tex: performance analysis

latex/content.tex

@@ -152,7 +152,12 @@ after each simulation.
 
 We set out to study the resource consumption of the algorithms. We implemented
 the above formulae to calculate the mean and variance of $ N = 10^6 $ random
-numbers. We wrote the following algorithms :
+numbers. We wrote the following algorithms \footnotemark :
+
+\footnotetext{The full code used to measure performance can be found in Annex X.}
+% TODO annex
+
+\paragraph{Intuitive algorithm} Store values first, calculate later
 
 \begin{lstlisting}[language=python]
 N = 10**6
@@ -161,9 +166,38 @@ mean = mean(values)
 variance = variance(values)
 \end{lstlisting}
 
+Execution time : $ ~ 4.8 $ seconds
 
-% TODO : code
+Memory usage : $ ~ 32 $ MB
-% TODO : add a graph
+
+\paragraph{Improved algorithm} Continuous calculation
+
+\begin{lstlisting}[language=python]
+N = 10**6
+Tot = 0
+Tot2 = 0
+for _ in range(N):
+    item = random()
+    Tot  += item
+    Tot2 += item ** 2
+mean = Tot / N
+variance = Tot2 / (N-1) - mean**2
+\end{lstlisting}
+
+Execution time : $ ~ 530 $ milliseconds
+
+Memory usage : $ ~ 1.3 $ kB
+
+\paragraph{Analysis} Memory usage is, as expected, much lower when calculating
+the statistics on the fly. Furthermore, something we hadn't anticipated is the
+execution time. The improved algorithm is nearly 10 times faster than the
+intuitive one. This can be explained by the time taken to allocate memory and
+then calculate the statistics (which iterates multiple times over the array).
+\footnotemark
+
+\footnotetext{Performance was measured on a single computer and will vary
+	between devices. Execution time and memory usage do not include the import of
+	libraries.}
 
 \subsection{NFBP vs NFDBP}