/code/*.tex
/images-dot/*.tex
/images-svg/*.pdf
+/images-gnuplot/*.pdf
+/images-gnuplot/*.tex
+/images-gnuplot/build_stamp
DOT_FOLDER=images-dot
DOT_TEX_FILES=${patsubst %.dot,%.tex,$(wildcard $(DOT_FOLDER)/*.dot)}
+GNUPLOT_FOLDER=images-gnuplot/
+GNUPLOT_FOLDER_GENERATOR_FILES=$(wildcard $(GNUPLOT_FOLDER)/*.gpi) $(wildcard $(GNUPLOT_FOLDER)/*.dat)
+GNUPLOT_FOLDER_BUILD_STAMP=$(GNUPLOT_FOLDER)/build_stamp
PDFLATEX_OUTPUT_LOG=pdflatex_output.log
+REWRITE_GNUPLOT_EPSLATEX=\
+for epsfile in *.eps; do epstopdf $${epsfile} && rm $${epsfile}; done &&\
+ESCAPED_BUILD_DIR=$$(echo $(1) | sed -r 's/(\/)/\\\1/g') &&\
+for texfile in *.tex; do sed -i -r "s/includegraphics\{([^\/]*)\}/includegraphics\{$${ESCAPED_BUILD_DIR}\/\1\}/g" $${texfile}; done
+
all: presentation.pdf
display: presentation.pdf
presentation-4up.pdf: presentation.pdf
pdfnup --nup 2x2 --a4paper --scale 0.95 --frame true presentation.pdf -o presentation-4up.pdf
-presentation.pdf: $(IMAGE_FILES) $(SVG_OUTPUTS) $(CODE_TEX_FILES) $(CODE_RAW_FILES) $(DOT_TEX_FILES) $(wildcard *.tex *.sty) pygments.sty
+presentation.pdf: $(IMAGE_FILES) $(SVG_OUTPUTS) $(CODE_TEX_FILES) $(CODE_RAW_FILES) $(DOT_TEX_FILES) $(GNUPLOT_FOLDER_BUILD_STAMP) $(wildcard *.tex *.sty) pygments.sty
pdflatex -draftmode presentation &&\
while(pdflatex presentation | tee $(PDFLATEX_OUTPUT_LOG) && grep "Rerun to get cross-references right" $(PDFLATEX_OUTPUT_LOG)); do true; done &&\
rm -f $(PDFLATEX_OUTPUT_LOG)
$(BASIS_FUNCTIONS_BUILD_STAMP) \
$(CODE_TEX_FILES) \
$(DOT_FOLDER)/*.tex \
+ $(GNUPLOT_FOLDER_BUILD_STAMP) \
+ $(GNUPLOT_FOLDER)/*.pdf \
+ $(GNUPLOT_FOLDER)/*.tex \
pygments.sty
upload: presentation.pdf
- rsync -C --progress presentation.pdf shell3.doc.ic.ac.uk:~/public_html/psl_presentation_2013.pdf
+ rsync -C --progress presentation.pdf shell3.doc.ic.ac.uk:~/public_html/psl_presentation_201306.pdf
%.pdf: %.svg
inkscape -D -A $@ $<
%.tex: %.dot
dot2tex --codeonly --usepdflatex -f tikz $< -o $@
+$(GNUPLOT_FOLDER_BUILD_STAMP): $(GNUPLOT_FOLDER_GENERATOR_FILES)
+ cd $(GNUPLOT_FOLDER) &&\
+ for gpifile in *.gpi; do gnuplot $${gpifile}; done &&\
+ ${call REWRITE_GNUPLOT_EPSLATEX, $(GNUPLOT_FOLDER)}
+ touch $@
+
.PHONY: all display clean upload 4up display-4up
--- /dev/null
+set terminal epslatex color 10
+set output "midpoints.eps"
+set style line 1 lc rgb '#0060ad' lw 2 pt 7 pi -1 ps 1.5
+set xzeroaxis
+unset xtics
+unset ytics
+set nokey
+set xrange [0:2*pi]
+set multiplot
+plot sin(2*x) + sin(4*x) + cos(3*x) with linespoints lc rgb '#ff0000' pi 8 linewidth 2 pointtype 7 pointsize 2.0 pi 4
+plot sin(2*x) + sin(4*x) + cos(3*x) with linespoints lc rgb '#0060ad' pi 8 linewidth 2 pointtype 7 pointsize 2.0 pi 8
--- /dev/null
+#size naive padding-aware phase-shift
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--- /dev/null
+set terminal epslatex color
+
+set xlabel "Problem Size"
+set ylabel "Time (seconds)"
+set key left top box
+set grid layerdefault linetype -1 linecolor rgb "gray" linewidth 0.2
+set ytics nomirror
+set xtics nomirror
+set xrange [0:*]
+set yrange [0:*]
+set output "resampling-standalone-fftw-filtered.eps"
+
+f(x) = int(x) % 10 == 0
+
+plot "resampling-standalone-fftw-filtered.dat" using 1:2 ti "naïve" with linespoints,\
+ "resampling-standalone-fftw-filtered.dat" using 1:3 ti "padding-aware (ONETEP)" with linespoints,\
+ "resampling-standalone-fftw-filtered.dat" using 1:4 ti "phase-shift" with linespoints
--- /dev/null
+#size naive padding-aware phase-shift
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--- /dev/null
+set terminal epslatex color
+
+set xlabel "Problem Size"
+set ylabel "Time (seconds)"
+set key left top box
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+set ytics nomirror
+set xtics nomirror
+set xrange [0:*]
+set yrange [0:0.8]
+set output "resampling-standalone-fftw.eps"
+plot "resampling-standalone-fftw.dat" using 1:2 ti "naïve" with linespoints,\
+ "resampling-standalone-fftw.dat" using 1:3 ti "padding-aware (ONETEP)" with linespoints,\
+ "resampling-standalone-fftw.dat" using 1:4 ti "phase-shift" with linespoints
--- /dev/null
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--- /dev/null
+\newcommand{\oneteproutinesphaseshiftfftw}{
+\begin{tabularx}{\textwidth}{cXXX}
+\hline
+\bf{Test} & \bf{Original (s)} & \bf{Modified (s)} & \bf{Reduction} \\
+\hline
+test01& 49.47& 35.27& 28.70\%\\
+test02& 61.51& 44.56& 27.56\%\\
+test03& 40.67& 29.66& 27.07\%\\
+test04& 90.99& 61.51& 32.40\%\\
+test05& 47.78& 34.46& 27.88\%\\
+test06& 3.73& 2.73& 26.81\%\\
+test07& 8.72& 6.46& 25.92\%\\
+test08& 93.33& 66.83& 28.39\%\\
+test09& 3.47& 2.35& 32.28\%\\
+test10& 361.81& 265.67& 26.57\%\\
+test11& 33.27& 23.04& 30.75\%\\
+test12& 57.65& 40.19& 30.29\%\\
+test13& 17.37& 12.30& 29.19\%\\
+test14& 40.55& 29.74& 26.66\%\\
+test15& 26.05& 18.55& 28.79\%\\
+test16& 33.93& 25.67& 24.34\%\\
+test18& 107.61& 77.48& 28.00\%\\
+test19& 73.72& 52.60& 28.65\%\\
+test20& 95.72& 62.37& 34.84\%\\
+test21& 2.68& 2.13& 20.52\%\\
+test22& 53.47& 39.34& 26.43\%\\
+test23& 22.55& 15.40& 31.71\%\\
+test24& 22.81& 15.42& 32.40\%\\
+%test26& 3.49& 2.46& 29.51\%\\
+%test27& 74.33& 52.47& 29.41\%\\
+%test28& 23.34& 15.77& 32.43\%\\
+%test29& 29.75& 21.55& 27.56\%\\
+%test30& 14.52& 10.73& 26.10\%\\
+%test31& 33.06& 20.72& 37.33\%\\
+\hline
+\end{tabularx}
+}
+
+\newcommand{\onetepoverallphaseshiftfftw}{
+\begin{tabularx}{\textwidth}{cXXX}
+\hline
+\bf{Test} & \bf{Original (s)} & \bf{Modified (s)} & \bf{Reduction} \\
+\hline
+test01& 131.43& 111.06& 15.49\%\\
+test02& 136.79& 118.22& 13.58\%\\
+test03& 619.04& 606.73& 1.99\%\\
+test04& 169.56& 139.72& 17.60\%\\
+test05& 107.47& 93.61& 12.90\%\\
+test06& 27.02& 26.35& 2.49\%\\
+test07& 49.99& 45.57& 8.85\%\\
+test08& 296.68& 247.57& 16.55\%\\
+test09& 15.82& 14.49& 8.44\%\\
+test10& 1126.06& 955.09& 15.18\%\\
+test11& 90.85& 77.61& 14.57\%\\
+test12& 154.00& 131.92& 14.34\%\\
+test13& 231.26& 223.75& 3.25\%\\
+test14& 272.05& 255.62& 6.04\%\\
+test15& 97.64& 83.10& 14.90\%\\
+test16& 98.63& 87.28& 11.51\%\\
+%test17& 55.70& 54.84& 1.55\%\\
+test18& 343.04& 294.95& 14.02\%\\
+test19& 180.72& 156.56& 13.37\%\\
+test20& 260.15& 221.94& 14.69\%\\
+test21& 11.45& 10.95& 4.35\%\\
+test22& 125.30& 109.90& 12.29\%\\
+test23& 46.18& 38.92& 15.72\%\\
+test24& 46.46& 38.85& 16.39\%\\
+%test26& 409.71& 407.21& 0.61\%\\
+%test27& 1700.92& 1662.08& 2.28\%\\
+%test28& 893.35& 886.74& 0.74\%\\
+%test29& 69.91& 61.32& 12.30\%\\
+%test30& 67.33& 62.03& 7.87\%\\
+%test31& 91.14& 73.04& 19.86\%\\
+\hline
+\end{tabularx}
+}
\usepackage{ucs}
\usepackage{alltt}
\usepackage[utf8x]{inputenc}
+\usepackage{tabularx}
\input{pygments.sty}
+\input{onetep-phase-shift-fftw}
\title[PSL Meeting]{PSL Meeting Presentation}
\subtitle{Exploring Performance Optimisation Opportunities in ONETEP}
\frame{
-\frametitle{Fourier Interpolation of FFT-boxes}
+\frametitle{ONETEP's Approach to Interpolation}
\small
ONETEP performs transforms in each dimension so each FFT only operates on 50\%
}
+\frame{
+
+\frametitle{Phase-Shift Approach to Interpolation}
+
+We have a signal discretely sampled at the blue points, but we want to know the
+value at both the blue and red points. We can find these if we shift the signal by
+half a sample.
+
+\centering
+\resizebox{0.80\textwidth}{!}{
+\input{images-gnuplot/midpoints}
+}
+
+}
+
+\frame{
+
+\frametitle{Phase-Shift Interpolation in 1D}
+
+\begin{itemize}
+
+\small
+\item We use a 1D FFT to compute the frequency representation, apply a phase shift,
+then trasform back to compute the values of the midpoints.
+
+\item We interleave the original data and midpoints to produce the interpolated
+ values.
+
+\item We never operate on zeros (except those in the original input).
+
+\end{itemize}
+
+\centering
+\resizebox{0.60\textwidth}{!}{
+\includegraphics{images-svg/interpolation-phase-shift-1d}
+}
+
+}
+
+\frame{
+
+\frametitle{Phase-Shift Interpolation in 3D}
+
+\begin{itemize}
+
+\item Interpolation is done by dimension, with the most cache inefficient done
+ first.
+
+\item We interleave the original data and the 7 interpolated blocks as a final
+ step.
+
+\end{itemize}
+
+\centering
+\resizebox{0.60\textwidth}{!}{
+\includegraphics{images-svg/per-dimension-interpolation}
+}
+
+}
+
+\frame{
+
+\frametitle{Performance Results with FFTW\footnote{Core i7-2600, 3.4GHz, 8MB L2
+cache, FFTW 3.3}}
+
+\footnotesize
+Results are difficult to interpret because of FFTW's performance at different
+problem sizes due to the factorisations it chooses.
+
+\centering
+\resizebox{0.85\textwidth}{!}{
+\input{images-gnuplot/resampling-standalone-fftw}
+}
+
+}
+
+\frame{
+
+\frametitle{Performance Results with FFTW\footnote{Core i7-2600, 3.4GHz, 8MB L2
+cache, FFTW 3.3}}
+
+\footnotesize
+We can filter the results to those which FFTW likes best (products of small
+primes). Specifically, sizes of the form $2^a3^b5^c7^d11^e13^f$ where $e+f<2$.
+
+\centering
+\resizebox{0.85\textwidth}{!}{
+\input{images-gnuplot/resampling-standalone-fftw-filtered}
+}
+
+}
+
+\frame
+{
+\frametitle{Performance within ONETEP}
+
+\begin{itemize}
+
+\item In our standalone benchmarks, our results give around a 35\% reduction in
+ execution time over ONETEP's approach for FFTW's preferred sizes.
+
+\item In practise, we found the actual reduction to be a lot less and overall
+reduction in execution time to usually be less than 5\%.
+
+\item When doing Fourier interpolation, ONETEP spends a lot of time in its
+ modifying data layouts before calling FFTW.
+
+\item Specifically, converting from a split to interleaved representation of
+ complex numbers. Sometimes this is due to two sets of real operands being
+ merged so interpolation can be done on both simultaneously.
+
+\vspace{1em}
+\centering
+\resizebox{0.8\textwidth}{!}{
+\includegraphics{images-svg/complex-formats}
+}
+
+
+
+\end{itemize}
+
+}
+
+\frame
+{
+\frametitle{Making the new interpolation work better with ONETEP}
+
+\begin{itemize}
+
+\item I discovered that FFTW provides a ``guru'' interface that makes it
+possible to pass in data in data in the split format.
+
+\item I wrote a new implementation of the interpolation routines that could
+ accept and return data in this format without remarshalling.
+
+\item Also wrote a routine that returned the product of the real and complex
+ parts as part of the re-interleave step, avoiding the need for the calling
+ routine in ONETEP to have to iterative over the data again.
+
+\end{itemize}
+}
+
+\frame{
+
+\frametitle{ONETEP Interpolation Routine Timings\footnote{Core i7-2600, 3.4GHz,
+8MB L2 182 cache, FFTW 3.3}}
+
+\centering
+\resizebox{0.65\textwidth}{!}{
+\oneteproutinesphaseshiftfftw
+}
+
+}
+
+\frame{
+
+\frametitle{ONETEP Total Execution Time Timings\footnote{Core i7-2600, 3.4GHz,
+8MB L2 182 cache, FFTW 3.3}}
+
+\centering
+\resizebox{0.65\textwidth}{!}{
+\onetepoverallphaseshiftfftw
+}
+
+}
+
+
\end{document}
projects / francis / psl_presentation_20130611.git / commitdiff
