More content

common/refs.bib

@@ -98,3 +98,10 @@
   publisher={IEEE}
 }
 
+@misc{sysdig_cpu,
+    author={Théophile Bastian and Noémie Cartier and Nathanaël Courant},
+    title={``Système digital'' project},
+    howpublished={\url{https://github.com/tobast/sysdig-full/}},
+    year=2016
+}
+

report/report.tex

@@ -9,6 +9,9 @@
 \usepackage{enumerate}
 \usepackage{caption}
 \usepackage{algorithmicx}
+%\usepgfplotslibrary{external}
+%\tikzexternalize
+
 \usepackage[backend=biber,style=trad-alpha]{biblatex}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 
@@ -21,6 +24,8 @@
 \usepackage{../common/internship}
 \usepackage{../common/math}
 
+\usepackage{pgfplots}
+
 \bibliography{../common/refs}
 
 \title{Pattern-matching and substitution in electronic circuits}
@@ -574,7 +579,84 @@ many times in the haystack. This simple check saved a lot of time.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Performance}
 
-\todo{}
+In this section, all the measures were made on a computer with an Intel
+i7-3770 CPU (3.40GHz) and 8\,GB of RAM\@. % chktex 8
+
+\subsection{Small processor}
+
+The example I used widely during my project to test my program and check its
+efficiency periodically was a small processor designed one year earlier as a
+school project~\cite{sysdig_cpu}. The processor implements a large subset of
+ARM, was conceived as a few hierarchized modules (ALU, registers, opcode
+decoder, \ldots) but was flattened as a plain netlist when generated from its
+python code, so I first had to patch its generator code to make its hierarchy
+apparent.
+
+The processor, in the end, has around 2000 leaf gates (but works at word level)
+and 240 hierarchy groups. \qtodo{Tell us more!}
+
+\paragraph{Signature.} First, the time required to sign the whole circuit with
+different levels of signature (\ie{} the order of signature computed for every
+part of the circuit). In practice, we never compute high order signatures for a
+whole circuit, as signature of subgroups are always computed by default at the
+order $2$, unless this particular group needs a more accurate signature.
+
+The measures were made for 100 consecutive runs of the program (then averaged
+for a single run) and measured by the command \texttt{time}.
+
+\begin{center}
+    \begin{tikzpicture}
+    \begin{axis}[
+        title={Signature time of the processor for different levels
+            of signature},
+        xlabel={Level of signature},
+        ylabel={Time (ms)},
+        xmin=0, xmax=16,
+        ymin=0, ymax=300,
+        legend pos=north west,
+        ymajorgrids=true,
+        grid style=dashed,
+    ]
+
+    \addplot[
+        color=blue,
+        mark=square,
+        ]
+        coordinates {
+            (2,105.4)
+            (3,122.6)
+            (4,140.1)
+            (5,155.4)
+            (6,171.2)
+            (7,183.9)
+            (8,198.3)
+            (9,211.2)
+            (10,224.3)
+            (11,236.7)
+            (12,248.5)
+            (13,259.3)
+            (14,271.7)
+            (15,281.4)
+        };
+        \legend{-O3}
+    \end{axis}
+    \end{tikzpicture}
+\end{center}
+
+
+\paragraph{Equality.} To test the circuit group equality, a small piece of
+code takes a circuit, scrambles it as much as possible
+--- without altering its structure ---, \eg{} by renaming randomly its parts,
+by randomly changing the order of the circuits and groups, \ldots The circuit
+is then matched with its unaltered counterpart.
+
+For the processor described above, it takes about \textbf{477\,ms} to
+prove it equal to its scrambled version, and then the other way around. Yet,
+the memoized results (essentially the signatures) are kept for the second one,
+considerably speeding it up: the same program proving only one way takes about
+\textbf{475\,ms}. \todo{explain why}
+
+
 
 \subsection{Corner cases}