101 lines
3.3 KiB
TeX
101 lines
3.3 KiB
TeX
\begin{frame}[fragile]{Numerical analysis with Verificarlo}
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\textbf{Verificarlo} is a tool for assessing the precision of floating point operations.
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It can be used to :
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\begin{columns}
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\column{0.3\textwidth}
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{\centering
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\includegraphics[width=80px, keepaspectratio]{img/verificarlo.png}
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}\\%
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{\footnotesize
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\url{https://github.com/verificarlo/verificarlo} GPL v3 \\
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}
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\column{0.7\textwidth}
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\begin{itemize}
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\item \textbf{Find numerical bugs} in codes \footnotemark[1]
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\begin{itemize}
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\item Stochastic arithmetic to simulate round-off and cancellations
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\item Localization techniques to pinpoint source of errors
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\end{itemize}
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\item \textbf{Optimize precision} \footnotemark[2]
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\begin{itemize}
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\item Simulate custom formats for mixed precision \\(float, bf16)
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\item Tune precision in math library calls
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\end{itemize}
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\end{itemize}
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\end{columns}
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\footnotetext[1]{
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C. Denis \textit{et al.} \href{https://dx.doi.org/10.1109/ARITH.2016.31}{doi:10.1109/ARITH.2016.31}
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}
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\footnotetext[2]{
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Y Chatelain \textit{et al.} \href{https://dx.doi.org/10.1007/978-3-030-29400-7\_34}{doi:10.1007/978-3-030-29400-7\_34}
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}
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\end{frame}
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\begin{frame}[fragile]{The Verificarlo pipeline}
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\begin{itemize}
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\item Each Floating-Point (FP) operation may introduce a $\delta$ error
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$$ z = fl[x+y] = (x+y)(1+\delta) $$
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\item When chaining multiple operations, errors can accumulate and snowball
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\item \structure{Monte Carlo Arithmetic key principle}
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\begin{itemize}
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\item Make $\delta$ a \structure{random variable}
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\item Use a Monte Carlo simulation to empirically estimate the FP error distribution
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\end{itemize}
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\end{itemize}
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\begin{center}
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\includegraphics[width=.8\textwidth]{img/verificarlo_pipeline.png}
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\end{center}
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\end{frame}
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\begin{frame}{Continuous-Integration precision tracking}
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\begin{itemize}
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\item Each push to \structure{QMCkl} triggers a Verificarlo analysis.
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\item QMCkl kernels unit tests are augmented with probes:
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\begin{itemize}
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\item track a scalar value precision
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\item ensure that a target precision is reached
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\end{itemize}
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\end{itemize}
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\vspace{2cm}\vfill
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vfc\_probe(\tikzmark{kernel}"Sherman-Morisson", \tikzmark{var}"residual", res) \\
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vfc\_probe\_assert("Sherman-Morisson", "res", res, \tikzmark{target}1e-7)
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\begin{tikzpicture}[
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remember picture,
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overlay,
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expl/.style={draw=orange,fill=orange!30,rounded corners,text width=3cm},
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arrow/.style={red!80!black,ultra thick,->,>=latex}
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]
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\node[expl]
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(kernelex)
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at (2,3cm)
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{Kernel name};
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\node[expl]
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(varex)
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at (7,3cm)
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{Variable name};
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\node[expl]
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(targetex)
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at (12,3cm)
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{Target precision};
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\draw[arrow]
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(kernelex.south) to[out=-90,in=90] ([yshift=1.2ex, xshift=1.7cm]{pic cs:kernel});
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\draw[arrow]
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(varex.south) to[out=-90,in=90] ([yshift=1.2ex, xshift=1cm]{pic cs:var});
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\draw[arrow]
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(targetex.south) to[out=-90,in=90] ([yshift=1.2ex, xshift=.5cm]{pic cs:target});
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\end{tikzpicture}
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\end{frame}
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