp} {
\draw [thick] ($(TL)+(\i*#4*\unit+\i*\latalu*\unit+\w*\unit, -\w*\h)$)
rectangle ++(\latalu*\unit, -\h);
}
}
}
\newcommand{\maxthrmem}[1]{
%% #1: number of warps
%% (memTL) should already be defined
\pgfmathsetmacro\warps{int(#1-1)}
\foreach \w in {0,...,\warps} {
\draw [thick, blue] ($(memTL)+(\w*\unit, -\w*\h)$)
rectangle ++(\latmem*\unit, -\h);
}
}
\newcommand{\drawwarp}[4]{
%% parameters same as \maxthralu
%% #1: \alpha, i.e. number of alu insts per warp
%% #2: number of warps
%% #3: starting index of the first warp in this group
%% #4: gap between consecutive alu insts
%% (TL) should already be defined
\maxthralu{#1}{#2}{#3}{#4};
\coordinate (memTL) at ($(TL)+(#1*\latalu*\unit+#1*#4*\unit-#4*\unit, 0)$);
\maxthrmem{#2};
}
\newcommand{\myPerfModel}[1]{
%% #1 scale
% \draw [help lines] (-4,3) grid (4, -3);
% \draw (0,0) circle (2pt);
\def\scale{#1}
%% Draw latency mode
\coordinate (origin) at (-3,0);
\coord{5}{3}{\scale};
\coordinate (P) at ($(origin)+(1.5,1.5)$);
\draw [ultra thick] (origin)
--node [midway, above, sloped, align=center, scale=.8*\scale] {latency mode} (P);
\draw [ultra thin, densely dashed] (P) -- (P |- origin)
node [below, scale=\scale] {$n_\text{lat}$};
\draw [ultra thin, densely dashed] (P) -- (P -| origin)
node [left, scale=\scale] {$\text{thr}_\text{lat}$};
%% Draw gradual saturate effect
\coordinate (Q) at ($(P)+(1,.5)$);
\draw [ultra thick] (P) to[out=40, in=185]
node [scale=.7*\scale, midway, align=center, below, yshift=-1ex, xshift=1.5ex]
{gradual\\saturate\\effect} (Q);
\draw [ultra thin, densely dashed] (Q) -- (Q |- origin)
node [below, scale=\scale] {$n_\text{thr}$};
\draw [ultra thin, densely dashed] (Q) -- (Q -| origin)
node [left, scale=\scale] {$\text{maxThr}_\text{warp}$};
%% Draw throughput mode
\draw [ultra thick] (Q) --node [midway, above, sloped, align=center, scale=.8*\scale]
{Throughput mode} ++(2, 0);
}
\newcommand{\volkovPerfModel}[1]{
%% #1 scale
% \draw [help lines] (-4,3) grid (4, -3);
% \draw (0,0) circle (2pt);
\def\scale{#1}
%% Draw latency mode
\coordinate (origin) at (-3,0);
\coord{5}{3}{\scale};
\coordinate (P) at ($(origin)+(2,2)$);
\draw [ultra thick] (origin)
--node [midway, above, sloped, align=center, scale=.9*\scale] {latency mode} (P);
\draw [ultra thin, densely dashed] (P) -- (P |- origin)
node [below, scale=\scale] {$n_\text{tran}$};
\draw [ultra thin, densely dashed] (P) -- (P -| origin)
node [left, scale=\scale] {$\text{maxThr}_\text{warp}$};
%% Draw gradual saturate effect
% \coordinate (Q) at ($(P)+(1,.5)$);
% \draw [ultra thick] (P) to[out=40, in=185]
% node [scale=.7*\scale, midway, align=center, below, yshift=-1ex, xshift=1.5ex]
% {gradual\\saturate\\effect} (Q);
% \draw [ultra thin, densely dashed] (Q) -- (Q |- origin)
% node [below, scale=\scale] {$n_\text{thr}$};
% \draw [ultra thin, densely dashed] (Q) -- (Q -| origin)
% node [left, scale=\scale] {$\text{maxThr}_\text{warp}$};
%% Draw throughput mode
\draw [ultra thick] (P) --node [midway, above, sloped, align=center, scale=.9*\scale]
{Throughput mode} ++(2.5, 0);
}
\newcommand{\demoLittle}{
\draw [help lines] (-4,3) grid (4, -3);
\draw (0,0) circle (2pt);
\defs{0}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap}
\pgfmathsetmacro\cycleh{\numwarps*\h}
\coordinate (TL) at (-4, 3);
\coordinate (origin) at (TL);
\cycles{\cycleh}{\span}
\coordinate (warp0TL) at (TL);
\drawwarp{\alpha}{1}{0}{\gap};
%% Draw label
\coordinate (left) at (TL);
\latlabel{\scale}
%% 1-5 warps
\foreach \row in {1,...,5}
{
%% Every line draws two warps
%% right: (TL) = ($(TL)+(5*\unit, -\h*\row)$)
%% left: (TL) = ($(TL)$+(-\latwarp, 0))
%% Right warp
\pgfmathsetmacro\lidx{int(2*\row-1)}
\pgfmathsetmacro\ridx{int(2*\row)}
\coordinate (TL) at ($(TL)+(5*\unit,-\h)$);
\coordinate (oldTL) at (TL);
\drawwarp{\alpha}{1}{\ridx}{\gap};
%% Left warp
\coordinate (TL) at ($(TL)+(-\latwarp, 0)$);
\drawwarp{\alpha}{1}{\lidx}{\gap};
\coordinate (TL) at (oldTL);
}
%% Draw period Dealt T
\coordinate (left) at ($(origin)+(0,-\numwarps*\h)$);
\mylabel{\latwarp}{$\Delta T$}{\scale}{below};
\coordinate (left) at ($(origin)+(3*\latalu*\unit+5*\unit,0)$);
\mylabel{2*\latalu*\unit}{$\Delta T'$}{\scale}{above};
}
\newcommand{\labelCycle}[1]{
%% #1: cycle number
%% (TL) should be defined
%% \numwarps should be defined
\coordinate (p) at ($(TL)+(#1*\unit, -\numwarps*\h)$);
\node [scale=\scale, below left, inner sep=0] (pNode) at ($(p)+(-.2,-.2)$) {cycle #1};
\draw [->, >=stealth] (pNode.north east) -- (p)
}
\newcommand{\labelCycleRight}[1]{
%% #1: cycle number
%% (TL) should be defined
%% \numwarps should be defined
\coordinate (p) at ($(TL)+(#1*\unit, -\numwarps*\h)$);
\node [scale=\scale, below right, inner sep=0] (pNode) at ($(p)+(.2,-.2)$) {cycle #1};
\draw [->, >=stealth] (pNode.north west) -- (p)
}
\newcommand{\labelCycleAbove}[1]{
%% #1: cycle number
%% (TL) should be defined
%% \numwarps should be defined
\coordinate (p) at ($(TL)+(#1*\unit, 0)$);
\node [scale=\scale, above left, inner sep=0, align=center] (pNode) at ($(p)+(-.2,.2)$) {cycle #1};
\draw [->, >=stealth] (pNode.south east) -- (p)
}
\newcommand{\labelCycleAboveRight}[1]{
%% #1: cycle number
%% (TL) should be defined
%% \numwarps should be defined
\coordinate (p) at ($(TL)+(#1*\unit, 0)$);
\node [scale=\scale, above right, inner sep=0, align=center] (pNode) at ($(p)+(.2,.2)$) {cycle #1};
\draw [->, >=stealth] (pNode.south west) -- (p)
}
\newcommand{\demoGap}{
%% #1: scale
\defs{0}
\def\scale{.7}
\coordinate (TL) at (-4, 3);
\coordinate (origin) at (TL);
\cycles{1.2}{\span}
\def\gap{0}
\drawwarp{\alpha}{\numwarps}{0}{\gap};
%% Draw label
\coordinate (left) at (origin);
\latlabel{\scale}
%% Draw arrows
\def\arrowl{3*\latalu*\unit}
\coordinate (ArrowL) at ($(origin)+(\latwarp+\numwarps*\unit+.4, -\numwarps/2*\h)$);
\draw [->, >=stealth, thick] (ArrowL) --
node[above, midway,scale=\scale] {Add 1 warp} ++(\arrowl,0);
\coordinate (TL) at ($(origin)+(\latwarp+\numwarps*\unit+.4+\arrowl+.4,0)$);
\def\gap{1}
\def\numwarps{7}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap+\numwarps-1}
\cycles{1.4}{\span}
\drawwarp{\alpha}{7}{0}{\gap};
%% Draw label
\coordinate (left) at (TL);
\latlabel{\scale}
%% Draw label for gap
\node [below, scale=\scale] (gapNode) at ($(TL)+(3*\latalu*\unit+8.5*\unit,-7*\h-.2)$)
{gaps};
\coordinate (gap) at ($(TL)+(\latalu*\unit+6.5*\unit,-7*\h)$);
\foreach \g in {0,1,2,3,4} {
\draw [->, >=stealth] (gapNode.north) -| ($(gap)+(\g*\latalu*\unit+\g*\unit,0)$);
}
\labelCycle{6};
%% Draw the victim alu inst
\draw [thick, fill=gray] ($(TL)+(\latalu*\unit+\gap*\unit,0)$) rectangle ++(\latalu*\unit, -\h);
}
\newcommand{\demoSmartSched}{
%% #1: scale
\defs{0}
\def\alpha{4}
\def\latalu{4}
\def\numwarps{4}
\def\latmem{32}
\pgfmathsetmacro\latwarp{\alpha*\latalu*\unit+\latmem*\unit+\alpha*\gap*\unit-\gap*\unit}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap+\numwarps-1}
\pgfmathsetmacro\height{\numwarps*\h}
\def\scale{.7}
%% Draw the old state of the system
\coordinate (TL) at (-4, 3);
\coordinate (origin) at (TL);
\cycles{\height}{\span}
\def\gap{0}
\drawwarp{\alpha}{\numwarps}{0}{\gap};
\coordinate (left) at (TL);
\mylabel{\latwarp}{$\Delta T$}{\scale}{above};
\coordinate (left) at ($(TL)+(0,-\numwarps*\h)$);
\mylabel{.5*\latwarp}{$\Delta T_1$}{\scale}{below};
\coordinate (left) at ($(TL)+(.5*\latwarp,-\numwarps*\h)$);
\mylabel{.5*\latwarp}{$\Delta T_2$}{\scale}{below};
%% Draw arrows
\def\arrowl{5*\latalu*\unit}
\coordinate (ArrowL) at ($(origin)+(\latwarp+\numwarps*\unit+.4, -\numwarps/2*\h)$);
\draw [->, >=stealth, thick] (ArrowL) --
node[above, midway,scale=\scale] {Add more warps} ++(\arrowl,0);
%% Draw the new state of the system
\coordinate (TL) at ($(origin)+(\latwarp+\numwarps*\unit+.4+\arrowl+.4,0)$);
\coordinate (origin) at (TL);
\pgfmathsetmacro\height{\numwarps*\h}
\cycles{\height}{\span}
\drawwarp{\alpha}{\numwarps}{0}{\gap};
\coordinate (TL) at ($(TL)+(\alpha*\latalu*\unit,-\numwarps*\h)$);
\cycles{\height}{\span}
\drawwarp{\alpha}{\numwarps}{4}{\gap};
\coordinate (TL) at ($(TL)+(\alpha*\latalu*\unit,-\numwarps*\h)$);
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap}
\cycles{\h}{\span}
\drawwarp{\alpha}{1}{8}{\gap};
\def\numwarps{9}
\coordinate (left) at ($(origin)+(0, -\numwarps*\h)$);
\mylabel{.5*\latwarp}{$\Delta T_1$}{\scale}{below};
\coordinate (left) at ($(origin)+(\latwarp*.5, -\numwarps*\h)$);
\mylabel{\latwarp*.5}{$\Delta T_2$}{\scale}{below};
%% label some cycles
\def\numwarps{9}
\coordinate (TL) at (origin);
\labelCycleAbove{48};
\labelCycleAbove{16};
\labelCycleAbove{4};
\labelCycleAbove{33};
}
\newcommand{\demoPerfectSched}{
%% #1: scale
\defs{0}
\def\alpha{4}
\def\latalu{4}
\def\numwarps{4}
\def\latmem{35}
\pgfmathsetmacro\latwarp{\alpha*\latalu*\unit+\latmem*\unit+\alpha*\gap*\unit-\gap*\unit}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap+\numwarps-1}
\pgfmathsetmacro\height{\numwarps*\h}
\def\scale{.7}
%% Draw the old state of the system
\coordinate (TL) at (-4, 3);
\coordinate (origin) at (TL);
% \cycles{\height}{\span}
% \def\gap{0}
% \drawwarp{\alpha}{\numwarps}{0}{\gap};
% \coordinate (left) at (TL);
% \mylabel{\latwarp}{$\Delta T$}{\scale}{above};
% \coordinate (left) at ($(TL)+(0,-\numwarps*\h)$);
% \mylabel{.5*\latwarp}{$\Delta T_1$}{\scale}{below};
% \coordinate (left) at ($(TL)+(.5*\latwarp,-\numwarps*\h)$);
% \mylabel{.5*\latwarp}{$\Delta T_2$}{\scale}{below};
% %% Draw arrows
% \def\arrowl{5*\latalu*\unit}
% \coordinate (ArrowL) at ($(origin)+(\latwarp+\numwarps*\unit+.4, -\numwarps/2*\h)$);
% \draw [->, >=stealth, thick] (ArrowL) --
% node[above, midway,scale=\scale] {Add more warps} ++(\arrowl,0);
%% Draw the new state of the system
%\coordinate (TL) at ($(origin)+(\latwarp+\numwarps*\unit+.4+\arrowl+.4,0)$);
%\coordinate (origin) at (TL);
\pgfmathsetmacro\height{\numwarps*\h}
\cycles{\height}{\span}
\drawwarp{\alpha}{\numwarps}{0}{\gap};
\coordinate (TL) at ($(TL)+(\alpha*\latalu*\unit,-\numwarps*\h)$);
\cycles{\height}{\span}
\drawwarp{\alpha}{\numwarps}{4}{\gap};
\coordinate (TL) at ($(TL)+(\alpha*\latalu*\unit,-\numwarps*\h)$);
%\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap}
\cycles{\height}{\span}
\drawwarp{\alpha}{\numwarps}{8}{\gap};
% \def\numwarps{9}
% \coordinate (left) at ($(origin)+(0, -\numwarps*\h)$);
% \mylabel{.5*\latwarp}{$\Delta T_1$}{\scale}{below};
% \coordinate (left) at ($(origin)+(\latwarp*.5, -\numwarps*\h)$);
% \mylabel{\latwarp*.5}{$\Delta T_2$}{\scale}{below};
%% label some cycles
\def\numwarps{12}
\coordinate (TL) at (origin);
\labelCycle{48};
\labelCycleAbove{16};
\labelCycleAbove{4};
\labelCycleRight{51};
}
\newcommand{\demoGapNew}{
%% #1: scale
\defs{0}
\def\scale{.7}
\coordinate (TL) at (-4, 3);
\coordinate (origin) at (TL);
\cycles{1.2}{\span}
%\def\gap{0}
%\drawwarp{\alpha}{\numwarps}{0}{\gap};
\def\gap{24}
\def\numwarps{30}
\pgfmathsetmacro\span{\alpha*\latalu+\latmem+\alpha*\gap-\gap+\numwarps-1}
\cycles{1.4}{\span}
\drawwarp{\alpha}{\numwarps}{0}{\gap};
%% Draw label
%\coordinate (left) at (TL);
%\latlabel{\scale}
%% Draw label for gap
}
\newcommand{\tensor}[4]{
%% (TL): predefined points of the TL corner of the tensor
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
\def\unit{#4}
\def\h{#1}
\def\w{#2}
\def\c{#3}
\pgfmathsetmacro\halfunit{0.5*\unit}
\pgfmathsetmacro\smallunit{0.3*\unit}
% \draw (TL) rectangle ++(\w*\unit, -\h*\unit);
%% horizontal lines
\foreach \i in {0,...,\h}{
\draw ($(TL)+(0,-\i*\unit)$) -- ++(\w*\unit,0);
}
\foreach \i in {1,...,\c}{
\draw ($(TL)+(\i*\halfunit,\i*\smallunit)$) -- ++(\w*\unit,0);
}
%% vertical lines
\foreach \i in {0,...,\w}{
\draw ($(TL)+(\i*\unit,0)$) -- ++(0, -\h*\unit);
}
\foreach \i in {1,...,\c}{
\draw ($(TL)+(\w*\unit+\i*\halfunit,\i*\smallunit)$) -- ++(0, -\h*\unit);
}
%% inclined lines
\foreach \i in {0,...,\w}{
\draw ($(TL)+(\i*\unit,0)$) -- ++(\c*\halfunit, \c*\smallunit);
}
\foreach \i in {1,...,\h}{
\draw ($(TL)+(\w*\unit,-\i*\unit)$) -- ++(\c*\halfunit,\c*\smallunit);
}
%% define some anchor points
\coordinate (backTL) at ($(TL)+(\c*\halfunit, \c*\smallunit)$);
\coordinate (backTR) at ($(TL)+(\c*\halfunit+\w*\unit, \c*\smallunit)$);
}
\newcommand{\fillTopParallelogram}[4]{
%% (BL) predefined point
%% #1: height
%% #2: width
%% #3: shift
%% #4: color
\def\h{#1}
\def\w{#2}
\def\shift{#3}
\def\color{#4}
\draw [fill=\color] (BL) -- ++(\w,0) -- ++(\shift, \h)
-- ++(-\w, 0) -- ++(-\shift, -\h);
}
\newcommand{\fillSideParallelogram}[4]{
%% (BL) predefined point
%% #1: height
%% #2: width
%% #3: shift
%% #4: color
\def\h{#1}
\def\w{#2}
\def\shift{#3}
\def\color{#4}
\draw [fill=\color] (BL) -- ++(\w,\shift) -- ++(0, \h)
-- ++(-\w, -\shift) -- ++(0, -\h);
}
\newcommand{\fillRec}[3]{
%% (TL) predefined point
%% #1: height
%% #2: width
%% #3: color
\def\h{#1}
\def\w{#2}
\def\color{#3}
\draw [fill=\color] (TL) rectangle ++(\w, -\h);
}
\newcommand{\colorTensorFront}[4]{
%% (TL): predefined points of the TL corner of the tensor
%% #1: height
%% #2: width
%% #3: unit
%% #4: color
\def\h{#1}
\def\w{#2}
\def\unit{#3}
\def\basecolor{#4}
\coordinate (orig) at (TL);
\coordinate (colorTensorFrontreturn) at (TL);
%% Color the front pixels
\foreach \row in {1,...,\h}{
\foreach \col in {1,...,\w}{
\coordinate (TL) at ($(orig)+(\col*\unit-\unit, -\row*\unit+\unit)$);
\fillRec{\unit}{\unit}{\basecolor}
}
}
%% restore TL
\coordinate (TL) at (colorTensorFrontreturn);
}
\newcommand{\colorTensorTopAndSide}[6]{
%% (TL): predefined points of the TL corner of the tensor
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: color
%% #6: step in color gradient
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\unit{#4}
\def\basecolor{#5}
\def\colorStep{#6}
\pgfmathsetmacro\halfunit{0.5*\unit}
\pgfmathsetmacro\smallunit{0.3*\unit}
\coordinate (orig) at (TL);
\coordinate (colorTensorTSreturn) at (TL);
%% Color the parallelograms with a gradient of basecolor
\coordinate (orig) at ($(orig)+(-\halfunit, -\smallunit)$);
\foreach \ch [count=\i from 0] in {1,...,\c}{
\pgfmathsetmacro\colorratio{100-\i*\colorStep}
\def\thisCol{\basecolor!\colorratio!white}
\coordinate (orig) at ($(orig)+(\halfunit, \smallunit)$);
\foreach \row in {1,...,\h}{
\coordinate (BL) at ($(orig)+(\w*\unit,-\row*\unit)$);
\fillSideParallelogram{\unit}{\halfunit}{\smallunit}{\thisCol}
}
\foreach \i in {1,...,\w}{
\coordinate (BL) at ($(orig)+(\i*\unit-\unit,0)$);
\fillTopParallelogram{\smallunit}{\unit}{\halfunit}{\thisCol}
}
}
%% restore TL
\coordinate (TL) at (colorTensorTSreturn);
}
\newcommand{\colorTensor}[6]{
%% (TL): predefined points of the TL corner of the tensor
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: color
%% #6: step in color gradient
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\unit{#4}
\def\basecolor{#5}
\def\colorStep{#6}
\coordinate (colorTensorreturn) at (TL);
\colorTensorFront{#1}{#2}{#4}{#5}
\colorTensorTopAndSide{#1}{#2}{#3}{#4}{#5}{#6}
%% restore TL
\coordinate (TL) at (colorTensorreturn);
}
\newcommand{\filterTensor}[5]{
%% (TL): predefined points of the TL corner of the first tensor
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: color step
\def\unit{#4}
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\colorStep{#5}
\coordinate (filterTensorreturn) at (TL);
%% Draw first filer/kernel and dimension names
\tensor{#1}{#2}{#3}{#4}
\colorTensor{#1}{#2}{#3}{#4}{\firstCol}{#5}
\node [scale=1.5, left] at ($(TL)+(0, -0.5*\h*\unit)$) {y};
\node [scale=1.5, below] at ($(TL)+(0.5*\w*\unit, -\h*\unit)$) {x};
\node [scale=1.5, above] at (TL) {c};
\coordinate (backTL1) at (backTL);
%% Draw second filter/kernel
\coordinate (TL) at ($(TL)+(\w*\unit+0.5*\c*\unit+.6*\unit,0)$);
\coordinate (secondTL) at (TL);
\tensor{#1}{#2}{#3}{#4}
\colorTensor{#1}{#2}{#3}{#4}{\secondCol}{#5}
\coordinate (midB) at ($(TL)+(0.5*\w*\unit,-\h*\unit)$);
%% Draw last filter/kernel
\coordinate (TL) at ($(TL)+(\w*\unit+0.5*\c*\unit+2*\unit,0)$);
\tensor{#1}{#2}{#3}{#4}
\colorTensor{#1}{#2}{#3}{#4}{\thirdCol}{#5}
\node [scale=1, left, xshift=.2em] at ($(TL)+(0,-0.5*\h*\unit)$) {$\cdots$};
\coordinate (backTR3) at (backTR);
%% Label dimension k
\draw [thick, decorate, decoration = {calligraphic brace,amplitude=5pt}]
($(backTL1)+(0,0.3*\unit)$) -- ($(backTR3)+(0,0.3*\unit)$)
node [scale=1.5, pos=0.5, above] (labelK) {k};
%% restore TL
\coordinate (TL) at (filterTensorreturn);
}
\newcommand{\fillRow}[5]{
%% (TL): predefined points of the TL corner of the row
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: basecolor
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\unit{#4}
\def\basecolor{#5}
\pgfmathsetmacro\temp{\h*\w*\unit}
\coordinate (fillRowreturn) at (TL);
\coordinate (TL) at ($(fillRowreturn)+(-\temp,0)$);
%\node at (return) {$\temp$};
\foreach \ch [count=\i from 0] in {1,...,\c}{
\pgfmathsetmacro\colorratio{100-\i*30}
\def\thisCol{\basecolor!\colorratio!white}
\coordinate (TL) at ($(TL)+(\temp,0)$);
\fillRec{\unit}{\temp}{\thisCol}
}
%% restore TL
\coordinate (TL) at (fillRowreturn);
}
\newcommand{\fillColumn}[5]{
%% (TL): predefined points of the TL corner of the column
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: basecolor
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\unit{#4}
\def\basecolor{#5}
\pgfmathsetmacro\temp{\h*\w*\unit}
\coordinate (fillColreturn) at (TL);
\coordinate (TL) at ($(fillColreturn)+(0,\temp)$);
\foreach \ch [count=\i from 0] in {1,...,\c}{
\pgfmathsetmacro\colorratio{100-\i*30}
\def\thisCol{\basecolor!\colorratio!white}
\coordinate (TL) at ($(TL)+(0, -\temp)$);
\fillRec{\temp}{\unit}{\thisCol}
}
%% restore TL
\coordinate (TL) at (fillColreturn);
}
\newcommand{\filterGemmA}[6]{
%% (TL): predefined points of the TL corner of the matrix
%% #1: height
%% #2: width
%% #3: channel
%% #4: k
%% #5: unit
%% #6: scale
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\k{#4}
\def\unit{#5}
\def\scale{#6}
\coordinate (fillGemmreturn) at (TL);
\fillRow{#1}{#2}{#3}{#5}{\firstCol}
\coordinate (TL) at ($(TL)+(0,-\unit)$);
\fillRow{#1}{#2}{#3}{#5}{\secondCol}
\coordinate (TL) at ($(fillGemmreturn)+(0,-\k*\unit+\unit)$);
\fillRow{#1}{#2}{#3}{#5}{\thirdCol}
\pgfmathsetmacro\colums{\h*\w*\c}
\foreach \row [count=\ri from 0] in {1,...,\k}{
\draw [thick] ($(fillGemmreturn)+(0,-\ri*\unit)$) -- ++(\colums*\unit, 0);
}
\foreach \col in {0,...,\colums}{
\draw [thick] ($(fillGemmreturn)+(\col*\unit,0)$) -- ++(0,-\k*\unit);
}
%% Labels
\coordinate (TL) at (fillGemmreturn);
%% Do we want to show k=???
%\node [right, scale=0.7*\scale] at ($(TL)+(\colums*\unit,-0.5*\unit)$) {$k=0$};
%\node [right, scale=0.7*\scale] at ($(TL)+(\colums*\unit,-1.5*\unit)$) {$k=1$};
%\node [right, scale=0.7*\scale] at ($(TL)+(\colums*\unit,-\k*\unit+.5*\unit)$) {$k=K-1$};
%% gemmK
\node [below, scale=1.5*\scale] (gemmK) at ($(TL)+(\c*\h*\w*\unit*0.2,-\k*\unit)$)
{gemmK};
\draw [->, >=stealth, thick] (gemmK.east) -- ++(0.5*\scale, 0)
node [right, scale=1.5*\scale] {\textbf{merge}[c,y,x]};
%% gemmM
% The following code should be used to generate the gemmM label for filter matrix A
%\node [scale=1.5*\scale, rotate=90, above] (gemmM) at ($(TL)+(0,-0.5*\k*\unit)$) {gemmM};
%\draw [->, >=stealth, thick] (gemmM.north) -- ++(-0.5*\scale,0)
%node [above, scale=1.5*\scale, rotate=90] {\textbf{passthrough}[k]};
%% y,c dimension info on the matrix
\foreach \ch [count=\ci from 0] in {1,...,\c}{
\foreach \row [count=\y from 0] in {1,...,\h}{
\draw [thick, decorate, decoration = {calligraphic brace,amplitude=3pt*\scale}]
($(fillGemmreturn)+(\ci*\w*\h*\unit+\y*\w*\unit,.1)$) -- ++(\w*\unit,0)
node [scale=.7*\scale, pos=0.5, above, yshift=.3em] {$y=\y$};
}
\draw [thick, decorate, decoration = {calligraphic brace,amplitude=5pt*\scale}]
($(fillGemmreturn)+(\ci*\w*\h*\unit,2*\unit)$) -- ++(\h*\w*\unit,0)
node [scale=1*\scale, pos=0.5, above, yshift=.3em] {$c=\ci$};
}
%% restore TL
\coordinate (TL) at (fillGemmreturn);
}
\newcommand{\filterGemmC}[6]{
%% (TL): predefined points of the TL corner of the matrix
%% #1: height
%% #2: width
%% #3: channel
%% #4: k
%% #5: unit
%% #6: scale
\def\h{#1}
\def\w{#2}
\def\c{#3}
\def\k{#4}
\def\unit{#5}
\def\scale{#6}
\filterGemmA{#1}{#2}{#3}{#4}{#5}{#6}
%% rewrite gemmK --> gemmN
%% gemmN
\node [below, scale=1.5*\scale,fill=white] at ($(TL)+(\c*\h*\w*\unit*0.2,-\k*\unit)$)
{gemmN};
%% gemmM
\node [scale=1.5*\scale, rotate=-90, above] (gemmM) at ($(TL)+(\h*\w*\c*\unit, -0.5*\k*\unit)$) {gemmM};
\draw [->, >=stealth, thick] (gemmM.north) -- ++(0.5*\scale, 0)
node [above, scale=1.5*\scale, rotate=-90] {\textbf{passthrough}[k]};
}
\newcommand{\pickElemInMatrix}[3]{
%% (TL) the TL of the matrix
%% #1: row
%% #2: col
%% #3: unit
\def\row{#1}
\def\col{#2}
\def\unit{#3}
\coordinate (TL) at ($(TL)+(\col*\unit,-\row*\unit)$);
\fillRec{\unit}{\unit}{blue}
%\draw [thick] (elemTL) -- ++(\unit,-\unit)
%\node [right, inner sep=0.3] at ($(TL)+(\unit,-0.5*\unit)$) {$\mathcal{P}$};
%\draw [thick] ($(elemTL)+(0,-\unit)$) -- ++(\unit,\unit);
}
\newcommand{\pickElemInTensor}[1]{
%% (TL) the TL of the tensor
%% #1: unit
\def\unit{#1}
\pgfmathsetmacro\halfunit{0.5*\unit}
\pgfmathsetmacro\smallunit{0.3*\unit}
\coordinate (BL) at ($(TL)+(2*\unit+2*\halfunit,2*\smallunit)$);
\fillTopParallelogram{\smallunit}{\unit}{\halfunit}{blue}
\coordinate (BL) at ($(TL)+(3*\unit+2*\halfunit,-\unit+2*\smallunit)$);
\fillSideParallelogram{\unit}{\halfunit}{\smallunit}{blue}
%\node [above right] at ($(BL)+(\halfunit,\smallunit)$) {$\mathcal{P}$};
}
\newcommand{\filterTransform}{
%% (TL): predefined TL of the node TL corner
\node [scale=1, below right, align=left] at (TL)
{$\mathcal{P}_\text{gemm}=[1,20]$\\
$\mathcal{P}_\text{tensor}=[\mathcal{P}_k,\mathcal{P}_c,\mathcal{P}_y,\mathcal{P}_x]$\\
$\mathcal{P}_k=\mathcal{P}_\text{gemmM}=1$\\
$\mathcal{P}_c=\floor{\mathcal{P}_\text{gemmK}/(Y\times X)}=2$\\
$\mathcal{P}_y=\floor{\mathcal{P}_\text{gemmK}\%(Y\times X)/X}=0$\\
$\mathcal{P}_x=\floor{\mathcal{P}_\text{gemmK}\%(Y\times X)\%X}=2$\\
$\mathcal{P}_\text{tensor}=[1,2,0,2]$};
}
\newcommand{\inputTensor}[7]{
%% (TL): predefined points of the TL corner of the first tensor
%% #1: height
%% #2: width
%% #3: channel
%% #4: unit
%% #5: h dim name