| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697 | /* StarPU --- Runtime system for heterogeneous multicore architectures. * * Copyright (C) 2011,2012,2015-2017                      Inria * Copyright (C) 2010-2019                                CNRS * Copyright (C) 2009-2011,2014-2017,2019                 Université de Bordeaux * * StarPU is free software; you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as published by * the Free Software Foundation; either version 2.1 of the License, or (at * your option) any later version. * * StarPU is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * * See the GNU Lesser General Public License in COPYING.LGPL for more details. *//*! \page OfflinePerformanceTools Offline Performance ToolsTo get an idea of what is happening, a lot of performance feedback is available,detailed in this chapter. The various informations should be checked for.<ul><li>What does the Gantt diagram look like? (see \ref CreatingAGanttDiagram)<ul>  <li> If it's mostly green (tasks running in the initial context) or context specific  color prevailing, then the machine is properly  utilized, and perhaps the codelets are just slow. Check their performance, see  \ref PerformanceOfCodelets.  </li>  <li> If it's mostly purple (FetchingInput), tasks keep waiting for data  transfers, do you perhaps have far more communication than computation? Did  you properly use CUDA streams to make sure communication can be  overlapped? Did you use data-locality aware schedulers to avoid transfers as  much as possible?  </li>  <li> If it's mostly red (Blocked), tasks keep waiting for dependencies,  do you have enough parallelism? It might be a good idea to check what the DAG  looks like (see \ref CreatingADAGWithGraphviz).  </li>  <li> If only some workers are completely red (Blocked), for some reason the  scheduler didn't assign tasks to them. Perhaps the performance model is bogus,  check it (see \ref PerformanceOfCodelets). Do all your codelets have a  performance model?  When some of them don't, the schedulers switches to a  greedy algorithm which thus performs badly.  </li></ul></li></ul>You can also use the Temanejo task debugger (see \ref UsingTheTemanejoTaskDebugger) tovisualize the task graph more easily.\section Off-linePerformanceFeedback Off-line Performance Feedback\subsection GeneratingTracesWithFxT Generating Traces With FxTStarPU can use the FxT library (seehttps://savannah.nongnu.org/projects/fkt/) to generate traceswith a limited runtime overhead.You can get a tarball from http://download.savannah.gnu.org/releases/fkt/Compiling and installing the FxT library in the <c>$FXTDIR</c> path isdone following the standard procedure:\verbatim$ ./configure --prefix=$FXTDIR$ make$ make install\endverbatimIn order to have StarPU to generate traces, StarPU should be configured withthe option \ref with-fxt "--with-fxt" :\verbatim$ ./configure --with-fxt=$FXTDIR\endverbatimOr you can simply point the <c>PKG_CONFIG_PATH</c> to<c>$FXTDIR/lib/pkgconfig</c> and pass\ref with-fxt "--with-fxt" to <c>configure</c>When FxT is enabled, a trace is generated when StarPU is terminated by callingstarpu_shutdown(). The trace is a binary file whose name has the form<c>prof_file_XXX_YYY</c> where <c>XXX</c> is the user name, and<c>YYY</c> is the pid of the process that used StarPU. This file is saved in the<c>/tmp/</c> directory by default, or by the directory specified bythe environment variable \ref STARPU_FXT_PREFIX.The additional \c configure option \ref enable-fxt-lock "--enable-fxt-lock" canbe used to generate trace events which describes the locks behaviour duringthe execution. It is however very heavy and should not be used unless debuggingStarPU's internal locking.The environment variable \ref STARPU_FXT_TRACE can be set to 0 to disable thegeneration of the <c>prof_file_XXX_YYY</c> file.When the FxT trace file <c>prof_file_something</c> has been generated,it is possible to generate different trace formats by calling:\verbatim$ starpu_fxt_tool -i /tmp/prof_file_something\endverbatimOr alternatively, setting the environment variable \ref STARPU_GENERATE_TRACEto <c>1</c> before application execution will make StarPU do it automatically atapplication shutdown.One can also set the environment variable \refSTARPU_GENERATE_TRACE_OPTIONS to specify options, see<c>starpu_fxt_tool --help</c>, for example:\verbatim$ export STARPU_GENERATE_TRACE=1$ export STARPU_GENERATE_TRACE_OPTIONS="-no-acquire"\endverbatimWhen running a MPI application, \ref STARPU_GENERATE_TRACE will notwork as expected (each node will try to generate trace files, thusmixing outputs...), you have to collect the trace files from the MPInodes, and specify them all on the command <c>starpu_fxt_tool</c>, forinstance:\verbatim$ starpu_fxt_tool -i /tmp/prof_file_something*\endverbatimBy default, the generated trace contains all informations. To reducethe trace size, various <c>-no-foo</c> options can be passed to<c>starpu_fxt_tool</c>, see <c>starpu_fxt_tool --help</c> .\subsubsection CreatingAGanttDiagram Creating a Gantt DiagramOne of the generated files is a trace in the Paje format. The file,located in the current directory, is named <c>paje.trace</c>. It canbe viewed with ViTE (http://vite.gforge.inria.fr/) a tracevisualizing open-source tool.  To open the file <c>paje.trace</c> withViTE, use the following command:\verbatim$ vite paje.trace\endverbatimTasks can be assigned a name (instead of the default \c unknown) byfilling the optional starpu_codelet::name, or assigning them aperformance model. The name can also be set with the fieldstarpu_task::name or by using \ref STARPU_NAME when callingstarpu_task_insert().Tasks are assigned default colors based on the worker which executedthem (green for CPUs, yellow/orange/red for CUDAs, blue for OpenCLs,red for MICs, ...). To use a different color for every type of task,one can specify the option <c>-c</c> to <c>starpu_fxt_tool</c> or in\ref STARPU_GENERATE_TRACE_OPTIONS. Tasks can also be given a specificcolor by setting the field starpu_codelet::color or thestarpu_task::color. Colors are expressed with the following format\c 0xRRGGBB (e.g \c 0xFF0000 for red). See<c>basic_examples/task_insert_color</c> for examples on how to assigncolors.To identify tasks precisely, the application can also set the fieldstarpu_task::tag_id or setting \ref STARPU_TAG_ONLY when callingstarpu_task_insert(). The value of the tag will then show up in thetrace.One can also introduce user-defined events in the diagram thanks to thestarpu_fxt_trace_user_event_string() function.One can also set the iteration number, by just calling starpu_iteration_push()at the beginning of submission loops and starpu_iteration_pop() at the end ofsubmission loops. These iteration numbers will show up in traces for all taskssubmitted from there.Coordinates can also be given to data with the starpu_data_set_coordinates() orstarpu_data_set_coordinates_array() function. In the trace, tasks will then beassigned the coordinates of the first data they write to.Traces can also be inspected by hand by using the tool <c>fxt_print</c>, for instance:\verbatim$ fxt_print -o -f /tmp/prof_file_something\endverbatimTimings are in nanoseconds (while timings as seen in ViTE are in milliseconds).\subsubsection CreatingADAGWithGraphviz Creating a DAG With GraphvizAnother generated trace file is a task graph described using the DOTlanguage. The file, created in the current directory, is named<c>dag.dot</c> file in the current directory.It is possible to get a graphical output of the graph by using the<c>graphviz</c> library:\verbatim$ dot -Tpdf dag.dot -o output.pdf\endverbatim\subsubsection TraceTaskDetails Getting Task DetailsAnother generated trace file gives details on the executed tasks. Thefile, created in the current directory, is named <c>tasks.rec</c>. This fileis in the recutils format, i.e. <c>Field: value</c> lines, and empty lines toseparate each task.  This can be used as a convenient input for various ad-hocanalysis tools. By default it only contains information about the actualexecution. Performance models can be obtained by running<c>starpu_tasks_rec_complete</c> on it:\verbatim$ starpu_tasks_rec_complete tasks.rec tasks2.rec\endverbatimwhich will add <c>EstimatedTime</c> lines which contain the performancemodel-estimated time (in µs) for each worker starting from 0. Since it needsthe performance models, it needs to be run the same way as the applicationexecution, or at least with <c>STARPU_HOSTNAME</c> set to the hostname of themachine used for execution, to get the performance models of that machine.Another possibility is to obtain the performance models as an auxiliary <c>perfmodel.rec</c> file, by using the <c>starpu_perfmodel_recdump</c> utility:\verbatim$ starpu_perfmodel_recdump tasks.rec -o perfmodel.rec\endverbatim\subsubsection MonitoringActivity Monitoring ActivityAnother generated trace file is an activity trace. The file, createdin the current directory, is named <c>activity.data</c>. A profile ofthe application showing the activity of StarPU during the execution ofthe program can be generated:\verbatim$ starpu_workers_activity activity.data\endverbatimThis will create a file named <c>activity.eps</c> in the current directory.This picture is composed of two parts.The first part shows the activity of the different workers. The green sectionsindicate which proportion of the time was spent executed kernels on theprocessing unit. The red sections indicate the proportion of time spent inStartPU: an important overhead may indicate that the granularity may be toolow, and that bigger tasks may be appropriate to use the processing unit moreefficiently. The black sections indicate that the processing unit was blockedbecause there was no task to process: this may indicate a lack of parallelismwhich may be alleviated by creating more tasks when it is possible.The second part of the picture <c>activity.eps</c> is a graph showing theevolution of the number of tasks available in the system during the execution.Ready tasks are shown in black, and tasks that are submitted but notschedulable yet are shown in grey.\subsubsection Animation Getting Modular Schedular AnimationWhen using modular schedulers (i.e. schedulers which use a modular architecture,and whose name start with "modular-"), the call to<c>starpu_fxt_tool</c> will also produce a <c>trace.html</c> filewhich can be viewed in a javascript-enabled web browser. It shows theflow of tasks between the components of the modular scheduler.\subsection LimitingScopeTrace Limiting The Scope Of The TraceFor computing statistics, it is useful to limit the trace to a given portion ofthe time of the whole execution. This can be achieved by calling\code{.c}starpu_fxt_autostart_profiling(0)\endcodebefore calling starpu_init(), toprevent tracing from starting immediately. Then\code{.c}starpu_fxt_start_profiling();\endcodeand\code{.c}starpu_fxt_stop_profiling();\endcodecan be used around the portion of code to be traced. This will show up as marksin the trace, and states of workers will only show up for that portion.\section PerformanceOfCodelets Performance Of CodeletsThe performance model of codelets (see \ref PerformanceModelExample)can be examined by using the tool <c>starpu_perfmodel_display</c>:\verbatim$ starpu_perfmodel_display -lfile: <malloc_pinned.hannibal>file: <starpu_slu_lu_model_21.hannibal>file: <starpu_slu_lu_model_11.hannibal>file: <starpu_slu_lu_model_22.hannibal>file: <starpu_slu_lu_model_12.hannibal>\endverbatimHere, the codelets of the example <c>lu</c> are available. We can examine theperformance of the kernel <c>22</c> (in micro-seconds), which is history-based:\verbatim$ starpu_perfmodel_display -s starpu_slu_lu_model_22performance model for cpu# hash      size       mean          dev           n57618ab0    19660800   2.851069e+05  1.829369e+04  109performance model for cuda_0# hash      size       mean          dev           n57618ab0    19660800   1.164144e+04  1.556094e+01  315performance model for cuda_1# hash      size       mean          dev           n57618ab0    19660800   1.164271e+04  1.330628e+01  360performance model for cuda_2# hash      size       mean          dev           n57618ab0    19660800   1.166730e+04  3.390395e+02  456\endverbatimWe can see that for the given size, over a sample of a few hundreds ofexecution, the GPUs are about 20 times faster than the CPUs (numbers are inus). The standard deviation is extremely low for the GPUs, and less than 10% forCPUs.This tool can also be used for regression-based performance models. It will thendisplay the regression formula, and in the case of non-linear regression, thesame performance log as for history-based performance models:\verbatim$ starpu_perfmodel_display -s non_linear_memset_regression_basedperformance model for cpu_impl_0	Regression : #sample = 1400	Linear: y = alpha size ^ beta		alpha = 1.335973e-03		beta = 8.024020e-01	Non-Linear: y = a size ^b + c		a = 5.429195e-04		b = 8.654899e-01		c = 9.009313e-01# hash		size		mean		stddev		na3d3725e	4096           	4.763200e+00   	7.650928e-01   	100870a30aa	8192           	1.827970e+00   	2.037181e-01   	10048e988e9	16384          	2.652800e+00   	1.876459e-01   	100961e65d2	32768          	4.255530e+00   	3.518025e-01   	100...\endverbatimThe same can also be achieved by using StarPU's library API, see\ref API_Performance_Model and notably the functionstarpu_perfmodel_load_symbol(). The source code of the tool<c>starpu_perfmodel_display</c> can be a useful example.An XML output can also be printed by using the <c>-x</c> option:\verbatimtools/starpu_perfmodel_display -x -s non_linear_memset_regression_based <?xml version="1.0" encoding="UTF-8"?><!DOCTYPE StarPUPerfmodel SYSTEM "starpu-perfmodel.dtd"><!-- symbol non_linear_memset_regression_based --><!-- All times in us --><perfmodel version="45">  <combination>    <device type="CPU" id="0" ncores="1"/>    <implementation id="0">      <!-- cpu0_impl0 (Comb0) -->      <!-- time = a size ^b + c -->      <nl_regression a="5.429195e-04" b="8.654899e-01" c="9.009313e-01"/>      <entry footprint="a3d3725e" size="4096" flops="0.000000e+00" mean="4.763200e+00" deviation="7.650928e-01" nsample="100"/>      <entry footprint="870a30aa" size="8192" flops="0.000000e+00" mean="1.827970e+00" deviation="2.037181e-01" nsample="100"/>      <entry footprint="48e988e9" size="16384" flops="0.000000e+00" mean="2.652800e+00" deviation="1.876459e-01" nsample="100"/>      <entry footprint="961e65d2" size="32768" flops="0.000000e+00" mean="4.255530e+00" deviation="3.518025e-01" nsample="100"/>    </implementation>  </combination></perfmodel>\endverbatimThe tool <c>starpu_perfmodel_plot</c> can be used to draw performancemodels. It writes a <c>.gp</c> file in the current directory, to berun with the tool <c>gnuplot</c>, which shows the corresponding curve.\image html starpu_non_linear_memset_regression_based.png\image latex starpu_non_linear_memset_regression_based.eps "" width=\textwidthWhen the field starpu_task::flops is set (or \ref STARPU_FLOPS is passed tostarpu_task_insert()), <c>starpu_perfmodel_plot</c> can directly draw a GFlopscurve, by simply adding the <c>-f</c> option:\verbatim$ starpu_perfmodel_plot -f -s chol_model_11\endverbatimThis will however disable displaying the regression model, for which we can notcompute GFlops.\image html starpu_chol_model_11_type.png\image latex starpu_chol_model_11_type.eps "" width=\textwidthWhen the FxT trace file <c>prof_file_something</c> has been generated, it is possible toget a profiling of each codelet by calling:\verbatim$ starpu_fxt_tool -i /tmp/prof_file_something$ starpu_codelet_profile distrib.data codelet_name\endverbatimThis will create profiling data files, and a <c>distrib.data.gp</c> file in the currentdirectory, which draws the distribution of codelet time over the applicationexecution, according to data input size.\image html distrib_data.png\image latex distrib_data.eps "" width=\textwidthThis is also available in the tool <c>starpu_perfmodel_plot</c>, by passing itthe fxt trace:\verbatim$ starpu_perfmodel_plot -s non_linear_memset_regression_based -i /tmp/prof_file_foo_0\endverbatimIt will produce a <c>.gp</c> file which contains both the performance modelcurves, and the profiling measurements.\image html starpu_non_linear_memset_regression_based_2.png\image latex starpu_non_linear_memset_regression_based_2.eps "" width=\textwidthIf you have the statistical tool <c>R</c> installed, you can additionally use\verbatim$ starpu_codelet_histo_profile distrib.data\endverbatimWhich will create one <c>.pdf</c> file per codelet and per input size, showing ahistogram of the codelet execution time distribution.\image html distrib_data_histo.png\image latex distrib_data_histo.eps "" width=\textwidth\section TraceStatistics Trace StatisticsMore than just codelet performance, it is interesting to get statistics over allkinds of StarPU states (allocations, data transfers, etc.). This is particularlyuseful to check what may have gone wrong in the accurracy of the simgridsimulation.This requires the <c>R</c> statistical tool, with the <c>plyr</c>,<c>ggplot2</c> and <c>data.table</c> packages. If your systemdistribution does not have packages for these, one can fetch them from<c>CRAN</c>:\verbatim$ R> install.packages("plyr")> install.packages("ggplot2")> install.packages("data.table")> install.packages("knitr")\endverbatimThe <c>pj_dump</c> tool from <c>pajeng</c> is also needed (seehttps://github.com/schnorr/pajeng)One can then get textual or <c>.csv</c> statistics over the trace states:\verbatim$ starpu_paje_state_stats -v native.trace simgrid.trace"Value"         "Events_native.csv" "Duration_native.csv" "Events_simgrid.csv" "Duration_simgrid.csv""Callback"      220                 0.075978              220                  0"chol_model_11" 10                  565.176               10                   572.8695"chol_model_21" 45                  9184.828              45                   9170.719"chol_model_22" 165                 64712.07              165                  64299.203$ starpu_paje_state_stats native.trace simgrid.trace\endverbatimAn other way to get statistics of StarPU states (without installing <c>R</c> and<c>pj_dump</c>) is to use the <c>starpu_trace_state_stats.py</c> script which parses thegenerated <c>trace.rec</c> file instead of the <c>paje.trace</c> file. The output is similarto the previous script but it doesn't need any dependencies.The different prefixes used in <c>trace.rec</c> are:\verbatimE: Event typeN: Event nameC: Event categoryW: Worker IDT: Thread IDS: Start time\endverbatimHere's an example on how to use it:\verbatim$ python starpu_trace_state_stats.py trace.rec | column -t -s ",""Name"		"Count" "Type"	"Duration""Callback"       220	Runtime	0.075978"chol_model_11"  10	Task	565.176"chol_model_21"  45	Task	9184.828"chol_model_22"  165	Task	64712.07\endverbatim<c>starpu_trace_state_stats.py</c> can also be used to compute the differentefficiencies. Refer to the usage description to show some examples.And one can plot histograms of execution times, of several states for instance:\verbatim$ starpu_paje_draw_histogram -n chol_model_11,chol_model_21,chol_model_22 native.trace simgrid.trace\endverbatimand see the resulting pdf file:\image html paje_draw_histogram.png\image latex paje_draw_histogram.eps "" width=\textwidthA quick statistical report can be generated by using:\verbatim$ starpu_paje_summary native.trace simgrid.trace\endverbatimit includes gantt charts, execution summaries, as well as state duration chartsand time distribution histograms.Other external Paje analysis tools can be used on these traces, one just needsto sort the traces by timestamp order (which not guaranteed to make recordingmore efficient):\verbatim$ starpu_paje_sort paje.trace\endverbatim\section TheoreticalLowerBoundOnExecutionTime Theoretical Lower Bound On Execution TimeStarPU can record a trace of what tasks are needed to complete theapplication, and then, by using a linear system, provide a theoretical lowerbound of the execution time (i.e. with an ideal scheduling).The computed bound is not really correct when not taking into accountdependencies, but for an application which have enough parallelism, it is verynear to the bound computed with dependencies enabled (which takes a huge lotmore time to compute), and thus provides a good-enough estimation of the idealexecution time.\ref TheoreticalLowerBoundOnExecutionTimeExample provides an example on how touse this.\section TheoreticalLowerBoundOnExecutionTimeExample Theoretical Lower Bound On Execution Time ExampleFor kernels with history-based performance models (and provided thatthey are completely calibrated), StarPU can very easily provide atheoretical lower bound for the execution time of a whole set oftasks. See for instance <c>examples/lu/lu_example.c</c>: beforesubmitting tasks, call the function starpu_bound_start(), and aftercomplete execution, call starpu_bound_stop().starpu_bound_print_lp() or starpu_bound_print_mps() can then be usedto output a Linear Programming problem corresponding to the scheduleof your tasks. Run it through <c>lp_solve</c> or any other linearprogramming solver, and that will give you a lower bound for the totalexecution time of your tasks. If StarPU was compiled with the library<c>glpk</c> installed, starpu_bound_compute() can be used to solve itimmediately and get the optimized minimum, in ms. Its parameter<c>integer</c> allows to decide whether integer resolution should becomputed and returnedThe <c>deps</c> parameter tells StarPU whether to take tasks, implicitdata, and tag dependencies into account. Tags released in a callbackor similar are not taken into account, only tags associated with a task are.It must be understood that the linear programmingproblem size is quadratic with the number of tasks and thus the time to solve itwill be very long, it could be minutes for just a few dozen tasks. You shouldprobably use <c>lp_solve -timeout 1 test.pl -wmps test.mps</c> to convert theproblem to MPS format and then use a better solver, <c>glpsol</c> might bebetter than <c>lp_solve</c> for instance (the <c>--pcost</c> option may beuseful), but sometimes doesn't manage to converge. <c>cbc</c> might lookslower, but it is parallel. For <c>lp_solve</c>, be sure to try at least all the<c>-B</c> options. For instance, we often just use <c>lp_solve -cc -B1 -Bb-Bg -Bp -Bf -Br -BG -Bd -Bs -BB -Bo -Bc -Bi</c> , and the <c>-gr</c> option canalso be quite useful. The resulting schedule can be observed by usingthe tool <c>starpu_lp2paje</c>, which converts it into the Pajeformat.Data transfer time can only be taken into account when <c>deps</c> is set. Onlydata transfers inferred from implicit data dependencies between tasks are takeninto account. Other data transfers are assumed to be completely overlapped.Setting <c>deps</c> to 0 will only take into account the actual computationson processing units. It however still properly takes into account the varyingperformances of kernels and processing units, which is quite more accurate thanjust comparing StarPU performances with the fastest of the kernels being used.The <c>prio</c> parameter tells StarPU whether to simulate taking into accountthe priorities as the StarPU scheduler would, i.e. schedule prioritizedtasks before less prioritized tasks, to check to which extend this resultsto a less optimal solution. This increases even more computation time.\section MemoryFeedback Memory FeedbackIt is possible to enable memory statistics. To do so, you need to passthe option \ref enable-memory-stats "--enable-memory-stats" when running <c>configure</c>. It is thenpossible to call the function starpu_data_display_memory_stats() todisplay statistics about the current data handles registered within StarPU.Moreover, statistics will be displayed at the end of the execution ondata handles which have not been cleared out. This can be disabled bysetting the environment variable \ref STARPU_MEMORY_STATS to <c>0</c>.For example, if you do not unregister data at the end of the complexexample, you will get something similar to:\verbatim$ STARPU_MEMORY_STATS=0 ./examples/interface/complexComplex[0] = 45.00 + 12.00 iComplex[0] = 78.00 + 78.00 iComplex[0] = 45.00 + 12.00 iComplex[0] = 45.00 + 12.00 i\endverbatim\verbatim$ STARPU_MEMORY_STATS=1 ./examples/interface/complexComplex[0] = 45.00 + 12.00 iComplex[0] = 78.00 + 78.00 iComplex[0] = 45.00 + 12.00 iComplex[0] = 45.00 + 12.00 i#---------------------Memory stats:#-------Data on Node #3#-----Data : 0x553ff40Size : 16#--Data access stats/!\ Work UnderwayNode #0	Direct access : 4	Loaded (Owner) : 0	Loaded (Shared) : 0	Invalidated (was Owner) : 0Node #3	Direct access : 0	Loaded (Owner) : 0	Loaded (Shared) : 1	Invalidated (was Owner) : 0#-----Data : 0x5544710Size : 16#--Data access stats/!\ Work UnderwayNode #0	Direct access : 2	Loaded (Owner) : 0	Loaded (Shared) : 1	Invalidated (was Owner) : 1Node #3	Direct access : 0	Loaded (Owner) : 1	Loaded (Shared) : 0	Invalidated (was Owner) : 0\endverbatim\section DataStatistics Data StatisticsDifferent data statistics can be displayed at the end of the executionof the application. To enable them, you need to define the environmentvariable \ref STARPU_ENABLE_STATS. When callingstarpu_shutdown() various statistics will be displayed,execution, MSI cache statistics, allocation cache statistics, and datatransfer statistics. The display can be disabled by setting theenvironment variable \ref STARPU_STATS to <c>0</c>.\verbatim$ ./examples/cholesky/cholesky_tagComputation took (in ms)518.16Synthetic GFlops : 44.21#---------------------MSI cache stats :TOTAL MSI stats	hit 1622 (66.23 %)	miss 827 (33.77 %)...\endverbatim\verbatim$ STARPU_STATS=0 ./examples/cholesky/cholesky_tagComputation took (in ms)518.16Synthetic GFlops : 44.21\endverbatim// TODO: data transfer stats are similar to the ones displayed when// setting STARPU_BUS_STATS*/
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