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Armin Friedl 2016-06-24 23:40:10 +02:00
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10
roofline/report/inputs/discussion.tex
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@ -1,8 +1,10 @@
According to the 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. The results are not really unexpected. 22 GFLOP/s for a consumer grade CPU are quite good. That the peak performance wasn't reached can have many reasons. One might be that the binary had to share it's CPU time with other things running on the same machine etc.
- worse results for 4 threads @ NUMA-STREAM not necessarily expected It bears some curiosity that the \verb|fma8| kernel is faster than the \verb|fma8manpack| kernel. But there's more to this story. The \verb|fma8| kernel performs much worse (~1/3) than the \verb|fma8manpack| at other optimization levels than \verb|-O3|. Taking a look at the disassembly reviels that \verb|fma8| uses some weird combination of packed and unpacked FMA instructions. It is not even a hundred percent sure that the optimization didn't tinker with the effective OI of the \verb|fma8| kernel.
- better results for triad possibly due to combined storage in FMA
- striding for arrays One baseline of this report is that a superficial OI of a kernel in a high-level language does not really resembles the OI of the kernel when compiled to the machine.
Please also refer to the header file \verb|aikern.h| for a more technical analysis of the disassembly of various kernels. The \verb|Makefile| generates many different variations of the kernels to play with. The \verb|log/| folder will contain details about time an GFLOP of every kernel when a binary is run.
%%% Local Variables: %%% Local Variables:
%%% mode: latex %%% mode: latex

51
roofline/report/inputs/results.tex
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@ -2,6 +2,8 @@ The best results for various kernels are given in~\prettyref{tbl:res-kernels}. T
Note how \verb|simple8| is clearly flawed with \verb|-ffast-math| enabled. This is due to the non IEEE compliant optimization as described in~\prettyref{sec:advanced-kernels}. At this level of optimization only \verb|simple8fastmath| (which is fastmath safe but flawed with lower optimization levels) should be considered as a \emph{replacement} of \verb|simple8|. Note how \verb|simple8| is clearly flawed with \verb|-ffast-math| enabled. This is due to the non IEEE compliant optimization as described in~\prettyref{sec:advanced-kernels}. At this level of optimization only \verb|simple8fastmath| (which is fastmath safe but flawed with lower optimization levels) should be considered as a \emph{replacement} of \verb|simple8|.
The simple* kernel are those kernels that do not make use of FMA but can be safely used with processors without an FMA unit. fma* kernels on the other hand are those that should make use of FMA. simple8fastmath is a simple8 that can be safely used with \verb|-ffast-math| optimization. And fma8manpack is the kernel which uses intrinsics to ensure that is solely operates with FMA instructions on packed floats.
\begin{table}[h!] \begin{table}[h!]
\centering \centering
\begin{tabular}{ll} \begin{tabular}{ll}
@ -30,6 +32,55 @@ The rooftop graph with the best runs of the 2 best kernels of each category (\ve
\label{fig:roofline-withres} \label{fig:roofline-withres}
\end{figure} \end{figure}
\FloatBarrier
Best results for an input size of 100000000 are given in~\prettyref{tbl:res-kernels-10} and~\prettyref{fig:roofline-withres-10}.
\begin{table}[h!]
\centering
\begin{tabular}{ll}
\toprule
Kernel & Max. GFLOP/s \\
\midrule
fma16 & 0.9816\\
fma8 & 21.8837 \\
\bottomrule
\end{tabular}
\caption{Best results for 100000000}
\label{tbl:res-kernels-10}
\end{table}
\begin{figure}
\begin{adjustbox}{center}
\includegraphics[width=0.8\linewidth]{res/rooftop_res10}
\end{adjustbox}
\caption{Roofline graph with best results for 100000000}
\label{fig:roofline-withres-10}
\end{figure}
Best results for an input size of 250000000 are given in~\prettyref{tbl:res-kernels-25} and~\prettyref{fig:roofline-withres-25}.
\begin{table}[h!]
\centering
\begin{tabular}{ll}
\toprule
Kernel & Max. GFLOP/s \\
\midrule
simple16 & 1.0476 \\
fma8 & 21.4297 \\
\bottomrule
\end{tabular}
\caption{Best results for 250000000}
\label{tbl:res-kernels-25}
\end{table}
\begin{figure}
\begin{adjustbox}{center}
\includegraphics[width=0.8\linewidth]{res/rooftop_res25}
\end{adjustbox}
\caption{Roofline graph with best results for 250000000}
\label{fig:roofline-withres-25}
\end{figure}
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roofline/report/report.aux
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\label{sec:results} \label{sec:results}
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\section{Discussion}
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[(B)-19(e)-59(s)-21(t)-114( )-40(1)-80(/)-60(1)-80(6)-80( )-40(O)-9(I)-17 [(B)-19(e)-59(s)-21(t)-114( )-40(1)-80(/)-60(1)-80(6)-80( )-40(O)-9(I)-17
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@ -1,5 +1,5 @@
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roofline/src/log/simple16
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@ -1,5 +1,5 @@
run,start,end,delta,GFLOP/s run,start,end,delta,GFLOP/s
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roofline/src/log/simple8
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roofline/src/log/simple8fastmath
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@ -1,5 +1,5 @@
run,start,end,delta,GFLOP/s run,start,end,delta,GFLOP/s
1,1466800744.3973,1466800746.6229,2.2256,8.6270 1,1466803565.2130,1466803568.8649,3.6519,8.7627
2,1466800746.6229,1466800748.8499,2.2270,8.6216 2,1466803568.8649,1466803572.6057,3.7408,8.5543
3,1466800748.8499,1466800751.1237,2.2738,8.4440 3,1466803572.6057,1466803576.3140,3.7084,8.6291
4,1466800751.1237,1466800753.3258,2.2022,8.7187 4,1466803576.3140,1466803580.0195,3.7054,8.6360