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391 <div class="document">
394 <div class="line-block">
395 <div class="line">Copyright</div>
396 <div class="line-block">
397 <div class="line">Markus Wittmann, 2016-2018</div>
398 <div class="line">RRZE, University of Erlangen-Nuremberg, Germany</div>
399 <div class="line">markus.wittmann -at- fau.de or hpc -at- rrze.fau.de</div>
400 <div class="line"><br /></div>
401 <div class="line">Viktor Haag, 2016</div>
402 <div class="line">LSS, University of Erlangen-Nuremberg, Germany</div>
403 <div class="line"><br /></div>
405 <div class="line">This file is part of the Lattice Boltzmann Benchmark Kernels (LbmBenchKernels).</div>
406 <div class="line"><br /></div>
407 <div class="line">LbmBenchKernels is free software: you can redistribute it and/or modify</div>
408 <div class="line">it under the terms of the GNU General Public License as published by</div>
409 <div class="line">the Free Software Foundation, either version 3 of the License, or</div>
410 <div class="line">(at your option) any later version.</div>
411 <div class="line"><br /></div>
412 <div class="line">LbmBenchKernels is distributed in the hope that it will be useful,</div>
413 <div class="line">but WITHOUT ANY WARRANTY; without even the implied warranty of</div>
414 <div class="line">MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</div>
415 <div class="line">GNU General Public License for more details.</div>
416 <div class="line"><br /></div>
417 <div class="line">You should have received a copy of the GNU General Public License</div>
418 <div class="line">along with LbmBenchKernels. If not, see <<a class="reference external" href="http://www.gnu.org/licenses/">http://www.gnu.org/licenses/</a>>.</div>
420 <p><strong>LBM Benchmark Kernels Documentation</strong></p>
421 <div class="contents topic" id="contents">
422 <p class="topic-title first">Contents</p>
423 <ul class="auto-toc simple">
424 <li><a class="reference internal" href="#introduction" id="id5">1 Introduction</a></li>
425 <li><a class="reference internal" href="#compilation" id="id6">2 Compilation</a><ul class="auto-toc">
426 <li><a class="reference internal" href="#debug-and-verification" id="id7">2.1 Debug and Verification</a></li>
427 <li><a class="reference internal" href="#release-and-verification" id="id8">2.2 Release and Verification</a></li>
428 <li><a class="reference internal" href="#benchmarking" id="id9">2.3 Benchmarking</a></li>
429 <li><a class="reference internal" href="#compilers" id="id10">2.4 Compilers</a></li>
430 <li><a class="reference internal" href="#floating-point-precision" id="id11">2.5 Floating Point Precision</a></li>
431 <li><a class="reference internal" href="#cleaning" id="id12">2.6 Cleaning</a></li>
432 <li><a class="reference internal" href="#options-summary" id="id13">2.7 Options Summary</a></li>
435 <li><a class="reference internal" href="#invocation" id="id14">3 Invocation</a><ul class="auto-toc">
436 <li><a class="reference internal" href="#command-line-parameters" id="id15">3.1 Command Line Parameters</a></li>
437 <li><a class="reference internal" href="#kernels" id="id16">3.2 Kernels</a></li>
440 <li><a class="reference internal" href="#id2" id="id17">4 Benchmarking</a><ul class="auto-toc">
441 <li><a class="reference internal" href="#intel-compiler" id="id18">4.1 Intel Compiler</a></li>
442 <li><a class="reference internal" href="#pinning" id="id19">4.2 Pinning</a></li>
443 <li><a class="reference internal" href="#general-remarks" id="id20">4.3 General Remarks</a></li>
444 <li><a class="reference internal" href="#padding" id="id21">4.4 Padding</a></li>
447 <li><a class="reference internal" href="#geometries" id="id22">5 Geometries</a></li>
448 <li><a class="reference internal" href="#performance-results" id="id23">6 Performance Results</a><ul class="auto-toc">
449 <li><a class="reference internal" href="#machine-specifications" id="id24">6.1 Machine Specifications</a></li>
450 <li><a class="reference internal" href="#single-socket-results" id="id25">6.2 Single Socket Results</a></li>
453 <li><a class="reference internal" href="#licence" id="id26">7 Licence</a></li>
454 <li><a class="reference internal" href="#acknowledgements" id="id27">8 Acknowledgements</a></li>
455 <li><a class="reference internal" href="#bibliography" id="id28">9 Bibliography</a></li>
458 <div class="section" id="introduction">
459 <h1><a class="toc-backref" href="#id5">1 Introduction</a></h1>
460 <p>The lattice Boltzmann (LBM) benchmark kernels are a collection of LBM kernel
462 <p><strong>AS SUCH THE LBM BENCHMARK KERNELS ARE NO FULLY EQUIPPED CFD SOLVER AND SOLELY
463 SERVES THE PURPOSE OF STUDYING POSSIBLE PERFORMANCE OPTIMIZATIONS AND/OR
464 EXPERIMENTS.</strong></p>
465 <p>Currently all kernels utilize a D3Q19 discretization and the
466 two-relaxation-time (TRT) collision operator <a class="citation-reference" href="#ginzburg-2008" id="id1">[ginzburg-2008]</a>.
467 All operations are carried out in double or single precision arithmetic.</p>
469 <div class="section" id="compilation">
470 <h1><a class="toc-backref" href="#id6">2 Compilation</a></h1>
471 <p>The benchmark framework currently supports only Linux systems and the GCC and
472 Intel compilers. Every other configuration probably requires adjustment inside
473 the code and the makefiles. Furthermore some code might be platform or at least
475 <p>The benchmark can be build via <tt class="docutils literal">make</tt> from the <tt class="docutils literal">src</tt> subdirectory. This will
476 generate one binary which hosts all implemented benchmark kernels.</p>
477 <p>Binaries are located under the <tt class="docutils literal">bin</tt> subdirectory and will have different names
478 depending on compiler and build configuration.</p>
479 <p>Compilation can target debug or release builds. Combined with both build types
480 verification can be enabled, which increases the runtime and hence is not
481 suited for benchmarking.</p>
482 <div class="section" id="debug-and-verification">
483 <h2><a class="toc-backref" href="#id7">2.1 Debug and Verification</a></h2>
484 <pre class="literal-block">
485 make BUILD=debug BENCHMARK=off
487 <p>Running <tt class="docutils literal">make</tt> with <tt class="docutils literal">BUILD=debug</tt> builds the debug version of
488 the benchmark kernels, where no optimizations are performed, line numbers and
489 debug symbols are included as well as <tt class="docutils literal">DEBUG</tt> will be defined. The resulting
490 binary will be found in the <tt class="docutils literal">bin</tt> subdirectory and named
491 <tt class="docutils literal"><span class="pre">lbmbenchk-linux-<compiler>-debug</span></tt>.</p>
492 <p>Specifying <tt class="docutils literal">BENCHMARK=off</tt> turns on verification
493 (<tt class="docutils literal">VERIFICATION=on</tt>), statistics (<tt class="docutils literal">STATISTICS=on</tt>), and VTK output
494 (<tt class="docutils literal">VTK_OUTPUT=on</tt>) enabled.</p>
495 <p>Please note that the generated binary will therefore
496 exhibit a poor performance.</p>
498 <div class="section" id="release-and-verification">
499 <h2><a class="toc-backref" href="#id8">2.2 Release and Verification</a></h2>
500 <p>Verification with the debug builds can be extremely slow. Hence verification
501 capabilities can be build with release builds:</p>
502 <pre class="literal-block">
506 <div class="section" id="benchmarking">
507 <h2><a class="toc-backref" href="#id9">2.3 Benchmarking</a></h2>
508 <p>To generate a binary for benchmarking run make with</p>
509 <pre class="literal-block">
512 <p>As default <tt class="docutils literal">BENCHMARK=on</tt> and <tt class="docutils literal">BUILD=release</tt> is set, where
513 <tt class="docutils literal">BUILD=release</tt> turns optimizations on and <tt class="docutils literal">BENCHMARK=on</tt> disables
514 verfification, statistics, and VTK output.</p>
515 <p>See Options Summary below for further description of options which can be
516 applied, e.g. TARCH as well as the Benchmarking section.</p>
518 <div class="section" id="compilers">
519 <h2><a class="toc-backref" href="#id10">2.4 Compilers</a></h2>
520 <p>Currently only the GCC and Intel compiler under Linux are supported. Between
521 both configuration can be chosen via <tt class="docutils literal"><span class="pre">CONFIG=linux-gcc</span></tt> or
522 <tt class="docutils literal"><span class="pre">CONFIG=linux-intel</span></tt>.</p>
524 <div class="section" id="floating-point-precision">
525 <h2><a class="toc-backref" href="#id11">2.5 Floating Point Precision</a></h2>
526 <p>As default double precision data types are used for storing PDFs and floating
527 point constants. Furthermore, this is the default for the intrincis kernels.
528 With the <tt class="docutils literal">PRECISION=sp</tt> variable this can be changed to single precision.</p>
529 <pre class="literal-block">
530 make PRECISION=sp # build for single precision kernels
532 make PRECISION=dp # build for double precision kernels (defalt)
535 <div class="section" id="cleaning">
536 <h2><a class="toc-backref" href="#id12">2.6 Cleaning</a></h2>
537 <p>For each configuration and build (debug/release) a subdirectory under the
538 <tt class="docutils literal">src/obj</tt> directory is created where the dependency and object files are
541 <pre class="literal-block">
542 make CONFIG=... BUILD=... clean
544 <p>a specific combination is select and cleaned, whereas with</p>
545 <pre class="literal-block">
548 <p>all object and dependency files are deleted.</p>
550 <div class="section" id="options-summary">
551 <h2><a class="toc-backref" href="#id13">2.7 Options Summary</a></h2>
552 <p>Options that can be specified when building the suite with make:</p>
553 <table border="1" class="docutils">
560 <thead valign="bottom">
561 <tr><th class="head">name</th>
562 <th class="head">values</th>
563 <th class="head">default</th>
564 <th class="head">description</th>
568 <tr><td>BENCHMARK</td>
571 <td>If enabled, disables VERIFICATION, STATISTICS, VTK_OUTPUT. If disabled enables the three former options.</td>
574 <td>debug, release</td>
576 <td>debug: no optimization, debug symbols, DEBUG defined. release: optimizations enabled.</td>
579 <td>linux-gcc, linux-intel</td>
581 <td>Select GCC or Intel compiler.</td>
586 <td>Determines which ISA extension is used for macro definitions of the intrinsics. This is <em>not</em> the architecture the compiler generates code for.</td>
591 <td>OpenMP, i.,e.. threading support.</td>
593 <tr><td>PRECISION</td>
596 <td>Floating point precision used for data type, arithmetic, and intrincics.</td>
598 <tr><td>STATISTICS</td>
601 <td>View statistics, like density etc, during simulation.</td>
606 <td>Via TARCH the architecture the compiler generates code for can be overridden. The value depends on the chosen compiler.</td>
608 <tr><td>VERIFICATION</td>
611 <td>Turn verification on/off.</td>
613 <tr><td>VTK_OUTPUT</td>
616 <td>Enable/Disable VTK file output.</td>
622 <div class="section" id="invocation">
623 <h1><a class="toc-backref" href="#id14">3 Invocation</a></h1>
624 <p>Running the binary will print among the GPL licence header a line like the following:</p>
625 <pre class="literal-block">
626 LBM Benchmark Kernels 0.1, compiled Jul 5 2017 21:59:22, type: verification
628 <p>if verfication was enabled during compilation or</p>
629 <pre class="literal-block">
630 LBM Benchmark Kernels 0.1, compiled Jul 5 2017 21:59:22, type: benchmark
632 <p>if verfication was disabled during compilation.</p>
633 <div class="section" id="command-line-parameters">
634 <h2><a class="toc-backref" href="#id15">3.1 Command Line Parameters</a></h2>
635 <p>Running the binary with <tt class="docutils literal"><span class="pre">-h</span></tt> list all available parameters:</p>
636 <pre class="literal-block">
640 [-dims XxYyZ] [-geometry box|channel|pipe|blocks[-<block size>]] [-iterations <iterations>] [-lattice-dump-ascii]
641 [-rho-in <density>] [-rho-out <density] [-omega <omega>] [-kernel <kernel>]
643 [-t <number of threads>]
646 -- <kernel specific parameters>
648 -list List available kernels.
650 -dims XxYxZ Specify geometry dimensions.
652 -geometry blocks-<block size>
653 Geometetry with blocks of size <block size> regularily layout out.
655 <p>If an option is specified multiple times the last one overrides previous ones.
656 This holds also true for <tt class="docutils literal"><span class="pre">-verify</span></tt> which sets geometry dimensions,
657 iterations, etc, which can afterward be override, e.g.:</p>
658 <pre class="literal-block">
659 $ bin/lbmbenchk-linux-intel-release-dp -verfiy -dims 32x32x32
661 <p>Kernel specific parameters can be obtained via selecting the specific kernel
662 and passing <tt class="docutils literal"><span class="pre">-h</span></tt> as parameter:</p>
663 <pre class="literal-block">
664 $ bin/lbmbenchk-linux-intel-release-dp -kernel kernel-name -- -h
667 [-blk <n>] [-blk-[xyz] <n>]
669 <p>A list of all available kernels can be obtained via <tt class="docutils literal"><span class="pre">-list</span></tt>:</p>
670 <pre class="literal-block">
671 $ ../bin/lbmbenchk-linux-gcc-debug-dp -list
672 Lattice Boltzmann Benchmark Kernels (LbmBenchKernels) Copyright (C) 2016, 2017 LSS, RRZE
673 This program comes with ABSOLUTELY NO WARRANTY; for details see LICENSE.
674 This is free software, and you are welcome to redistribute it under certain conditions.
676 LBM Benchmark Kernels 0.1, compiled Jul 5 2017 21:59:22, type: verification
677 Available kernels to benchmark:
682 list-pull-split-nt-1s-soa
683 list-pull-split-nt-2s-soa
698 <div class="section" id="kernels">
699 <h2><a class="toc-backref" href="#id16">3.2 Kernels</a></h2>
700 <p>The following list shortly describes available kernels:</p>
702 <li><strong>push-soa/push-aos/pull-soa/pull-aos</strong>:
703 Unoptimized kernels (but stream/collide are already fused) using two grids as
704 source and destination. Implement push/pull semantics as well structure of
705 arrays (soa) or array of structures (aos) layout.</li>
706 <li><strong>blk-push-soa/blk-push-aos/blk-pull-soa/blk-pull-aos</strong>:
707 The same as the unoptimized kernels without the blk prefix, except that they support
708 spatial blocking, i.e. loop blocking of the three loops used to iterate over
709 the lattice. Here manual work sharing for OpenMP is used.</li>
710 <li><strong>aa-aos/aa-soa</strong>:
711 Straight forward implementation of AA pattern on full array with blocking support.
712 Manual work sharing for OpenMP is used. Domain is partitioned only along the x dimension.</li>
713 <li><strong>aa-vec-soa/aa-vec-sl-soa</strong>:
714 Optimized AA kernel with intrinsics on full array. aa-vec-sl-soa uses only
715 one loop for iterating over the lattice instead of three nested ones.</li>
716 <li><strong>list-push-soa/list-push-aos/list-pull-soa/list-pull-aos</strong>:
717 The same as the unoptimized kernels without the list prefix, but for indirect addressing.
718 Here only a 1D vector of is used to store the fluid nodes, omitting the
719 obstacles. An adjacency list is used to recover the neighborhood associations.</li>
720 <li><strong>list-pull-split-nt-1s-soa/list-pull-split-nt-2s-soa</strong>:
721 Optimized variant of list-pull-soa. Chunks of the lattice are processed as
722 once. Postcollision values are written back via nontemporal stores in 18 (1s)
723 or 9 (2s) loops.</li>
724 <li><strong>list-aa-aos/list-aa-soa</strong>:
725 Unoptimized implementation of the AA pattern for the 1D vector with adjacency
726 list. Supported are array of structures (aos) and structure of arrays (soa)
727 data layout is supported.</li>
728 <li><strong>list-aa-ria-soa</strong>:
729 Implementation of AA pattern with intrinsics for the 1D vector with adjacency
730 list. Furthermore it contains a vectorized even time step and run length
731 coding to reduce the loop balance of the odd time step.</li>
732 <li><strong>list-aa-pv-soa</strong>:
733 All optimizations of list-aa-ria-soa. Additional with partial vectorization
734 of the odd time step.</li>
736 <p>Note that all array of structures (aos) kernels might require blocking
737 (depending on the domain size) to reach the performance of their structure of
738 arrays (soa) counter parts.</p>
739 <p>The following table summarizes the properties of the kernels. Here <strong>D</strong> means
740 direct addressing, i.e. full array, <strong>I</strong> means indirect addressing, i.e. 1D
741 vector with adjacency list, <strong>x</strong> means supported, whereas <strong>--</strong> means unsupported.
742 The loop balance B_l is computed for D3Q19 model with <strong>double precision</strong> floating
743 point for PDFs (8 byte) and 4 byte integers for the index (adjacency list).
744 As list-aa-ria-soa and list-aa-pv-soa support run length coding their effective
745 loop balance depends on the geometry. The effective loop balance is printed
747 <table border="1" class="docutils">
757 <thead valign="bottom">
758 <tr><th class="head">kernel name</th>
759 <th class="head">prop. step</th>
760 <th class="head">data layout</th>
761 <th class="head">addr.</th>
762 <th class="head">parallel</th>
763 <th class="head">blocking</th>
764 <th class="head">B_l [B/FLUP]</th>
768 <tr><td>push-soa</td>
776 <tr><td>push-aos</td>
784 <tr><td>pull-soa</td>
792 <tr><td>pull-aos</td>
800 <tr><td>blk-push-soa</td>
808 <tr><td>blk-push-aos</td>
816 <tr><td>blk-pull-soa</td>
824 <tr><td>blk-pull-aos</td>
848 <tr><td>aa-vec-soa</td>
856 <tr><td>aa-vec-sl-soa</td>
864 <tr><td>list-push-soa</td>
872 <tr><td>list-push-aos</td>
880 <tr><td>list-pull-soa</td>
888 <tr><td>list-pull-aos</td>
896 <tr><td>list-pull-split-nt-1s</td>
904 <tr><td>list-pull-split-nt-2s</td>
912 <tr><td>list-aa-soa</td>
920 <tr><td>list-aa-aos</td>
928 <tr><td>list-aa-ria-soa</td>
936 <tr><td>list-aa-pv-soa</td>
948 <div class="section" id="id2">
949 <h1><a class="toc-backref" href="#id17">4 Benchmarking</a></h1>
950 <p>Correct benchmarking is a nontrivial task. Whenever benchmark results should be
951 created make sure the binary was compiled with:</p>
953 <li><tt class="docutils literal">BENCHMARK=on</tt> (default if not overriden) and</li>
954 <li><tt class="docutils literal">BUILD=release</tt> (default if not overriden) and</li>
955 <li>the correct ISA for macros is used, selected via <tt class="docutils literal">ISA</tt> and</li>
956 <li>use <tt class="docutils literal">TARCH</tt> to specify the architecture the compiler generates code for.</li>
958 <div class="section" id="intel-compiler">
959 <h2><a class="toc-backref" href="#id18">4.1 Intel Compiler</a></h2>
960 <p>For the Intel compiler one can specify depending on the target ISA extension:</p>
962 <li>AVX: <tt class="docutils literal"><span class="pre">TARCH=-xAVX</span></tt></li>
963 <li>AVX2 and FMA: <tt class="docutils literal"><span class="pre">TARCH=-xCORE-AVX2,-fma</span></tt></li>
964 <li>AVX512: <tt class="docutils literal"><span class="pre">TARCH=-xCORE-AVX512</span></tt></li>
965 <li>KNL: <tt class="docutils literal"><span class="pre">TARCH=-xMIC-AVX512</span></tt></li>
967 <p>Compiling for an architecture supporting AVX (Sandy Bridge, Ivy Bridge):</p>
968 <pre class="literal-block">
969 make ISA=avx TARCH=-xAVX
971 <p>Compiling for an architecture supporting AVX2 (Haswell, Broadwell):</p>
972 <pre class="literal-block">
973 make ISA=avx TARCH=-xCORE-AVX2,-fma
975 <p>WARNING: ISA is here still set to <tt class="docutils literal">avx</tt> as currently we have the FMA intrinsics not
976 implemented. This might change in the future.</p>
977 <p>Compiling for an architecture supporting AVX-512 (Skylake):</p>
978 <pre class="literal-block">
979 make ISA=avx TARCH=-xCORE-AVX512
981 <p>WARNING: ISA is here still set to <tt class="docutils literal">avx</tt> as currently we have no implementation for the
982 AVX512 intrinsics. This might change in the future.</p>
984 <div class="section" id="pinning">
985 <h2><a class="toc-backref" href="#id19">4.2 Pinning</a></h2>
986 <p>During benchmarking pinning should be used via the <tt class="docutils literal"><span class="pre">-pin</span></tt> parameter. Running
987 a benchmark with 10 threads and pin them to the first 10 cores works like</p>
988 <pre class="literal-block">
989 $ bin/lbmbenchk-linux-intel-release-dp ... -t 10 -pin $(seq -s , 0 9)
992 <div class="section" id="general-remarks">
993 <h2><a class="toc-backref" href="#id20">4.3 General Remarks</a></h2>
994 <p>Things the binary does nor check or control:</p>
996 <li>transparent huge pages: when allocating memory small 4 KiB pages might be
997 replaced with larger ones. This is in general a good thing, but if this is
998 really the case, depends on the system settings (check e.g. the status of
999 <tt class="docutils literal">/sys/kernel/mm/transparent_hugepage/enabled</tt>).
1000 Currently <tt class="docutils literal">madvise(MADV_HUGEPAGE)</tt> is used for allocations which are aligned to
1001 a 4 KiB page, which should be the case for the lattices.
1002 This should result in huge pages except THP is disabled on the machine.
1003 (NOTE: madvise() is used if <tt class="docutils literal">HAVE_HUGE_PAGES</tt> is defined, which is currently
1004 hard coded defined in <tt class="docutils literal">Memory.c</tt>).</li>
1005 <li>CPU/core frequency: For reproducible results the frequency of all cores
1006 should be fixed.</li>
1007 <li>NUMA placement policy: The benchmark assumes a first touch policy, which
1008 means the memory will be placed at the NUMA domain the touching core is
1009 associated with. If a different policy is in place or the NUMA domain to be
1010 used is already full memory might be allocated in a remote domain. Accesses
1011 to remote domains typically have a higher latency and lower bandwidth.</li>
1012 <li>System load: interference with other application, especially on desktop
1013 systems should be avoided.</li>
1014 <li>Padding: For SoA based kernels the number of (fluid) nodes is automatically
1015 adjusted so that no cache or TLB thrashing should occur. The parameters are
1016 optimized for current Intel based systems. For more details look into the
1017 padding section.</li>
1018 <li>CPU dispatcher function: the compiler might add different versions of a
1019 function for different ISA extensions. Make sure the code you might think is
1020 executed is actually the code which is executed.</li>
1023 <div class="section" id="padding">
1024 <h2><a class="toc-backref" href="#id21">4.4 Padding</a></h2>
1025 <p>With correct padding cache and TLB thrashing can be avoided. Therefore the
1026 number of (fluid) nodes used in the data layout is artificially increased.</p>
1027 <p>Currently automatic padding is active for kernels which support it. It can be
1028 controlled via the kernel parameter (i.e. parameter after the <tt class="docutils literal"><span class="pre">--</span></tt>)
1029 <tt class="docutils literal"><span class="pre">-pad</span></tt>. Supported values are <tt class="docutils literal">auto</tt> (default), <tt class="docutils literal">no</tt> (to disable padding),
1030 or a manual padding.</p>
1031 <p>Automatic padding tries to avoid cache and TLB thrashing and pads for a 32
1032 entry (huge pages) TLB with 8 sets and a 512 set (L2) cache. This reflects the
1033 parameters of current Intel based processors.</p>
1034 <p>Manual padding is done via a padding string and has the format
1035 <tt class="docutils literal"><span class="pre">mod_1+offset_1(,mod_n+offset_n)</span></tt>, which specifies numbers of bytes.
1036 SoA data layouts can exhibit TLB thrashing. Therefore we want to distribute the
1037 19 pages with one lattice (36 with two lattices) we are concurrently accessing
1038 over as much sets in the TLB as possible.
1039 This is controlled by the distance between the accessed pages, which is the
1040 number of (fluid) nodes in between them and can be adjusted by adding further
1042 We want the distance d (in bytes) between two accessed pages to be e.g.
1043 <strong>d % (PAGE_SIZE * TLB_SETS) = PAGE_SIZE</strong>.
1044 This would distribute the pages evenly over the sets. Hereby <strong>PAGE_SIZE * TLB_SETS</strong>
1045 would be our <tt class="docutils literal">mod_1</tt> and <strong>PAGE_SIZE</strong> (after the =) our <tt class="docutils literal">offset_1</tt>.
1046 Measurements show that with only a quarter of half of a page size as offset
1047 higher performance is achieved, which is done by automatic padding.
1048 On top of this padding more paddings can be added. They are just added to the
1049 padding string and are separated by commas.</p>
1050 <p>A zero modulus in the padding string has a special meaning. Here the
1051 corresponding offset is just added to the number of nodes. A padding string
1052 like <tt class="docutils literal"><span class="pre">-pad</span> 0+16</tt> would at a static padding of two nodes (one node = 8 b).</p>
1055 <div class="section" id="geometries">
1056 <h1><a class="toc-backref" href="#id22">5 Geometries</a></h1>
1057 <p>TODO: supported geometries: channel, pipe, blocks, fluid</p>
1059 <div class="section" id="performance-results">
1060 <h1><a class="toc-backref" href="#id23">6 Performance Results</a></h1>
1061 <p>The sections lists performance values measured on several machines for
1062 different kernels and geometries and <strong>double precision</strong> floating point data/arithmetic.
1063 The <strong>RFM</strong> column denotes the expected performance as predicted by the
1064 Roofline performance model <a class="citation-reference" href="#williams-2008" id="id3">[williams-2008]</a>.
1065 For performance prediction of each kernel a memory bandwidth benchmark is used
1066 which mimics the kernels memory access pattern and the kernel's loop balance
1067 (see <a class="citation-reference" href="#kernels" id="id4">[kernels]</a> for details).</p>
1068 <div class="section" id="machine-specifications">
1069 <h2><a class="toc-backref" href="#id24">6.1 Machine Specifications</a></h2>
1070 <p><strong>Ivy Bridge, Intel Xeon E5-2660 v2</strong></p>
1072 <li>Ivy Bridge architecture, AVX</li>
1073 <li>10 cores, 2.2 GHz</li>
1074 <li>SMT enabled</li>
1075 <li>memoy bandwidth:<ul>
1076 <li>copy-19 32.7 GB/s</li>
1077 <li>copy-19-nt-sl 35.6 GB/s</li>
1078 <li>update-19 37.4 GB/s</li>
1082 <p><strong>Haswell, Intel Xeon E5-2695 v3</strong></p>
1084 <li>Haswell architecture, AVX2, FMA</li>
1085 <li>14 cores, 2.3 GHz</li>
1086 <li>2 x 7 cores in cluster-on-die (CoD) mode enabled</li>
1087 <li>SMT enabled</li>
1088 <li>memory bandwidth:<ul>
1089 <li>copy-19 47.3 GB/s</li>
1090 <li>copy-19-nt-sl 47.1 GB/s</li>
1091 <li>update-19 44.0 GB/s</li>
1095 <p><strong>Broadwell, Intel Xeon E5-2630 v4</strong></p>
1097 <li>Broadwell architecture, AVX2, FMA</li>
1098 <li>10 cores, 2.2 GHz</li>
1099 <li>SMT disabled</li>
1100 <li>memory bandwidth:<ul>
1101 <li>copy-19 48.0 GB/s</li>
1102 <li>copy-nt-sl-19 48.2 GB/s</li>
1103 <li>update-19 51.1 GB/s</li>
1107 <p><strong>Skylake, Intel Xeon Gold 6148</strong></p>
1108 <p>NOTE: currently we only use AVX2 intrinsics.</p>
1110 <li>Skylake server architecture, AVX2, AVX512, 2 FMA units</li>
1111 <li>20 cores, 2.4 GHz</li>
1112 <li>SMT enabled</li>
1113 <li>memory bandwidth:<ul>
1114 <li>copy-19 89.7 GB/s</li>
1115 <li>copy-19-nt-sl 92.4 GB/s</li>
1116 <li>update-19 93.6 GB/s</li>
1120 <p><strong>Zen, AMD EPYC 7451</strong></p>
1122 <li>Zen architecture, AVX2, FMA</li>
1123 <li>24 cores, 2.3 GHz</li>
1124 <li>SMT enabled</li>
1125 <li>memory bandwidth:<ul>
1126 <li>copy-19 111.9 GB/s</li>
1127 <li>copy-19-nt-sl 111.7 GB/s</li>
1128 <li>update-19 109.2 GB/s</li>
1132 <p><strong>Zen, AMD Ryzen 7 1700X</strong></p>
1134 <li>Zen architecture, AVX2, FMA</li>
1135 <li>8 cores, 3.4 GHz</li>
1136 <li>SMT enabled</li>
1137 <li>memory bandwidth:<ul>
1138 <li>copy-19 27.2 GB/s</li>
1139 <li>copy-19-nt-sl 27.1 GB/s</li>
1140 <li>update-19 26.1 GB/s</li>
1145 <div class="section" id="single-socket-results">
1146 <h2><a class="toc-backref" href="#id25">6.2 Single Socket Results</a></h2>
1148 <li>Geometry dimensions are for all measurements 500x100x100 nodes.</li>
1149 <li>Note the <strong>different scaling on the y axis</strong> of the plots!</li>
1151 <table border="1" class="docutils">
1153 <col width="100%" />
1155 <tbody valign="top">
1156 <tr><td>Ivy Bridge, Intel Xeon E5-2660 v2, Double Precision</td>
1158 <tr><td><img alt="perf_emmy_dp" src="images/benchmark-emmy-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1160 <tr><td>Ivy Bridge, Intel Xeon E5-2660 v2, Single Precision</td>
1162 <tr><td><img alt="perf_emmy_sp" src="images/benchmark-emmy-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1164 <tr><td>Haswell, Intel Xeon E5-2695 v3, Double Precision</td>
1166 <tr><td><img alt="perf_hasep1_dp" src="images/benchmark-hasep1-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1168 <tr><td>Haswell, Intel Xeon E5-2695 v3, Single Precision</td>
1170 <tr><td><img alt="perf_hasep1_sp" src="images/benchmark-hasep1-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1172 <tr><td>Broadwell, Intel Xeon E5-2630 v4, Double Precision</td>
1174 <tr><td><img alt="perf_meggie_dp" src="images/benchmark-meggie-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1176 <tr><td>Broadwell, Intel Xeon E5-2630 v4, Single Precision</td>
1178 <tr><td><img alt="perf_meggie_sp" src="images/benchmark-meggie-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1180 <tr><td>Skylake, Intel Xeon Gold 6148, Double Precision, <strong>NOTE: currently we only use AVX2 intrinsics.</strong></td>
1182 <tr><td><img alt="perf_skylakesp2_dp" src="images/benchmark-skylakesp2-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1184 <tr><td>Skylake, Intel Xeon Gold 6148, Single Precision, <strong>NOTE: currently we only use AVX2 intrinsics.</strong></td>
1186 <tr><td><img alt="perf_skylakesp2_sp" src="images/benchmark-skylakesp2-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1188 <tr><td>Zen, AMD Ryzen 7 1700X, Double Precision</td>
1190 <tr><td><img alt="perf_summitridge1_dp" src="images/benchmark-summitridge1-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1192 <tr><td>Zen, AMD Ryzen 7 1700X, Single Precision</td>
1194 <tr><td><img alt="perf_summitridge1_sp" src="images/benchmark-summitridge1-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1196 <tr><td>Zen, AMD EPYC 7451, Double Precision</td>
1198 <tr><td><img alt="perf_naples1_dp" src="images/benchmark-naples1-dp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1200 <tr><td>Zen, AMD EPYC 7451, Single Precision</td>
1202 <tr><td><img alt="perf_naples1_sp" src="images/benchmark-naples1-sp.png" style="width: 1000.0px; height: 250.0px;" /></td>
1208 <div class="section" id="licence">
1209 <h1><a class="toc-backref" href="#id26">7 Licence</a></h1>
1210 <p>The Lattice Boltzmann Benchmark Kernels are licensed under GPLv3.</p>
1212 <div class="section" id="acknowledgements">
1213 <h1><a class="toc-backref" href="#id27">8 Acknowledgements</a></h1>
1214 <p>This work was funded by BMBF, grant no. 01IH15003A (project SKAMPY).</p>
1215 <p>This work was funded by KONWHIR project OMI4PAPS.</p>
1217 <div class="section" id="bibliography">
1218 <h1><a class="toc-backref" href="#id28">9 Bibliography</a></h1>
1219 <table class="docutils citation" frame="void" id="ginzburg-2008" rules="none">
1220 <colgroup><col class="label" /><col /></colgroup>
1221 <tbody valign="top">
1222 <tr><td class="label"><a class="fn-backref" href="#id1">[ginzburg-2008]</a></td><td>I. Ginzburg, F. Verhaeghe, and D. d'Humières.
1223 Two-relaxation-time lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions.
1224 Commun. Comput. Phys., 3(2):427-478, 2008.</td></tr>
1227 <table class="docutils citation" frame="void" id="williams-2008" rules="none">
1228 <colgroup><col class="label" /><col /></colgroup>
1229 <tbody valign="top">
1230 <tr><td class="label"><a class="fn-backref" href="#id3">[williams-2008]</a></td><td>S. Williams, A. Waterman, and D. Patterson.
1231 Roofline: an insightful visual performance model for multicore architectures.
1232 Commun. ACM, 52(4):65-76, Apr 2009. doi:10.1145/1498765.1498785</td></tr>
1235 <p>Document was generated at 2018-01-09 11:54.</p>