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+startxref +52548 +%%EOF diff --git a/Project1/project_1_maggioni_claudio.pdf b/Project1/project_1_maggioni_claudio.pdf index c342322..d3825c0 100644 Binary files a/Project1/project_1_maggioni_claudio.pdf and b/Project1/project_1_maggioni_claudio.pdf differ diff --git a/Project1/project_1_maggioni_claudio.tex b/Project1/project_1_maggioni_claudio.tex index 872ec4e..4d939b5 100644 --- a/Project1/project_1_maggioni_claudio.tex +++ b/Project1/project_1_maggioni_claudio.tex @@ -18,6 +18,8 @@ on the ICS Cluster . \section{Explaining Memory Hierarchies \punkte{25}} +\subsection{Memory Hierarchy Parameters of the Cluster} + By identifying the memory hierarchy parameters through \texttt{likwid-topology} for the cache topology and \texttt{free -g} for the amount of primary memory I find the following values: @@ -70,6 +72,44 @@ Socket 1: +---------------------------------------------------------------------------------------------------------------+ \end{Verbatim} +\subsection{Memory Access Pattern of \texttt{membench.c}} + +The benchmark \texttt{membench.c} measures the average time of repeated read and +write overations across a set of indices of a stack-allocated array of 32-bit +signed integers. The indices vary according to the access pattern used, which in +turn is defined by two variables, \texttt{csize} and \texttt{stride}. +\texttt{csize} is an upper bound on the index value, i.e. (one more of) the +highest index used to access the array in the pattern. \texttt{stride} +determines the difference between array indexes over access iterations, i.e. a +\texttt{stride} of 1 will access every array index, a \texttt{stride} of 2 will +skip every other index, a \texttt{stride} of 4 will access one index then skip 3 +and so on and so forth. + +Therefore, for \texttt{csize = 128} and \texttt{stride = 1} the array will +access all indexes between 0 and 127 sequentially, and for \texttt{csize = +$2^{20}$} and \texttt{stride = $2^{10}$} the benchmark will access index 0, then +index $2^{10}-1$, and finally index $2^{20}-1$i. + +\subsection{Analyzing Benchmark Results} + +The \texttt{membench.c} benchmark results for my personal laptop (Macbook Pro +2018 with a Core i7-8750H CPU) and the cluster are shown below respectively: + +\begin{center} +\includegraphics[width=12cm]{generic_macos.pdf} +\includegraphics[width=12cm]{generic_cluster.pdf} +\end{center} + +The memory access graph for the cluster's benchmark results shows that temporal +locality is best for small array sizes and for small \texttt{stride} values. +In particular, for array memory sizes of 16MB or lower (\texttt{csize} of $4 +\cdot 2^{20}$ or lower) and \texttt{stride} values of 2048 or lower the mean +read+write time is less than 10 nanoseconds. Temporal locality is worst for +large sizes and strides, although the largest values of \texttt{stride} for each +size (like \texttt{csize / 2} and \texttt{csize / 4}) achieve better mean times +due to the few elements accessed in the pattern (this observation is also valid +for the largest strides of each size series shown in the graph). + \section{Optimize Square Matrix-Matrix Multiplication \punkte{60}} diff --git a/Project1/project_1_maggioni_claudio/membench/generic_macos.ps b/Project1/project_1_maggioni_claudio/membench/generic_macos.ps index 3981e64..4d814ed 100644 --- a/Project1/project_1_maggioni_claudio/membench/generic_macos.ps +++ b/Project1/project_1_maggioni_claudio/membench/generic_macos.ps @@ -1650,11 +1650,11 @@ LTb LCb setrgbcolor LCb setrgbcolor 3774 4829 M -[ [(Helvetica) 140.0 0.0 true true 0 (10-Core Intel\(R\) Xeon\(R\) CPU E3-1585L v5 )] +[ [(Helvetica) 140.0 0.0 true true 0 (6-Core Intel\(R\) Core\(R\) CPU i7-8750H )] XYsave [(Helvetica) 140.0 0.0 true true 0 ( )] XYrestore -[(Helvetica) 140.0 0.0 true true 0 (3.00GHz Read+Write \(ns\) Versus Stride)] +[(Helvetica) 140.0 0.0 true true 0 (4.10GHz Read+Write \(ns\) Versus Stride)] ] -46.7 MCshow /Helvetica findfont 140 scalefont setfont LTb