From 85d20472b35a854e4e7545c86ddebe3c317b8153 Mon Sep 17 00:00:00 2001 From: Armin Friedl Date: Thu, 23 Jun 2016 21:22:30 +0200 Subject: [PATCH] report kernels+8er kernel bug behoben --- reduce/reduce | Bin 0 -> 18920 bytes roofline/report/inputs/discussion.tex | 2 + roofline/report/inputs/kernels.tex | 112 + roofline/report/inputs/roofline.tex | 2 +- roofline/report/report.aux | 25 +- roofline/report/report.bbl | 27 +- roofline/report/report.bcf | 6 +- roofline/report/report.blg | 24 +- roofline/report/report.fdb_latexmk | 40 +- roofline/report/report.fls | 42 +- roofline/report/report.log | 197 +- roofline/report/report.pdf | Bin 290073 -> 328260 bytes roofline/report/report.tex | 13 +- roofline/report/report.toc | 6 + .../report/res/rooftop-eps-converted-to.pdf | Bin 0 -> 22114 bytes roofline/report/res/rooftop.eps | 2350 +++++++++++++++++ roofline/report/res/rooftop.png | Bin 38798 -> 0 bytes roofline/report/roofline.bib | 16 +- roofline/src/Makefile | 20 +- roofline/src/aikern.c | 59 +- roofline/src/roofline | Bin 18136 -> 26432 bytes roofline/src/roofline_avx | Bin 18136 -> 26328 bytes roofline/src/roofline_avxfma | Bin 14040 -> 14040 bytes roofline/src/roofline_avxfmafast | Bin 0 -> 18136 bytes roofline/src/roofline_o3 | Bin 18136 -> 22232 bytes roofline/src/roofline_o3avx | Bin 18136 -> 18136 bytes 26 files changed, 2743 insertions(+), 198 deletions(-) create mode 100755 reduce/reduce create mode 100644 roofline/report/res/rooftop-eps-converted-to.pdf create mode 100644 roofline/report/res/rooftop.eps delete mode 100644 roofline/report/res/rooftop.png create mode 100755 roofline/src/roofline_avxfmafast diff --git a/reduce/reduce b/reduce/reduce new file mode 100755 index 0000000000000000000000000000000000000000..0d1319adea704242ddd5c0985fa20575f7cd4b5a GIT binary patch literal 18920 zcmeHPe{@vUoxhU=i2Rrd8YLpalN~g)CQJgR0d$$k4}8%HL=qs%kI5vNkmw|n&P*Us zRMrrdXN((L*Mn_$WqbNVd-klf$5o(Kf~ZK3yYi#9)}NGC`-T*Vpcu3=`}y8?@64OY zjJ41Vn)rs=D 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definition used the arithmetic intensity is measured by operations per byte. This might not be adequat for haswell processors (and later). Due to the fused multiply-add\footnote{although called multiply-add there are 36 different slightly instructions} extension two floating point operations can be performed with a single instruction. - worse results for 4 threads @ NUMA-STREAM not necessarily expected +- better results for triad possibly due to combined storage in FMA +- striding for arrays %%% Local Variables: %%% mode: latex diff --git a/roofline/report/inputs/kernels.tex b/roofline/report/inputs/kernels.tex index 09e87b3..c69863b 100644 --- a/roofline/report/inputs/kernels.tex +++ b/roofline/report/inputs/kernels.tex @@ -1,3 +1,115 @@ +Kernels with operational intensity (OI) of $\rfrac{1}{16}$ and $8$ have been implemented. The kernels are introduced in the following sections. + +However the effective operational intensity of a given kernel in a high-level language (as C) is not obvious when compiled to processor instructions. Furthermore, due to today's advanced processor architecture, adaptions had to be made to account for special capabilites. This resulted in several different kernels. Not all of them are machine independent with regard to operational intensity. + +All kernels were compiled with \verb|gcc 5.3.1| and different options. The compilation was checked with \verb|objdump -d -M intel-mnemonics|. For a more elaborate analysis of the disassembly on the testers computer, please refer to the header file \verb|aikern.h| that should come with this report. Additionally \verb|Makefile| provides all informations about the used and tested compiler options. + +Good results\footnote{all, including the special FMA kernels, use only expected memory access, doing everything else in registers} were achieved with \verb|-O2 -mavx -mfma|. But \verb|-O2 -maxv -mfma| is a tradeoff between the best possible results and obviously correct compiled code. In fact the assembly almost looks like handwritten. If even more optimization is wanted \verb|-O3| can be used. To fully utilize FMA with packed doubles \verb|-Ofast| or \verb|-Ofast -ffast-math| has to be used. Be aware that more optimization than \verb|-O2 -maxv -mfma| results in a very hard to understand disassembly. \verb|-ffast-math| can even introduce rounding errors. It is not completely obvious that the highly optimized compiled code still has the wanted operational intensity. \verb|-O0| never works out. + +\bigskip +\bigskip +\begin{footnotesize} +\noindent\emph{Remark:} Contrary to popular believe the roofline model is built atop the notion of operational intensity\footnote{FLOPs against bytes written to DRAM} kernels. The differences to arithmetic intensities are outlined in~\textcite{williams2009}. Depending on the definition used these two terms are not necessarily interchangeable. The notion of operational intensity in the following sections might be what some would understand by the term arithmetic itensity. +\end{footnotesize} + +\subsection{1/16 $\neq$ 1/16. Or: The Fancy Arithmetics of a Compiler} + +In order to understand why the following kernels are implemented the way they are, an example of a badly behaving $\rfrac{1}{16}$ OI kernel is given in~\prettyref{lst:1-16-simple-dangerous}. The kernel has one FP operation ($*$) and reads 16 bytes (a[i], b[i]) from memory. But in practice this algorithm does not work as expected. There are several ways how one could write the same kernel. + +\begin{itemize} +\item Submitting \verb|volatile|. This results in the loop being optimized away completely for optimization levels above \verb|-O0|. +\item Using no optimization i.e. \verb|-O0|. No advanced features of the processor will be used (e.g., FMA requires at least \verb|-O2|). Also just about everything is read and written from and to the stack. Even loop variables. One may now assume that this is cached anyway --- or one ain't so. +\item Using \verb|volatile| and optimization. When volatile is used gcc reads and writes variable \verb|tmp| from and to the stack, even in \verb|-O3|. If tmp is cached or not is hard to predict. It's not improbable but relying on that assumption can yield wrong results. +\item Using \verb|register|, \verb|volatile| and optimization. Unfortunately \verb|register| just \emph{advises} the compiler to use a register. It does not force the compiler to do so. Seemingly \verb|volatile| overrules \verb|register| in this case -- \verb|tmp| is read and written from and to the stack. Again assuming any caching behaviour is adventurous at least. +\end{itemize} + +In the worst case found (no optimization, no volatile, no register) this results in reads of 16 bytes (a[i],b[i]) plus 8 bytes (i), and writes of 16 bytes (i, tmp assignment). Making no caching assumptions this results in an effective operational intensity of $\rfrac{1}{40}$ for a superficial $\rfrac{1}{16}$ OI kernel. For more complex kernels the results get even worse. A triad \verb|t=a*b+c| will store easy-to-miss intermediate results on the stack if no special care is taken. + +To prevent this, one could write assembly directly or rely on compiler intrinsics. The kernels in this report though consist just of normal C code which was hand-crafted until an acceptable compilation was reached. The generated machine code was disassembled and manually checked for hidden memory access. The results are therefore compiler and machine specific, but should be quite generalizable for the most part. + +\bigskip +\begin{lstlisting}[caption={Simple $\rfrac{1}{16}$ kernel with questionable compiled form}, label=lst:1-16-simple-dangerous] +volatile register double tmp = 0.1; +for(size_t i=0; iintel2016 intel2016 intel2016 - intel2 + intelvfmadd132pd shimpi2012 shimpi2012 berstrom bergstrom2 williams2009 + williams2009 + williams2009 + intelvfmadd132sd + intelvfmadd132pd diff --git a/roofline/report/report.blg b/roofline/report/report.blg index 93cbf64..0acc198 100644 --- a/roofline/report/report.blg +++ b/roofline/report/report.blg @@ -1,14 +1,14 @@ [0] Config.pm:318> INFO - This is Biber 1.8 [0] Config.pm:321> INFO - Logfile is 'report.blg' -[71] biber:275> INFO - === Thu Jun 23, 2016, 02:25:38 -[71] Biber.pm:333> INFO - Reading 'report.bcf' -[152] Biber.pm:630> INFO - Found 7 citekeys in bib section 0 -[164] Biber.pm:3053> INFO - Processing section 0 -[187] Biber.pm:3190> INFO - Looking for bibtex format file 'roofline.bib' for section 0 -[188] bibtex.pm:937> INFO - Decoding LaTeX character macros into UTF-8 -[189] bibtex.pm:812> INFO - Found BibTeX data source 'roofline.bib' -[236] Biber.pm:2939> INFO - Overriding locale 'en_US.UTF-8' default tailoring 'variable = shifted' with 'variable = non-ignorable' -[236] Biber.pm:2945> INFO - Sorting 'entry' list 'nty' keys -[236] Biber.pm:2949> INFO - No sort tailoring available for locale 'en_US.UTF-8' -[252] bbl.pm:482> INFO - Writing 'report.bbl' with encoding 'UTF-8' -[254] bbl.pm:555> INFO - Output to report.bbl +[53] biber:275> INFO - === Thu Jun 23, 2016, 19:53:59 +[53] Biber.pm:333> INFO - Reading 'report.bcf' +[116] Biber.pm:630> INFO - Found 8 citekeys in bib section 0 +[127] Biber.pm:3053> INFO - Processing section 0 +[142] Biber.pm:3190> INFO - Looking for bibtex format file 'roofline.bib' for section 0 +[144] bibtex.pm:937> INFO - Decoding LaTeX character macros into UTF-8 +[144] bibtex.pm:812> INFO - Found BibTeX data source 'roofline.bib' +[179] Biber.pm:2939> INFO - Overriding locale 'en_US.UTF-8' default tailoring 'variable = shifted' with 'variable = non-ignorable' +[179] Biber.pm:2945> INFO - Sorting 'entry' list 'nty' keys +[179] Biber.pm:2949> INFO - No sort tailoring available for locale 'en_US.UTF-8' +[197] bbl.pm:482> INFO - Writing 'report.bbl' with encoding 'UTF-8' +[198] bbl.pm:555> INFO - Output to report.bbl diff --git a/roofline/report/report.fdb_latexmk b/roofline/report/report.fdb_latexmk index 67f1e53..aa0cc97 100644 --- a/roofline/report/report.fdb_latexmk +++ b/roofline/report/report.fdb_latexmk @@ -1,11 +1,11 @@ # Fdb version 3 -["biber report"] 1466641538 "report.bcf" "report.bbl" "report" 1466642333 - "report.bcf" 1466642333 92144 b16bb4d23ff7f0d4a3e0ee2f3a7b2c36 "" - "roofline.bib" 1466632630 3723 5c74ca6da23b4936d86117884f95cb33 "" +["biber report"] 1466704438 "report.bcf" "report.bbl" "report" 1466709195 + "report.bcf" 1466709195 92382 2683b542d57d2326e3b37a6a44222b52 "" + "roofline.bib" 1466704433 4157 226e47c750579a202f66b6f0e4df67bb "" (generated) "report.bbl" "report.blg" -["pdflatex"] 1466642332 "report.tex" "report.pdf" "report" 1466642333 +["pdflatex"] 1466709193 "report.tex" "report.pdf" "report" 1466709195 "/usr/share/texlive/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc" 1136849721 2971 def0b6c1f0b107b3b936def894055589 "" "/usr/share/texlive/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc" 1136849721 2900 1537cc8184ad1792082cd229ecc269f4 "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1272929888 3287 e6b82fe08f5336d4d5ebc73fb1152e87 "" @@ -20,6 +20,7 @@ "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm0900.tfm" 1136768653 3584 d3d8ac8b25ca19c0a40b86a5db1e8ccc "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1095.tfm" 1136768653 3584 929cdff2b7a8c11bd4d49fd68cb0ae70 "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1440.tfm" 1136768653 3584 3169d30142b88a27d4ab0e3468e963a2 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecti0900.tfm" 1136768653 3072 a603fa6d934ebc72197ed1c389943d86 "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecti1095.tfm" 1136768653 3072 b73d2778cc3af44970de4de5e032d7f6 "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ectt1095.tfm" 1136768653 1536 a988bfe554c1f79514bd46d13c3c64ce "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/tcrm1095.tfm" 1136768653 1536 02c06700a42be0f5a28664c7273f82e7 "" @@ -56,6 +57,7 @@ "/usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary9.tfm" 1302307949 848 594c171945930dfc7cc52fb30457c803 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1248133631 32722 d7379af29a190c3f453aba36302ff5a9 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1248133631 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfbx1095.pfb" 1215737283 154600 ea54091d31de803b613ba9e80ca51709 "" @@ -68,6 +70,7 @@ "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm0900.pfb" 1215737283 149037 995a6f1e12c1d647b99b1cf55db78699 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm1095.pfb" 1215737283 145929 f25e56369a345c4ff583b067cd87ce8e "" "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm1440.pfb" 1215737283 131078 d96015a2fa5c350129e933ca070b2484 "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfti0900.pfb" 1215737283 183673 6df73819bb3e1246a6315a4913a2d331 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfti1095.pfb" 1215737283 196446 8fbbe4b97b83e5182def6d29a44e57fb "" "/usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sftt1095.pfb" 1215737283 169670 48d12e69c9a3b23c81f6d703ccbd4554 "" "/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii" 1337017135 71627 94eb9990bed73c364d7f53f960cc8c5b "" @@ -158,8 +161,6 @@ "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg" 1394061314 1828 1429ae58d32ff215bffb2acf697ae41a "" "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty" 1394061314 80361 048fe35275a1096660ea67eecd2213f4 "" "/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty" 1394061314 93168 df9863fadbf023e458067a158925eff9 "" - "/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty" 1394061314 89980 e97cebbc4f0eae4011a8bea389a05d0a "" - "/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty" 1394061314 86841 4fa558f6bbd8f3d49e175c0dd27ff41a "" "/usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty" 1394061314 77029 dfe676ac1c76cfa220c8107472a1da27 "" "/usr/share/texlive/texmf-dist/tex/latex/logreq/logreq.def" 1284153563 1620 fb1c32b818f2058eca187e5c41dfae77 "" "/usr/share/texlive/texmf-dist/tex/latex/logreq/logreq.sty" 1284153563 6187 b27afc771af565d3a9ff1ca7d16d0d46 "" @@ -195,21 +196,22 @@ "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1455657841 31706 2be2b4306fae7fc20493e3b90c2ad04d "" "/usr/share/texlive/texmf-var/web2c/pdftex/pdflatex.fmt" 1457104667 3492982 6abaa3262ef9227a797168d32888676c "" "inputs/introduction.tex" 1466184626 76 eaf0f76fa74815989416f6f6d1c36f8b "" - "inputs/kernels.tex" 1466184646 75 4edfbf753fb138c9886dd119053949bf "" - "inputs/roofline.tex" 1466642331 5522 4541d608767a130965ef6af1061bff79 "" - "report.aux" 1466642333 3974 fbce129a17c9c0f39751b7114db01f4a "" - "report.bbl" 1466641538 6814 69377a156548dd41d6fce56d0861beda "biber report" - "report.out" 1466642333 334 a1cec9b42f1ecf30af112fc058dd7354 "" - "report.run.xml" 1466642333 2317 80d7743117fafc51b1e42b536d793f68 "" - "report.tex" 1466626391 4716 59f1e8b52a6969670880343126dbe52a "" - "report.toc" 1466642333 818 cfda5e6b9084ed337791b495536ef0b7 "" - "res/rooftop.png" 1466641296 38798 e83f8157e0a63985f174d5bf3128cc98 "" + "inputs/kernels.tex" 1466709193 10203 9325fb415b03bebae73e25df31a02d19 "" + "inputs/roofline.tex" 1466704311 5532 18ef3b0c3e19883f9e4d68e1bd73b31b "" + "report.aux" 1466709195 6200 ef3b9dffee45c82bc6071014e35f58b8 "" + "report.bbl" 1466704439 7655 4b5f697a70789470cde9f922b6440ee7 "biber report" + "report.out" 1466709195 566 365a3bdfdb786abd7e70ca003f732afb "" + "report.run.xml" 1466709195 2317 80d7743117fafc51b1e42b536d793f68 "" + "report.tex" 1466708164 4496 4af727a449506efbfccac9df327ec9fe "" + "report.toc" 1466709195 1210 9050233c7a77a885db53f60f534c1c7a "" + "res/rooftop-eps-converted-to.pdf" 1466670002 22114 f6f2c1d53d8b6a5f4042e202648c7b36 "" + "res/rooftop.eps" 1466669975 36013 2a6358f72820d80a6e87ee15e92d5669 "" (generated) - "report-blx.bib" "report.out" "report.toc" - "report.log" - "report.run.xml" "report.bcf" - "report.pdf" + "report.run.xml" + "report-blx.bib" + "report.log" "report.aux" + "report.pdf" diff --git a/roofline/report/report.fls b/roofline/report/report.fls index 0745291..dc0ecc7 100644 --- a/roofline/report/report.fls +++ b/roofline/report/report.fls @@ -218,22 +218,6 @@ INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.dfu INPUT /usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.dfu INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/biblatex/lbx/english.lbx @@ -345,15 +329,25 @@ INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary9.tfm INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary5.tfm -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty -INPUT res/rooftop.png -INPUT ./res/rooftop.png -INPUT ./res/rooftop.png +INPUT res/rooftop.eps +INPUT ./res/rooftop.eps +INPUT ./res/rooftop.eps +INPUT ./res/rooftop-eps-converted-to.pdf +INPUT ./res/rooftop-eps-converted-to.pdf +INPUT ./res/rooftop.eps +INPUT ./res/rooftop-eps-converted-to.pdf +INPUT ./res/rooftop-eps-converted-to.pdf +INPUT ./res/rooftop-eps-converted-to.pdf INPUT inputs/kernels.tex INPUT inputs/kernels.tex +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecti0900.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr12.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmex10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm +INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary10.tfm INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/eccc1095.tfm INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/tcti1095.tfm INPUT report.aux @@ -365,6 +359,7 @@ INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfbx1095.pfb @@ -377,5 +372,6 @@ INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm0800.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm0900.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm1095.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfrm1440.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfti0900.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sfti1095.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sftt1095.pfb diff --git a/roofline/report/report.log b/roofline/report/report.log index 9c6e2da..7f036bc 100644 --- a/roofline/report/report.log +++ b/roofline/report/report.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded format=pdflatex 2016.3.4) 23 JUN 2016 02:38 +This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded format=pdflatex 2016.3.4) 23 JUN 2016 21:13 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1184,30 +1184,6 @@ Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 340. (/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty File: lstlang1.sty 2014/03/04 1.5c listings language file ) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -File: lstlang2.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -File: lstlang3.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -File: lstlang1.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -File: lstlang2.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -File: lstlang3.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang1.sty -File: lstlang1.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang2.sty -File: lstlang2.sty 2014/03/04 1.5c listings language file -) -(/usr/share/texlive/texmf-dist/tex/latex/listings/lstlang3.sty -File: lstlang3.sty 2014/03/04 1.5c listings language file -) (/usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty File: lstmisc.sty 2014/03/04 1.5c (Carsten Heinz) ) @@ -1226,26 +1202,26 @@ Package biblatex Warning: 'babel/polyglossia' detected but 'csquotes' missing. (./report.aux) \openout1 = `report.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 81. -LaTeX Font Info: ... okay on input line 81. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 81. -LaTeX Font Info: Try loading font information for TS1+cmr on input line 81. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 80. +LaTeX Font Info: ... okay on input line 80. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 80. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 80. (/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd File: ts1cmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) -LaTeX Font Info: ... okay on input line 81. +LaTeX Font Info: ... okay on input line 80. (/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] @@ -1276,7 +1252,7 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv e )) \c@lstlisting=\count308 -LaTeX Info: Redefining \microtypecontext on input line 81. +LaTeX Info: Redefining \microtypecontext on input line 80. Package microtype Info: Generating PDF output. Package microtype Info: Character protrusion enabled (level 2). Package microtype Info: Using default protrusion set `alltext'. @@ -1292,7 +1268,7 @@ File: mt-cmr.cfg 2013/05/19 v2.2 microtype config. file: Computer Modern Roman (RS) ) \AtBeginShipoutBox=\box37 -Package hyperref Info: Link coloring ON on input line 81. +Package hyperref Info: Link coloring ON on input line 80. (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section @@ -1302,9 +1278,9 @@ Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO) ) \c@section@level=\count309 ) -LaTeX Info: Redefining \ref on input line 81. -LaTeX Info: Redefining \pageref on input line 81. -LaTeX Info: Redefining \nameref on input line 81. +LaTeX Info: Redefining \ref on input line 80. +LaTeX Info: Redefining \pageref on input line 80. +LaTeX Info: Redefining \nameref on input line 80. (./report.out) (./report.out) \@outlinefile=\write4 @@ -1316,7 +1292,7 @@ Package lastpage Info: Please have a look at the pageslts package at (lastpage) or (lastpage) http://www.ctan.org/tex-archive/ (lastpage) install/macros/latex/contrib/pageslts.tds.zip -(lastpage) ! on input line 81. +(lastpage) ! on input line 80. Package caption Info: Begin \AtBeginDocument code. Package caption Info: End \AtBeginDocument code. Package biblatex Info: Input encoding 'utf8' detected. @@ -1327,9 +1303,9 @@ Package biblatex Info: Automatic encoding selection. Package biblatex Info: Trying to load bibliographic data... Package biblatex Info: ... file 'report.bbl' found. (./report.bbl) -Package biblatex Info: Reference section=0 on input line 81. -Package biblatex Info: Reference segment=0 on input line 81. -LaTeX Font Info: Try loading font information for U+msa on input line 91. +Package biblatex Info: Reference section=0 on input line 80. +Package biblatex Info: Reference segment=0 on input line 80. +LaTeX Font Info: Try loading font information for U+msa on input line 90. (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A @@ -1337,7 +1313,7 @@ File: umsa.fd 2013/01/14 v3.01 AMS symbols A (/usr/share/texlive/texmf-dist/tex/latex/microtype/mt-msa.cfg File: mt-msa.cfg 2006/02/04 v1.1 microtype config. file: AMS symbols (a) (RS) ) -LaTeX Font Info: Try loading font information for U+msb on input line 91. +LaTeX Font Info: Try loading font information for U+msb on input line 90. 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b/roofline/report/report.tex index f0662fc..7688648 100644 --- a/roofline/report/report.tex +++ b/roofline/report/report.tex @@ -46,6 +46,8 @@ \newrefformat{sec}{\hyperref[#1]{Section~\ref*{#1}}} \renewcommand{\arraystretch}{1.2} +\newcommand*\rfrac[2]{{}^{#1}\!/_{#2}}%running fraction with slash - requires math mode + \newcommand\bigforall{\mbox{\Large $\mathsurround0pt\forall$}} \everymath{\displaystyle} @@ -59,7 +61,7 @@ extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8 frame=single, % adds a frame around the code keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible) - language=TeX, % the language of the code + language=C, % the language of the code numbers=left, % where to put the line-numbers; possible values are (none, left, right) numbersep=5pt, % how far the line-numbers are from the code numberstyle=\tiny\color{gray}, % the style that is used for the line-numbers @@ -70,12 +72,9 @@ stepnumber=1, % the step between two line-numbers. If it's 1, each line will be numbered tabsize=2, % sets default tabsize to 2 spaces title=\lstname, % show the filename of files included with \lstinputlisting; also try caption instead of title - emph=[3]{int:,array,set,of,int,if,then,else,constraint,var,union,endif,function,where,in,div,predicate,let,opt,full,format,def,for,True,False,return,or}, - emphstyle=[3]\color{ForestGreen}, - emph=[2]{length,max,forall,startEmptyBuffer,fix,startEmptyBufferShow,exactly,cumulative,occurs,deopt,sum,,all}, - emphstyle=[2]\color{blue}, - commentstyle=\color{BrickRed}, - stringstyle =\color{red}, + keywordstyle=\color{blue}, + morekeywords={size_t}, + commentstyle=\color{ForestGreen} } \begin{document} diff --git a/roofline/report/report.toc b/roofline/report/report.toc index 32f06ea..31e6e11 100644 --- a/roofline/report/report.toc +++ b/roofline/report/report.toc @@ -13,3 +13,9 @@ \contentsline {subsection}{\numberline {2.3}Graph}{3}{subsection.2.3} \defcounter {refsection}{0}\relax \contentsline {section}{\numberline {3}Kernels}{4}{section.3} +\defcounter {refsection}{0}\relax +\contentsline {subsection}{\numberline {3.1}1/16 $\not =$ 1/16. Or: The Fancy Arithmetics of a Compiler}{5}{subsection.3.1} +\defcounter {refsection}{0}\relax +\contentsline {subsection}{\numberline {3.2}The 1/16 OI Kernel}{6}{subsection.3.2} +\defcounter {refsection}{0}\relax +\contentsline {subsection}{\numberline {3.3}The 8 OI Kernel}{6}{subsection.3.3} diff --git a/roofline/report/res/rooftop-eps-converted-to.pdf b/roofline/report/res/rooftop-eps-converted-to.pdf new file mode 100644 index 0000000000000000000000000000000000000000..09ab90bfc48ee30155f8ca77517034d5e950af05 GIT binary patch literal 22114 zcmch<1z1&0*FP*N91*1iqz)w^a0(6_Qo5xPq~p-tp>&soARr(h-616sO1FR_DkUhO zNQr=i@a==%k9zaG|G(dNz1N2qGJE#ynKf(u)|y#sf>l*Yh8xDi2V(8{d?y#g2Zn+j zO>IEJ!Vo32gQc4l7zyO4Lu9P&+|Vvyh>V?y8(Io&=4g%<6$QDvxu8w#L0%c2< z$cy347Tz3>3ltwq+b3zS8>e(+zQUFcoH7;34sR@cM0~LmE0KPG-Lp|XPhvF3$e2oH z-pP+eEGmO!+cX;&|I^X@`a<+{WucGPm-V%->%`wILuf;?UA*>2HkLMSo$W}niYGsR zZL~^gR?W1GWGY+BRXWvGJvcstjQcE48sRp5Zbj*tiGs^aX)Ud^M{ld&VbyPuA0PL= 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8 + COMM: 1 read+1 write = 16 byte + COMP: 128 FLOPs + -> AI = 128/16 = 8 */ - a[i] = a[i] * a[i] * a[i] * - a[i] * a[i] * a[i] * - a[i] * a[i] * a[i] * - a[i] * a[i] * a[i] * - a[i] * a[i] * a[i] * - a[i] * a[i]; + a[i] = REP100(a[i]*) + REP20(a[i]*) + REP8(a[i]*) + REP1(a[i]); } } @@ -76,28 +96,25 @@ void kernel_8_1_fuseaware(double* a, double* b, double* c, size_t size) With FMA (and -O2): vmovsd xmm0,QWORD PTR [rdi] # 1 read - vfmadd132sd xmm0,xmm0,xmm0 # 8x 2 FLOPs+register shuffling + vfmadd132sd xmm0,xmm0,xmm0 # 64 x 2 FLOPs+register shuffling vmovsd QWORD PTR [rdi-0x8],xmm0 # 1 write + + Uses packed doubles with -Ofast. */ #pragma omp parallel for for(size_t i=0; i AI = 8 */ - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; - a[i] = a[i] * a[i] + a[i]; + REP60(a[i] = a[i] * a[i] + a[i];) + REP4(a[i] = a[i] * a[i] + a[i];) } } + 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