Merge branch 'master' of bitbucket.org:winfried/hpc
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7c2a8a1dbb
7 changed files with 45 additions and 33 deletions
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/*
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* bin_reduce.c
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*
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* Created on: 16 Jun 2016
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* Author: johannes
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*/
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#include <stdio.h>
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#include <string.h>
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#include <mpi.h>
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/*
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* binom_reduce.c
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*
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* Created on: 18 Jun 2016
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* Author: johannes
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*/
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#include <mpi.h>
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#include <string.h>
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#include <stdio.h>
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/*
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* fib_reduce.c
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*
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* Created on: 18 Jun 2016
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* Author: johannes
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*/
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#include <stdio.h>
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#include <string.h>
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#include <mpi.h>
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@ -1,18 +1,10 @@
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/*
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============================================================================
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Name : hpc_mpi.c
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Author :
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Version :
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Copyright : Your copyright notice
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Description : Hello MPI World in C
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============================================================================
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*/
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#include <stdio.h>
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#include <string.h>
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#include <mpi.h>
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#include <unistd.h>
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#include <stdlib.h>
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#include <time.h>
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#include <getopt.h>
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#include "bin_reduce.h"
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#include "binom_reduce.h"
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#include "fib_reduce.h"
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BIN
reduce/report/nodeplot.pdf
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reduce/report/nodeplot.pdf
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reduce/report/report.pdf
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reduce/report/report.pdf
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@ -106,7 +106,7 @@ As a baseline for the comparison serves a given implementation of the MPI standa
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A binomial tree has a non-fixed degree where each tree $B_i$ has exactly $i$ subtrees of size $B_0$ to $B_{i-1}$.
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The number of nodes in such a tree is equal to $2^i$ and the depth is $i$.
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\item[Fibonacci Tree]
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The Fibonacci tree uses a fixed degree of $2$ where a tree of size $F_i$ has one subtree of size $T_{i-1}$ and one of $T_{i-2}$.
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The Fibonacci tree uses a fixed degree of $2$ where a tree of size $F_i$ has one subtree of size $F_{i-1}$ and one of $F_{i-2}$.
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Therefore the number of nodes in this kind of tree is $fib(i+3)-1$ using the Fibonacci function $fib(x) = fib(x-1)+fib(x-2)$ and its depth is as well $i$.
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\item[Binary Tree]
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The binary tree used for reduction is a common complete binary tree where a tree $T_i$ has two subtrees $T_{i-1}$.
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@ -285,7 +285,11 @@ There is again a comparison between a tree $T_2$ and $T_3$ which is shown in \pr
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\begin{figure}
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\begin{center}
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\begin{tikzpicture}
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\begin{tikzpicture}[
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auto,
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level 1/.style={sibling distance=40mm},
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level 2/.style={sibling distance=20mm},
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level 3/.style={sibling distance=10mm}]
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\begin{scope}
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\node [circle,draw]{$0$}
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child { node [circle,draw]{$1$}
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@ -295,7 +299,7 @@ child { node [circle,draw]{$4$}
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child { node [circle,draw]{$5$}}
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child { node [circle,draw]{$6$}}};
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\end{scope}
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\begin{scope}[shift={(5,0)}]
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\begin{scope}[shift={(7,0)}]
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\node [circle,draw]{$0$}
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child { node [circle,draw]{$1$}
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child { node [circle,draw]{$2$}
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@ -328,6 +332,43 @@ As a result the number of rounds for this algorithm is the size of the tree plus
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\section{Results}
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\label{sec:results}
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Before we compared the runtime of our algorithms the correctness has to be tested by a reasonable amount.
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As already stated in the project description this process can be done easily by comparing each result to the MPI\_Reduce function.
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This can be done for all implementations at once to quickly test them for correctness.
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With this method we tried various combinations of array sizes, process numbers as well as different operations and the result always turned out to be correct.
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After doing those tests to show the correctness we started doing some benchmarking comparisons of our implementations.
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To do this we utilized 36 nodes of the jupiter system with 16 processes each.
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We did two kinds of tests which will be explained now to compare the runtime of our implementations as well as the MPI\_Reduce function.
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\subsection{Process Count}
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For the first benchmark we used a different number of processes to check the scaling of all methods.
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The size of the array on each process for this test is $1000$.
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This is a rather low value, but since we are using tree reduction which is not optimal for high amounts of data such a value makes sense.
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The amount of processes used was increased from starting with only one node up to using all available 36 nodes.
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On each node all 16 processes where used in all tests.
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Therefore the total process count ranged from 16 to 576.
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For all out tests in this project we used a repetition count of 30 which allowed us to run a high number of different inputs in a reasonable amount of time.
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\begin{figure}
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\begin{adjustbox}{center}
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\includegraphics[width=0.8\linewidth]{nodeplot}
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\end{adjustbox}
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\caption{Average runtimes on 1 to 36 nodes with 16 processes each.}
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\label{fig:roofline}
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\end{figure}
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\subsection{Array Size}
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Our second used a fixed number of processes but the size of the local arrays was increasing.
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This should show how the different implementations perform for small arrays or even a single number.
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But it also shows how they perform with a large amount of data on each process.
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The amount of nodes was fixed at 36 for the complete test.
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The size of the local arrays was increased by a factor of 10 in each iteration starting with just 1 and increased it up to 1000000.
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The number of repetitions is the same as for the last test at 30.
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\FloatBarrier
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\section{Analysis}
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